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Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena

T0 review · 1 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Periodic driving can engineer topological band structures, but only when drive-induced heating is beaten.

desk verdict A reliable, pedagogical review of Floquet topological phases; no new results, but it is the clearest map of the field and its open problems. read the letter →

arxiv 1909.02008 v1 pith:JRCM527K submitted 2019-09-04 cond-mat.mes-hall quant-ph

Mark S. Rudner , Netanel H. Lindner This is my paper · ORCID
classification cond-mat.mes-hallquant-ph
keywords FloquettopologicalinsulatorperiodicdrivingquasienergyChernnumberanomalousedgestatesprethermalizationmany-bodylocalizationFloquet-Landauertransport
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This review argues that time-periodic fields like laser or microwave light can reshape the quantum band structure of a crystal, creating topologically nontrivial Floquet bands whose quasienergy spectrum is organized around the drive frequency. The central problem it identifies is that a many-body system under such a drive generically absorbs energy and drifts toward a featureless, infinite-temperature-like state that destroys all topological order. The paper's core thesis is that three distinct stabilization mechanisms—long-lived prethermal states, disorder-induced many-body localization, and engineered coupling to external baths—can each protect Floquet topological phases, and it surveys the physical signatures and experimental realizations associated with each.

What carries the argument

The central object is the Floquet operator $U(T)=\mathcal{T}e^{-(i/\hbar)\int_0^T H(t')dt'}$, whose eigenvalues $e^{-i\varepsilon T/\hbar}$ define quasienergies on the compact Floquet-Brillouin zone $[\varepsilon_0,\varepsilon_0+\hbar\omega)$. The periodicity of quasienergy is what enables topological phenomena without equilibrium analogues: quasienergy winding in one dimension, anomalous chiral edge states in two dimensions even when all Floquet band Chern numbers vanish, and $0$ and $\pi$ modes at the Floquet zone edge. The micromotion within a drive period, encoded in the harmonic components of Floquet states, carries topological information that the Chern numbers alone do not, and the effective Hamiltonian $H_{\rm eff}$ defined by $U(T)=e^{-iH_{\rm eff}T/\hbar}$ fails exactly when this micromotion matters.

What would settle it

A clean, disorder-free, interacting driven system—with no engineered bath and no MBL—that, over time scales far exceeding the predicted heating times, shows persistent non-thermal local observables such as a time-periodic density pattern or a quantized Hall response would directly falsify the premise; this could be tested with interacting fermions in a clean optical lattice under circular shaking by measuring the momentum distribution or Hall response as a function of time.

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Extended reading notes

Core claim

The central claim is that periodic driving is a viable control knob for non-equilibrium topological phases, provided the driven many-body system is prevented from heating up. At the single-particle level, an off-resonant circular drive opens gaps at Dirac points and endows Floquet bands with nonzero Chern numbers, while a resonant drive can induce a true band inversion with the coupling phase winding through 4π and Chern numbers changing by ±2. In the many-body setting, the review argues that topological edge states can appear in transport in the mesoscopic regime, although their conductance is generally not simply quantized because photon sidebands couple edge states to lead states far from the chemical potential. For bulk phases, the paper identifies three routes to stabilization—prethermalization, MBL, and engineered baths—and describes the distinct topological phenomena each can sustain, from universal currents in restricted infinite-temperature states to Floquet time crystals and Floquet-Gibbs steady states with quantized Hall response.

Load-bearing premise

The review's entire problem framing rests on the assertion, cited in Sec. I as 'widely believed' rather than proven, that a generic closed, interacting, periodically driven system will inexorably absorb energy and drift toward an infinite-temperature state; if that premise fails, no special stabilization is needed to host a Floquet topological phase.

Editorial extensions

If this is right

  • Off-resonant circularly polarized light on graphene-like systems opens Dirac gaps and yields Floquet bands with Chern numbers ±1, while resonant driving between valence and conduction bands can invert bands and change Chern numbers by ±2 when the pseudospin winds around the resonance contour.
  • The periodicity of quasienergy introduces features without equilibrium analogues: quasienergy winding in 1D corresponds to quantized Thouless pumping, and 2D systems can host anomalous chiral edge states with trivial bulk Chern numbers, such as the anomalous Floquet Anderson insulator that quantizes current at large source-drain bias.
  • Transport through Floquet edge states is generically not quantized in the standard two-terminal conductance because photon sidebands spoil the ideal filling of the Floquet modes; quantization is recovered only through sum rules such as $\sum_n \sigma(\mu_n)=2e^2/h$.
  • Each stabilization route supports distinct Floquet topological phases: prethermal Floquet insulators with exponentially suppressed heating at high frequency or across a large gap, MBL-stabilized Floquet time crystals with protected $0$ and $\pi$ edge modes, and bath-engineered steady states whose Hall response is quantized when the density matrix is diagonal in the Floquet basis.
  • Because delocalized states destabilize MBL in 2D and 3D, the review concludes that intrinsic Floquet topological insulators with nonzero Chern index are unstable in closed systems without a bath, while anomalous Floquet phases with localized bulk and winding edge modes can remain stable.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extension: If the heating premise is not universal—if some clean, disorder-free interacting driven systems can settle into non-thermal states on their own—then the review's entire taxonomy of stabilization routes becomes over-engineered, and the research question shifts from 'how to avoid heating' to 'which systems naturally avoid it.'
  • Extension: The review's claim that a Floquet-diagonal steady state suffices for quantized Hall response suggests a practical diagnostic: measure the steady-state populations of Floquet bands directly, for example via the spectral weights of photon sidebands, and use those populations to predict whether transport measurements will show quantization.
  • Extension: The anomalous Floquet Anderson insulator suggests a general design principle that goes beyond the review's examples: chiral edge modes that close on themselves across the quasienergy zone can carry quantized current even when the bulk is fully localized, a principle that might be transplanted to photonic or circuit-QED simulators where fermion statistics and particle conservation differ
  • Extension: The review's discussion of prethermalization implies that in real materials the practical operating window for Floquet topological phases may be set by the nearest high-lying band gap rather than by the drive frequency alone, so platforms with deep lattice potentials or large single-particle gaps may be the most promising targets for observing robust signatures.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 5 minor

Summary. The manuscript is a review of Floquet topological insulators. It presents the single-particle Floquet band structure framework, including off-resonant and resonant driving mechanisms in Sec. II, and in Sec. III discusses quasienergy winding, Floquet zone-edge transitions, and anomalous chiral edge states that are not captured by the Chern numbers of the Floquet bands. Section IV turns to many-body physics: mesoscopic transport through Floquet-Landauer and Floquet-Kubo methods, transient and prethermal behavior, many-body localization as a stabilization route, and open-system steady states. The organizing thesis is that periodic driving can engineer topologically nontrivial Floquet bands, but that a generic closed interacting driven system tends to heat to a featureless state, so stable Floquet topological phases require one of three routes: prethermalization, MBL, or engineered baths. The review contains no new results but synthesizes a large literature and includes a Supplementary Material for technical details.

Significance. This is a useful, technically reliable review by two leading contributors to the field. Its strengths are the careful presentation of Floquet band engineering, the explicit treatment of topological phenomena unique to Floquet systems (quasienergy winding, anomalous edge states, the failure of bulk Chern numbers to fix edge-state chirality), and the honest framing of the many-body heating problem as a 'widely believed' premise rather than an established theorem. The Floquet-Landauer formula, the Thouless-pump quantization argument, and the Floquet-Kubo conductivity discussion are all stated in a way that is substantially correct. The main structural assumption, that closed driven interacting systems generically heat to infinite temperature without special stabilization, is clearly labeled as a consensus premise with citations; I do not regard this as circular or internally inconsistent. The paper will serve as a reliable entry point for researchers entering the field.

major comments (1)
  1. [Sec. IV.A, Eq. (2)] The prefactor and the normalization of the transmission probabilities in Eq. (2) need to be clarified. If T^(k)_RL(E) and T^(k)_LR(E) are the standard dimensionless Floquet transmission probabilities, the two-terminal current should be I = (e/h) ∫ dE Σ_k {T^(k)_RL(E) f_L(E) - T^(k)_LR(E) f_R(E)}; in units with ħ = 1 and e = 1 this carries a prefactor 1/(2π), not 2π. If a different normalization is intended (for example, T includes a density-of-states factor or spin degeneracy), that should be stated explicitly. As written, the formula is ambiguous, and a reader cannot reproduce the subsequent statements about quantized conductance from it.
minor comments (5)
  1. [Sec. III, Eq. (3)] In the expansion of the Floquet mode, the symbol Ω is used without definition, and the summation index n does not match the sideband label m on |φ^m_ε⟩; replace Ω by the drive frequency ω and align the summation and sideband indices.
  2. [Sec. IV.D] The 'generalized Floquet insulator' state is introduced via a physical-expectation argument; the text should explicitly mark this as a working hypothesis or design condition rather than a consequence of the Floquet-Kubo formula, since the latter applies once a diagonal steady state is assumed.
  3. [Sec. I] There is a typo in the first paragraph: 'can addressed in many-body Floquet systems' should read 'can be addressed in many-body Floquet systems'.
  4. [Sec. IV.A] The word 'guaranty' in the discussion of the anomalous 2D phase should be 'guarantee'.
  5. [Reference style] The citation style is inconsistent: some references are given as 'Ref. 78' rather than 'Ref. [78]' (e.g., Sec. IV.A), and the bibliography should be harmonized throughout.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the review derives no new results, and its self-cited core content (winding invariant, anomalous edge states) is independently published and experimentally corroborated.

full rationale

This paper is a review, not a derivation: it presents no new results, fits no parameters, and offers no prediction that is statistically forced by a fitted input, so the self-definitional and fitted-input patterns do not apply. The central single-particle content of Sec. II (off-resonant gap opening in graphene and resonant band inversion, around Eqs. (1)) is attributed to original papers by other groups (Refs [5, 43] for the driven Dirac model; Ref [7] for the band-inversion proposal), with the calculations either sketched in the text or deferred to the paper's own Supplementary Material [41]. The topological claims in Sec. III — the winding invariant nu_1 and the 'anomalous edge states' that coexist with trivial Floquet Chern numbers — are cited to the authors' own prior works (Refs [6, 16-19, 72]). This is a genuine self-citation layer, but it is not load-bearing in the circularity sense: those results were published as independent, refereed papers with their own proofs, and the review explicitly notes external experimental corroboration ('the first experimental demonstration of anomalous 0 and pi edge states' in discrete time quantum walks [73]; waveguide arrays and microwave resonator arrays [86-89]). The one deferred technical item, the vanishing of nu_1 (and the GNVW index) for unitary evolution under a finite local Hamiltonian in one dimension, is explicitly assigned to the paper's own Supplementary Material [41], so the review is self-contained rather than resting on an unverified self-citation. The motivating premise that generic closed interacting driven systems heat toward featureless infinite-temperature states is presented as 'widely believed' with external citations [8, 9] and is used only to organize Sec. IV; the review does not prove it as a theorem, and it explicitly hedges all three stabilization routes (prethermalization as a finite-time route, MBL as incompatible with delocalized Chern bands via Ref [139], and open-system steady states as generically bath-dependent). No equation in the paper reduces by construction to its own input, no fitted parameter is renamed as a prediction, and no uniqueness result is imported silently from the authors' own work. Verdict: no significant circularity; the self-citation presence is a normal feature of a review by field-leading authors whose cited results carry independent external support.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

As a synthesis, the review carries no fitted free parameters and introduces no invented entities. Model parameters in Sec. II (v, Delta, A0, omega) are inputs inherited from cited single-particle models, and heating-rate estimates are reproduced from cited works rather than fit here. The listed axioms are the background commitments the reviewed framework depends on: Floquet's theorem (standard math), the generic-heating premise (domain assumption, explicitly flagged), the rotating wave approximation (domain assumption), and the single-particle stage assumption. None are introduced ad hoc by this paper, so the circularity burden is low.

assumptions (4)
  • standard math Floquet's theorem: a time-periodic Hamiltonian H(t)=H(t+T) admits a complete set of solutions |psi(t)> = e^{-i epsilon t / hbar} |Phi(t)> with |Phi(t)> = |Phi(t+T)>; quasienergy epsilon is defined modulo hbar omega.
    Basis for defining Floquet bands and the Floquet-Brillouin zone throughout Sec. II; standard theorem of periodic linear differential equations.
  • domain assumption A generic closed, interacting, periodically driven many-body system absorbs energy from the drive and tends to an infinite-temperature-like featureless state at long times.
    Stated in Sec. I as 'widely believed' with citations [8,9]; this premise motivates the entire structure of Sec. IV (three routes to stabilization). It is asserted, not proven in this paper.
  • domain assumption Rotating wave approximation (RWA): in the rotating frame, rapidly oscillating terms can be discarded to obtain the effective Rabi-type splitting near the resonance ring.
    Used in Sec. II for the resonant-drive band inversion picture; the review notes the discarded terms generate multiphoton resonances, discussed qualitatively later.
  • domain assumption The single-particle Floquet band structure is the correct starting point ('stage') for describing the driven system's many-body dynamics and observables.
    Stated in Sec. I: 'The single particle Floquet band structure provides a stage on which the system's dynamics play out'; the transport and conductivity analyses in Secs. IV A and IV D assume Floquet band populations capture the physics.

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Cite this review

Pith. "Pith review of Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena." pith.science (2026). https://pith.science/paper/JRCM527K

@misc{pith2026190902008,
  author       = {Pith},
  title        = {Pith review of: Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum phenomena},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JRCM527K}},
  note         = {Machine review of arXiv:1909.02008}
}
read the original abstract

We review methods for using time-periodic fields (e.g., laser or microwave fields) to induce non-equilibrium topological phenomena in quantum many-body systems. We discuss how such fields can be used to change the topological properties of the single particle spectrum, and key experimental demonstrations in solid state, cold atomic, and photonic systems. The single particle Floquet band structure provides a stage on which the system's dynamics play out; the crucial question is then how to obtain robust topological behaviour in the many-particle setting. In the regime of mesoscopic transport, we discuss manifestations of topological edge states induced in the Floquet spectrum. Outside the context of mesoscopic transport, the main challenge of inducing stable topological phases in many-body Floquet systems is their tendency to absorb energy from the drive and thereby to heat up. We discuss three routes to overcoming this challenge: long-lived transient dynamics and prethermalization, disorder-induced many-body localization, and engineered couplings to external baths. We discuss the types of phenomena that can be explored in each of these regimes, and their experimental realizations.

Figures

Figures reproduced from arXiv: 1909.02008 by the authors.

Figure 1
Figure 1. FIG. 1. Floquet band engineering. (a) Circularly polarized [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Topological features of Floquet bands without ana [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Edge state transport in FTIs. a) Time-averaged spec [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Heating via energy absorption from the drive. a) [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Steady states of FTIs coupled to external baths. a) [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

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Works this paper leans on

176 extracted references · 78 canonical work pages

  1. [1]

    Towards properties on demand in quantum materials,

    D. N. Basov, R. D. Averitt, and D. Hsieh, “Towards properties on demand in quantum materials,” Nature Materials 16, 1077 (2017)

    2017

  2. [2]

    Sur les equations differentielles lin- eaires a coefficients periodiques,

    Gaston Floquet, “Sur les equations differentielles lin- eaires a coefficients periodiques,” Annales de l’Ecole Normale Superieure 12, 47 (1883)

  3. [3]

    Optical Con- trol of Topological Quantum Transport in Semiconduc- tors,

    W. Yao, A. H. MacDonald, and Q. Niu, “Optical Con- trol of Topological Quantum Transport in Semiconduc- tors,” Phys. Rev. Lett. 99, 047401 (2007)

    2007

  4. [4]

    Colloquium: Topological insulators,

    M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Rev. Mod. Phys. 82, 3045–3067 (2010)

    2010

  5. [5]

    Photovoltaic Hall effect in graphene,

    Takashi Oka and Hideo Aoki, “Photovoltaic Hall effect in graphene,” Phys. Rev. B 79, 081406 (2009)

    2009

  6. [6]

    Topological characterization of period- ically driven quantum systems,

    Takuya Kitagawa, Erez Berg, Mark Rudner, and Eu- gene Demler, “Topological characterization of period- ically driven quantum systems,” Phys. Rev. B 82, 235114 (2010)

    2010

  7. [7]

    Floquet topological insulator in semiconductor quan- tum wells,

    Netanel H. Lindner, Gil Refael, and Victor Galitski, “Floquet topological insulator in semiconductor quan- tum wells,” Nature Phys. 7, 490 (2011)

    2011

  8. [8]

    Long-time behav- ior of isolated periodically driven interacting lattice sys- tems,

    Luca D’Alessio and Marcos Rigol, “Long-time behav- ior of isolated periodically driven interacting lattice sys- tems,” Phys. Rev. X 4, 041048 (2014)

    2014

Show all 176 references
  1. [9]

    Equilibrium states of generic quantum systems subject to periodic driving,

    A. Lazarides, A. Das, and R. Moessner, “Equilibrium states of generic quantum systems subject to periodic driving,” Phys. Rev. E 90, 012110 (2014)

    2014

  2. [10]

    Exceptions to the runaway heating scenario, e.g., based on localization in energy space [166–170] or finite-size effects [171], are also being explored

  3. [11]

    Floquet fractional Chern insulators,

    Adolfo G. Grushin, ´Alvaro G´ omez-Le´ on, and Titus Ne- upert, “Floquet fractional Chern insulators,” Phys. Rev. Lett. 112, 156801 (2014)

    2014

  4. [12]

    Topological Floquet Phases in Driven Coupled Rashba Nanowires,

    Jelena Klinovaja, Peter Stano, and Daniel Loss, “Topological Floquet Phases in Driven Coupled Rashba Nanowires,” Phys. Rev. Lett. 116, 176401 (2016)

    2016

  5. [13]

    Flo- quet engineering of multiorbital mott insulators: Ap- plications to orthorhombic titanates,

    Jianpeng Liu, Kasra Hejazi, and Leon Balents, “Flo- quet engineering of multiorbital mott insulators: Ap- plications to orthorhombic titanates,” Phys. Rev. Lett. 121, 107201 (2018)

    2018

  6. [14]

    Enhancement and sign change of magnetic correlations in a driven quantum many-body system,

    Frederik G¨ org, Michael Messer, Kilian Sandholzer, Gre- gor Jotzu, Remi Desbuquois, and Tilman Esslinger, “Enhancement and sign change of magnetic correlations in a driven quantum many-body system,” Nature 553, 481 (2018)

    2018

  7. [15]

    Floquet Engineering in Quantum Chains,

    D. M. Kennes, A. de la Torre, A. Ron, D. Hsieh, and A. J. Millis, “Floquet Engineering in Quantum Chains,” Phys. Rev. Lett. 120, 127601 (2018)

    2018

  8. [16]

    Anomalous edge states and the bulk-edge correspondence for periodically driven two- dimensional systems,

    Mark S. Rudner, Netanel H. Lindner, Erez Berg, and Michael Levin, “Anomalous edge states and the bulk-edge correspondence for periodically driven two- dimensional systems,” Phys. Rev. X 3, 031005 (2013)

    2013

  9. [17]

    Topological sin- gularities and the general classification of Floquet-Bloch systems,

    Frederik Nathan and Mark S. Rudner, “Topological sin- gularities and the general classification of Floquet-Bloch systems,” New J. Phys. 17, 125014 (2015)

    2015

  10. [18]

    Floquet topological phases with symmetry in all dimensions,

    Rahul Roy and Fenner Harper, “Floquet topological phases with symmetry in all dimensions,” Phys. Rev. B 95, 195128 (2017)

    2017

  11. [19]

    Periodic table for Flo- quet topological insulators,

    Rahul Roy and Fenner Harper, “Periodic table for Flo- quet topological insulators,” Phys. Rev. B 96, 155118 (2017)

    2017

  12. [21]

    Floquet-Bloch Theory and Topology in Periodically Driven Lattices,

    A. G´ omez-Le´ on and G. Platero, “Floquet-Bloch Theory and Topology in Periodically Driven Lattices,” Phys. Rev. Lett. 110, 200403 (2013)

    2013

  13. [22]

    Bulk-Edge Correspondence for Two-Dimensional Floquet Topological Insulators,

    G. M. Graf and C. Tauber, “Bulk-Edge Correspondence for Two-Dimensional Floquet Topological Insulators,” Ann. Henri Poincare 19, 709 (2018)

    2018

  14. [23]

    Strongly Dis- ordered Floquet Topological Systems,

    Jacob Shapiro and Cl´ ement Tauber, “Strongly Dis- ordered Floquet Topological Systems,” Annales Henri Poincare 20, 1837 (2019)

    2019

  15. [24]

    Phase Structure of Driven Quantum Systems,

    V. Khemani, A. Lazarides, R. Moessner, and S. L. Sondhi, “Phase Structure of Driven Quantum Systems,” Phys. Rev. Lett. 116, 250401 (2016)

    2016

  16. [25]

    Floquet time crystals,

    Dominic V. Else, Bela Bauer, and Chetan Nayak, “Floquet time crystals,” Phys. Rev. Lett. 117, 090402 (2016)

    2016

  17. [26]

    Prethermal Phases of Matter Protected by Time- Translation Symmetry,

    Dominic V. Else, Bela Bauer, and Chetan Nayak, “Prethermal Phases of Matter Protected by Time- Translation Symmetry,” Phys. Rev. X7, 011026 (2017)

    2017

  18. [27]

    Self- induced Berry flux and spontaneous non-equilibrium magnetism,

    Mark S. Rudner and Justin C. W. Song, “Self- induced Berry flux and spontaneous non-equilibrium magnetism,” Nature Physics (2019)

    2019

  19. [28]

    Dynamical synchronization transition in interacting electron systems,

    Tanay Nag, Robert-Jan Slager, Takuya Higuchi, and Takashi Oka, “Dynamical synchronization transition in interacting electron systems,” arXiv:1802.02161 (2018)

    2018 arXiv

  20. [29]

    Holographic floquet states ii: Floquet condensation of vector mesons in nonequilibrium phase diagram,

    Shunichiro Kinoshita, Keiju Murata, and Takashi Oka, “Holographic floquet states ii: Floquet condensation of vector mesons in nonequilibrium phase diagram,” Jour- nal of High Energy Physics 2018, 96 (2018)

    2018

  21. [30]

    Topology and Broken Symmetry in Floquet Systems,

    Fenner Harper, Rahul Roy, Mark S. Rudner, and S. L. Sondhi, “Topology and Broken Symmetry in Floquet Systems,” arXiv:1905.01317 (2019)

    2019 arXiv

  22. [31]

    Phase struc- ture of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases,

    C. W. von Keyserlingk and S. L. Sondhi, “Phase struc- ture of one-dimensional interacting Floquet systems. I. Abelian symmetry-protected topological phases,” Phys. Rev. B 93, 245145 (2016)

    2016

  23. [32]

    Classification of Interacting Topological Floquet Phases in One Dimension,

    Andrew C. Potter, Takahiro Morimoto, and Ashvin Vishwanath, “Classification of Interacting Topological Floquet Phases in One Dimension,” Phys. Rev. X 6, 041001 (2016)

    2016

  24. [33]

    Classification of topological phases in periodically driven interacting sys- tems,

    Dominic V. Else and Chetan Nayak, “Classification of topological phases in periodically driven interacting sys- tems,” Phys. Rev. B 93, 201103 (2016)

    2016

  25. [34]

    Floquet Topological Or- der in Interacting Systems of Bosons and Fermions,

    Fenner Harper and Rahul Roy, “Floquet Topological Or- der in Interacting Systems of Bosons and Fermions,” Phys. Rev. Lett. 118, 115301 (2017)

    2017

  26. [35]

    Equilibration and order in quantum Floquet matter,

    R. Moessner and S. L. Sondhi, “Equilibration and order in quantum Floquet matter,” Nature Physics 13, 424 (2017). 14

    2017

  27. [36]

    Experimen- tal realization of the topological Haldane model with ultracold fermions,

    G. Jotzu, M. Messer, R. Desbuquois, M. Lebrat, T. Uehlinger, D. Greif, and T. Esslinger, “Experimen- tal realization of the topological Haldane model with ultracold fermions,” Nature 515, 237 (2014)

    2014

  28. [37]

    Ex- perimental reconstruction of the Berry curvature in a Floquet Bloch band,

    N. Flaschner, B. S. Rem, M. Tarnowski, D. Vogel, D.- S. L¨ uhmann, K. Sengstock, and C. Weitenberg, “Ex- perimental reconstruction of the Berry curvature in a Floquet Bloch band,” Science 352, 1091 (2016)

    2016

  29. [38]

    Photonic Floquet topological insulators,

    Mikael C. Rechtsman, Julia M. Zeuner, Yonatan Plot- nik, Yaakov Lumer, Daniel Podolsky, Felix Dreisow, Stefan Nolte, Mordechai Segev, and Alexander Szameit, “Photonic Floquet topological insulators,” Nature 496, 196 (2013)

    2013

  30. [39]

    Observation of Floquet-Bloch states on the surface of a topological insulator,

    Y. H. Wang, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, “Observation of Floquet-Bloch states on the surface of a topological insulator,” Science 342, 453 (2013)

    2013

  31. [40]

    Light-induced anomalous Hall effect in graphene,

    J. W. McIver, B. Schulte, F.-U. Stein, T. Matsuyama, G. Jotzu, G. Meier, and A. Cavalleri, “Light-induced anomalous Hall effect in graphene,” 1811.03522 (2018)

    2018 arXiv

  32. [41]

    IV A, and iv) a derivation of the period- averaged conductivity via the Floquet-Kubo formula

    See Supplementary Material for: i) an explicit calcu- lation demonstrating Floquet gap opening due an off- resonant drive, ii) a discussion of the vanishing of ν1 for any evolution derived from a local Hamiltonian, iii) the definition of the time-averaged spectral function dis- ...

  33. [42]

    Floquet engineering with quasienergy bands of periodically driven optical lattices,

    Martin Holthaus, “Floquet engineering with quasienergy bands of periodically driven optical lattices,” Journal of Physics B: Atomic, Molecular and Optical Physics 49, 013001 (2016)

    2016

  34. [43]

    Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels,

    Takuya Kitagawa, Takashi Oka, Arne Brataas, Liang Fu, and Eugene Demler, “Transport properties of nonequilibrium systems under the application of light: Photoinduced quantum Hall insulators without Landau levels,” Phys. Rev. B 84, 235108 (2011)

    2011

  35. [44]

    Valley-selective op- tical Stark effect in monolayer WS 2,

    Edbert J. Sie, James W. McIver, Yi-Hsien Lee, Liang Fu, Jing Kong, and Nuh Gedik, “Valley-selective op- tical Stark effect in monolayer WS 2,” Nature Materials 14, 290 (2015)

    2015

  36. [45]

    Irradiated graphene as a tunable Floquet topological insulator,

    G. Usaj, P. M. Perez-Piskunow, L. E. F. Foa Torres, and C. A. Balseiro, “Irradiated graphene as a tunable Floquet topological insulator,” Phys. Rev. B 90, 115423 (2014)

    2014

  37. [46]

    Bandwidth-resonant Floquet states in honeycomb op- tical lattices,

    A. Quelle, M. O. Goerbig, and C. Morais Smith, “Bandwidth-resonant Floquet states in honeycomb op- tical lattices,” New J. Phys. 18, 015006 (2016)

    2016

  38. [47]

    Floquet Spectrum and Transport through an Irradiated Graphene Ribbon,

    Zhenghao Gu, H. A. Fertig, Daniel P. Arovas, and Assa Auerbach, “Floquet Spectrum and Transport through an Irradiated Graphene Ribbon,” Phys. Rev. Lett. 107, 216601 (2011)

    2011

  39. [48]

    Universal Fluc- tuations of Floquet Topological Invariants at Low Fre- quencies,

    M. Rodriguez-Vega and B. Seradjeh, “Universal Fluc- tuations of Floquet Topological Invariants at Low Fre- quencies,” Phys. Rev. Lett. 121, 036402 (2018)

    2018

  40. [49]

    Merging of Dirac points and Floquet topo- logical transitions in ac-driven graphene,

    Pierre Delplace, ´Alvaro G´ omez-Le´ on, and Gloria Platero, “Merging of Dirac points and Floquet topo- logical transitions in ac-driven graphene,” Phys. Rev. B 88, 245422 (2013)

    2013

  41. [50]

    Theory of Floquet band formation and local pseudospin tex- tures in pump-probe photoemission of graphene,

    M. A. Sentef, M. Claassen, A. F. Kemper, B. Moritz, T. Oka, J. K. Freericks, and T. P. Devereaux, “Theory of Floquet band formation and local pseudospin tex- tures in pump-probe photoemission of graphene,” Na- ture Comm. 6, 7047 (2015)

    2015

  42. [51]

    Materials Design from Nonequi- librium Steady States: Driven Graphene as a Tun- able Semiconductor with Topological Properties,

    Thomas Iadecola, David Campbell, Claudio Chamon, Chang-Yu Hou, Roman Jackiw, So-Young Pi, and Sil- via Viola Kusminskiy, “Materials Design from Nonequi- librium Steady States: Driven Graphene as a Tun- able Semiconductor with Topological Properties,” Phys. Rev. Lett. 110, 1766...

    2013

  43. [52]

    Majorana Fermions in Equilibrium and in Driven Cold- Atom Quantum Wires,

    Liang Jiang, Takuya Kitagawa, Jason Alicea, A. R. Akhmerov, David Pekker, Gil Refael, J. Ignacio Cirac, Eugene Demler, Mikhail D. Lukin, and Peter Zoller, “Majorana Fermions in Equilibrium and in Driven Cold- Atom Quantum Wires,” Phys. Rev. Lett. 106, 220402 (2011)

    2011

  44. [53]

    Floquet Majorana fermions and parafermions in driven Rashba nanowires,

    M. Thakurathi, D. Loss, and J. Klinovaja, “Floquet Majorana fermions and parafermions in driven Rashba nanowires,” Phys. Rev. B 95, 155407 (2017)

    2017

  45. [54]

    Chiral 1D Floquet topological insulators beyond rotating wave approximation,

    Dante M. Kennes, Niclas M¨ uller, Mikhail Pletyukhov, Clara Weber, Christoph Bruder, Fabian Hassler, Jelena Klinovaja, Daniel Loss, and Herbert Schoeller, “Chiral 1D Floquet topological insulators beyond rotating wave approximation,” arXiv:1811.12062 (2018)

    2018 arXiv

  46. [55]

    Topological Floquet spectrum in three dimensions via a two-photon resonance,

    Netanel H. Lindner, Doron L. Bergman, Gil Refael, and Victor Galitski, “Topological Floquet spectrum in three dimensions via a two-photon resonance,” Phys. Rev. B 87, 235131 (2013)

    2013

  47. [56]

    Floquet Weyl semimetal induced by off- resonant light,

    Rui Wang, Baigeng Wang, Rui Shen, L. Sheng, and D. Y. Xing, “Floquet Weyl semimetal induced by off- resonant light,” Europhys. Lett. 105, 17004 (2014)

    2014

  48. [57]

    When chiral photons meet chiral fermions: photoinduced anomalous Hall ef- fects in Weyl semimetals,

    Ching-Kit Chan, Patrick A. Lee, Kenneth S. Burch, Jung Hoon Han, and Ying Ran, “When chiral photons meet chiral fermions: photoinduced anomalous Hall ef- fects in Weyl semimetals,” Phys. Rev. Lett.116, 026805 (2016)

    2016

  49. [58]

    Type-II Weyl cone transitions in driven semimetals,

    Ching-Kit Chan, Yun-Tak Oh, Jung Hoon Han, and Patrick A. Lee, “Type-II Weyl cone transitions in driven semimetals,” Phys. Rev. B 94, 121106 (2016)

    2016

  50. [59]

    Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials,

    H. H¨ ubener, M. A. Sentef, U. de Giovannini, A. F. Kemper, and A. Rubio, “Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials,” Na- ture Comm. 8, 13940 (2017)

    2017

  51. [60]

    Colloquium: Artificial gauge po- tentials for neutral atoms,

    Jean Dalibard, Fabrice Gerbier, Gediminas Juzeli¯ unas, and Patrik ¨Ohberg, “Colloquium: Artificial gauge po- tentials for neutral atoms,” Rev. Mod. Phys. 83, 1523– 1543 (2011)

    2011

  52. [61]

    Light-induced gauge fields for ultracold atoms,

    N Goldman, G Juzeli¯ unas, P hberg, and I B Spiel- man, “Light-induced gauge fields for ultracold atoms,” Reports on Progress in Physics 77, 126401 (2014)

    2014

  53. [62]

    Topo- logical bands for ultracold atoms,

    N. R. Cooper, J. Dalibard, and I. B. Spielman, “Topo- logical bands for ultracold atoms,” Rev. Mod. Phys. 91, 015005 (2019)

    2019

  54. [63]

    Periodic table for topological insulators and superconductors,

    A. Kitaev, “Periodic table for topological insulators and superconductors,” AIP Conf. Proc. 1134, 22 (2009)

    2009

  55. [64]

    Topological insulators and su- perconductors: tenfold way and dimensional hierarchy,

    Shinsei Ryu, Andreas P. Schnyder, Akira Furusaki, and Andreas W. W. Ludwig, “Topological insulators and su- perconductors: tenfold way and dimensional hierarchy,” New J. Phys. 12, 065010 (2010)

    2010

  56. [65]

    Quantization of particle transport,

    D. J. Thouless, “Quantization of particle transport,” Phys. Rev. B 27, 6083 (1983)

    1983

  57. [66]

    Index theory of one dimensional quantum walks and cellular automata,

    D. Gross, V. Nesme, H. Vogts, and R. F. Werner, “Index theory of one dimensional quantum walks and cellular automata,” Communications in Mathematical Physics 310, 419 (2012)

    2012

  58. [67]

    Floquet chiral magnetic effect,

    Sho Higashikawa, Masaya Nakagawa, and Masahito Ueda, “Floquet chiral magnetic effect,” Phys. Rev. Lett. 15 123, 066403 (2019)

    2019

  59. [68]

    Three-Dimensional Chiral Lattice Fermion in Floquet Systems,

    Xiao-Qi Sun, Meng Xiao, Tom´ a ˇ s Bzduˇ sek, Shou-Cheng Zhang, and Shanhui Fan, “Three-Dimensional Chiral Lattice Fermion in Floquet Systems,” Phys. Rev. Lett. 121, 196401 (2018)

    2018

  60. [69]

    Quantum Spin Hall Effect and Topolog- ical Phase Transition in HgTe Quantum Wells,

    B. Andrei Bernevig, Taylor L. Hughes, and Shou- Cheng Zhang, “Quantum Spin Hall Effect and Topolog- ical Phase Transition in HgTe Quantum Wells,” Science 314, 1757 (2006)

    2006

  61. [70]

    Quantized Hall conductance, current- carrying edge states, and the existence of extended states in a two-dimensional disordered potential,

    B. I. Halperin, “Quantized Hall conductance, current- carrying edge states, and the existence of extended states in a two-dimensional disordered potential,” Phys. Rev. B 25, 2185–2190 (1982)

    1982

  62. [71]

    Chern number and edge states in the integer quantum Hall effect,

    Yasuhiro Hatsugai, “Chern number and edge states in the integer quantum Hall effect,” Phys. Rev. Lett. 71, 3697 (1993)

    1993

  63. [72]

    Topological index for period- ically driven time-reversal invariant 2d systems,

    David Carpentier, Pierre Delplace, Michel Fruchart, and Krzysztof Gawedzki, “Topological index for period- ically driven time-reversal invariant 2d systems,” Phys. Rev. Lett. 114, 106806 (2015)

    2015

  64. [73]

    Discrete single-photon quantum walks with tunable decoher- ence,

    M. A. Broome, A. Fedrizzi, B. P. Lanyon, I. Kas- sal, A. Aspuru-Guzik, and A. G. White, “Discrete single-photon quantum walks with tunable decoher- ence,” Phys. Rev. Lett. 104, 153602 (2010)

    2010

  65. [74]

    Floquet Majorana Fermions for Topological Qubits in Superconducting Devices and Cold-Atom Systems,

    Dong E. Liu, Alex Levchenko, and Harold U. Baranger, “Floquet Majorana Fermions for Topological Qubits in Superconducting Devices and Cold-Atom Systems,” Phys. Rev. Lett. 111, 047002 (2013)

    2013

  66. [75]

    Chiral symmetry and bulk-boundary correspondence in peri- odically driven one-dimensional systems,

    J. K. Asb´ oth, B. Tarasinski, and P. Delplace, “Chiral symmetry and bulk-boundary correspondence in peri- odically driven one-dimensional systems,” Phys. Rev. B 90, 125143 (2014)

    2014

  67. [76]

    Flo- quet topological transitions in a driven one-dimensional topological insulator,

    V. Dal Lago, M. Atala, and L. E. F. Foa Torres, “Flo- quet topological transitions in a driven one-dimensional topological insulator,” Phys. Rev. A 92, 023624 (2015)

    2015

  68. [77]

    Topologically protected braiding in a single wire using Floquet Majorana modes,

    Bela Bauer, T. Pereg-Barnea, Torsten Karzig, Maria- Theresa Rieder, Gil Refael, Erez Berg, and Yuval Oreg, “Topologically protected braiding in a single wire using Floquet Majorana modes,” Phys. Rev. B 100, 041102 (2019)

    2019

  69. [78]

    Driven quantum transport on the nanoscale,

    Sigmund Kohler, Jorg Lehmann, and Peter Hanggi, “Driven quantum transport on the nanoscale,” Physics Reports 406, 379 (2005)

    2005

  70. [79]

    Bulk-boundary correspondence for chiral symmetric quantum walks,

    J´ anos K. Asb´ oth and Hideaki Obuse, “Bulk-boundary correspondence for chiral symmetric quantum walks,” Phys. Rev. B 88, 121406 (2013)

    2013

  71. [80]

    Counter-propagating Edge Modes and Topolog- ical Phases of a Kicked Quantum Hall System,

    Mahmoud Lababidi, Indubala I. Satija, and Erhai Zhao, “Counter-propagating Edge Modes and Topolog- ical Phases of a Kicked Quantum Hall System,” Phys. Rev. Lett. 112, 026805 (2014)

    2014

  72. [81]

    Flo- quet edge states in a harmonically driven integer quan- tum Hall system,

    Zhenyu Zhou, Indubala I. Satija, and Erhai Zhao, “Flo- quet edge states in a harmonically driven integer quan- tum Hall system,” Phys. Rev. B 90, 205108 (2014)

    2014

  73. [82]

    Topo- logical invariants of Floquet systems: General formu- lation, special properties, and Floquet topological de- fects,

    Shunyu Yao, Zhongbo Yan, and Zhong Wang, “Topo- logical invariants of Floquet systems: General formu- lation, special properties, and Floquet topological de- fects,” Phys. Rev. B 96, 195303 (2017)

    2017

  74. [83]

    Floquet topological phases protected by time glide symmetry,

    Takahiro Morimoto, Hoi Chun Po, and Ashvin Vish- wanath, “Floquet topological phases protected by time glide symmetry,” Phys. Rev. B 95, 195155 (2017)

    2017

  75. [84]

    Space-time crystal and space-time group,

    Shenglong Xu and Congjun Wu, “Space-time crystal and space-time group,” Phys. Rev. Lett. 120, 096401 (2018)

    2018

  76. [85]

    Floquet second-order topo- logical insulators from nonsymmorphic space-time sym- metries,

    Yang Peng and Gil Refael, “Floquet second-order topo- logical insulators from nonsymmorphic space-time sym- metries,” Phys. Rev. Lett. 123, 016806 (2019)

    2019

  77. [86]

    Measurement of a Topological Edge Invariant in a Microwave Network,

    Wenchao Hu, Jason C. Pillay, Kan Wu, Michael Pasek, Perry Ping Shum, and Y. D. Chong, “Measurement of a Topological Edge Invariant in a Microwave Network,” Phys. Rev. X 5, 011012 (2015)

    2015

  78. [87]

    Experimental observation of anomalous topologi- cal edge modes in a slowly-driven photonic lattice,

    S. Mukherjee, A. Spracklen, M. Valiente, E. Ander- sson, O. Ohberg, N. Goldman, and R. R. Thom- son, “Experimental observation of anomalous topologi- cal edge modes in a slowly-driven photonic lattice,” Na- ture Comm. 8, 13918 (2017)

    2017

  79. [88]

    Observation of photonic anomalous Floquet topological insulators,

    Lukas J. Maczewsky, Julia M. Zeuner, Stefan Nolte, and Alexander Szameit, “Observation of photonic anomalous Floquet topological insulators,” Nature Comm. 8, 13756 (2017)

    2017

  80. [89]

    Observation of Anomalousπ Modes in Photonic Floquet Engineering,

    Qingqing Cheng, Yiming Pan, Huaiqiang Wang, Chaoshi Zhang, Dong Yu, Avi Gover, Haijun Zhang, Tao Li, Lei Zhou, and Shining Zhu, “Observation of Anomalousπ Modes in Photonic Floquet Engineering,” Phys. Rev. Lett. 122, 173901 (2019)

    2019

  81. [90]

    Topological Thouless pumping of ultracold fermions,

    S. Nakajima, T. Tomita, S. Taie, T. Ichinose, H. Ozawa, L. Wang, M. Troyer, and Y. Takahashi, “Topological Thouless pumping of ultracold fermions,” Nature Phys. 12, 296 (2016)

    2016

  82. [91]

    A Thouless quantum pump with ultra- cold bosonic atoms in an optical superlattice,

    M. Lohse, C. Schweizer, O. Zilberberg, M. Aidelsburger, and I. Bloch, “A Thouless quantum pump with ultra- cold bosonic atoms in an optical superlattice,” Nature Phys. 12, 350 (2016)

    2016

  83. [92]

    Driving protocol for a Floquet topo- logical phase without static counterpart,

    A. Quelle, C. Weitenberg, K. Sengstock, and C. Morais Smith, “Driving protocol for a Floquet topo- logical phase without static counterpart,” New Journal of Physics 19, 113010 (2017)

    2017

  84. [93]

    Flo- quet Majorana zero and π modes in planar Josephson junctions,

    Dillon T. Liu, Javad Shabani, and Aditi Mitra, “Flo- quet Majorana zero and π modes in planar Josephson junctions,” Phys. Rev. B 99, 094303 (2019)

    2019

  85. [94]

    Transport signa- tures of Floquet Majorana fermions in driven topolog- ical superconductors,

    Arijit Kundu and Babak Seradjeh, “Transport signa- tures of Floquet Majorana fermions in driven topolog- ical superconductors,” Phys. Rev. Lett. 111, 136402 (2013)

    2013

  86. [95]

    Multiterminal Conductance of a Floquet Topological Insulator,

    L. E. F. Foa Torres, P. M. Perez-Piskunow, C. A. Bal- seiro, and Gonzalo Usaj, “Multiterminal Conductance of a Floquet Topological Insulator,” Phys. Rev. Lett. 113, 266801 (2014)

    2014

  87. [96]

    Photon-inhibited topological transport in quantum well heterostruc- tures,

    Aaron Farrell and T. Pereg-Barnea, “Photon-inhibited topological transport in quantum well heterostruc- tures,” Phys. Rev. Lett. 115, 106403 (2015)

    2015

  88. [97]

    Edge-state trans- port in Floquet topological insulators,

    Aaron Farrell and T. Pereg-Barnea, “Edge-state trans- port in Floquet topological insulators,” Phys. Rev. B 93, 045121 (2016)

    2016

  89. [98]

    Quantized large-bias cur- rent in the anomalous Floquet-Anderson insulator,

    Arijit Kundu, Mark S. Rudner, Erez Berg, and Netanel H. Lindner, “Quantized large-bias cur- rent in the anomalous Floquet-Anderson insulator,” arXiv:1708.05023 (2017)

    2017 arXiv

  90. [99]

    Hierarchy of Floquet gaps and edge states for driven honeycomb lattices,

    P. M. Perez-Piskunow, L. E. F. Foa Torres, and Gonzalo Usaj, “Hierarchy of Floquet gaps and edge states for driven honeycomb lattices,” Phys. Rev. A 91, 043625 (2015)

    2015

  91. [100]

    Positivity of the Spectral Densities of Retarded Floquet Green Functions,

    G¨ otz S. Uhrig, Mona H. Kalthoff, and James K. Fre- ericks, “Positivity of the Spectral Densities of Retarded Floquet Green Functions,” Phys. Rev. Lett.122, 130604 (2019)

    2019

  92. [101]

    Midgap edge states and pairing symmetry of quasi-one-dimensional organic 16 superconductors,

    K. Sengupta, Igor ˇZuti´ c, Hyok-Jon Kwon, Victor M. Yakovenko, and S. Das Sarma, “Midgap edge states and pairing symmetry of quasi-one-dimensional organic 16 superconductors,” Phys. Rev. B 63, 144531 (2001)

    2001

  93. [102]

    Ma- jorana fermion induced resonant andreev reflection,

    K. T. Law, Patrick A. Lee, and T. K. Ng, “Ma- jorana fermion induced resonant andreev reflection,” Phys. Rev. Lett. 103, 237001 (2009)

    2009

  94. [103]

    Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump,

    Paraj Titum, Erez Berg, Mark S. Rudner, Gil Refael, and Netanel H. Lindner, “Anomalous Floquet-Anderson Insulator as a Nonadiabatic Quantized Charge Pump,” Phys. Rev. X 6, 021013 (2016)

    2016

  95. [104]

    Magnetization Signatures of Light-Induced Quantum Hall Edge States,

    Jan P. Dahlhaus, Benjamin M. Fregoso, and Joel E. Moore, “Magnetization Signatures of Light-Induced Quantum Hall Edge States,” Phys. Rev. Lett. 114, 246802 (2015)

    2015

  96. [105]

    Quantized magnetization density in periodically driven systems,

    Frederik Nathan, Mark S. Rudner, Netanel H. Lindner, Erez Berg, and Gil Refael, “Quantized magnetization density in periodically driven systems,” Phys. Rev. Lett. 119, 186801 (2017)

    2017

  97. [106]

    Selective scattering between Floquet-Bloch and Volkov states in a topolog- ical insulator,

    F. Mahmood, C.-K. Chan, Z. Alpichshev, D. Gardner, Y. Lee, P. A. Lee, and N. Gedik, “Selective scattering between Floquet-Bloch and Volkov states in a topolog- ical insulator,” Nature Phys. 12, 306 (2016)

    2016

  98. [107]

    Driven electronic states at the surface of a topological insulator,

    Benjamin M. Fregoso, Y. H. Wang, N. Gedik, and Vic- tor Galitski, “Driven electronic states at the surface of a topological insulator,” Phys. Rev. B 88, 155129 (2013)

    2013

  99. [108]

    Dirac cones, Floquet side bands, and theory of time- resolved angle-resolved photoemission,

    Aaron Farrell, A. Arsenault, and T. Pereg-Barnea, “Dirac cones, Floquet side bands, and theory of time- resolved angle-resolved photoemission,” Phys. Rev. B 94, 155304 (2016)

    2016

  100. [109]

    Many-body dynamics and gap opening in interacting periodically driven systems,

    Ervand Kandelaki and Mark S. Rudner, “Many-body dynamics and gap opening in interacting periodically driven systems,” Phys. Rev. Lett. 121, 036801 (2018)

    2018

  101. [110]

    Universal high-frequency behavior of periodically driven systems: from dynamical stabi- lization to Floquet engineering,

    Marin Bukov, Luca D’Alessio, and Anatoli Polkovnikov, “Universal high-frequency behavior of periodically driven systems: from dynamical stabi- lization to Floquet engineering,” Advances in Physics 64, 139 (2015)

    2015

  102. [111]

    High-frequency approx- imation for periodically driven quantum systems from a Floquet-space perspective,

    A. Eckardt and E. Anisimovas, “High-frequency approx- imation for periodically driven quantum systems from a Floquet-space perspective,” New J. Phys. 17, 093039 (2015)

    2015

  103. [112]

    Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems,

    T. Kuwahara, T. Mori, and K. Saito, “Floquet-Magnus theory and generic transient dynamics in periodically driven many-body quantum systems,” Ann. Phys. 367, 96 (2016)

    2016

  104. [113]

    Effective Hamiltonians, prethermalization, and slow energy absorption in peri- odically driven many-body systems,

    Dmitry A. Abanin, Wojciech De Roeck, Wen Wei Ho, and Francois Huveneers, “Effective Hamiltonians, prethermalization, and slow energy absorption in peri- odically driven many-body systems,” Phys. Rev. B 95, 014112 (2017)

    2017

  105. [114]

    Universal Chiral Quasisteady States in Period- ically Driven Many-Body Systems,

    Netanel H. Lindner, Erez Berg, and Mark S. Rud- ner, “Universal Chiral Quasisteady States in Period- ically Driven Many-Body Systems,” Phys. Rev. X 7, 011018 (2017)

    2017

  106. [115]

    Thermalization and prethermal- ization in isolated quantum systems: a theoretical overview,

    Takashi Mori, Tatsuhiko N. Ikeda, Eriko Kamanishi, and Masahito Ueda, “Thermalization and prethermal- ization in isolated quantum systems: a theoretical overview,” J. Phys. B: At. Mol. Opt. Phys. 51, 112001 (2018)

    2018

  107. [116]

    Heating and many-body resonances in a periodically driven two-band system,

    Marin Bukov, Markus Heyl, David A. Huse, and Ana- toli Polkovnikov, “Heating and many-body resonances in a periodically driven two-band system,” Phys. Rev. B 93, 155132 (2016)

    2016

  108. [117]

    Exponentially Slow Heating in Periodically Driven Many-Body Systems,

    Dmitry A. Abanin, Wojciech De Roeck, and Fran¸ cois Huveneers, “Exponentially Slow Heating in Periodically Driven Many-Body Systems,” Phys. Rev. Lett. 115, 256803 (2015)

    2015

  109. [118]

    Interaction dependent heating and atom loss in a periodically driven optical lattice,

    Martin Reitter, Jakob N¨ ager, Karen Wintersperger, Christoph Str¨ ater, Immanuel Bloch, Andr´ e Eckardt, and Ulrich Schneider, “Interaction dependent heating and atom loss in a periodically driven optical lattice,” Phys. Rev. Lett. 119, 200402 (2017)

    2017

  110. [119]

    Note that this low-frequency driving regime does not imply adiabaticity; while a large gap in the single spec- trum is required, the system need not have a many-body gap

  111. [120]

    A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems,

    D. Abanin, W. De Roeck, W. W. Ho, and F. Huveneers, “A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems,” Comm. Math Phys. 354, 809 (2017)

    2017

  112. [121]

    Fractional Chern insulator,

    N. Regnault and B. Andrei Bernevig, “Fractional Chern insulator,” Phys. Rev. X 1, 021014 (2011)

    2011

  113. [122]

    Dynamical time-reversal sym- metry breaking and photo-induced chiral spin liquids in frustrated mott insulators,

    Martin Claassen, Hong-Chen Jiang, Brian Mortiz, and Thomas P. Devereaux, “Dynamical time-reversal sym- metry breaking and photo-induced chiral spin liquids in frustrated mott insulators,” Nature Communications 8, 1192 (2017)

    2017

  114. [123]

    Flo- quet engineering of multiorbital Mott insulators: ap- plications to orthorhombic titanates,

    Jianpeng Liu, Kasra Hejazi, and Leon Balents, “Flo- quet engineering of multiorbital Mott insulators: ap- plications to orthorhombic titanates,” Phys. Rev. Lett. 121, 107201 (2018)

    2018

  115. [124]

    Quasi-adiabatic dynamics and state preparation in Floquet many-body systems,

    Wen Wei Ho and Dmitry A. Abanin, “Quasi-adiabatic dynamics and state preparation in Floquet many-body systems,” arXiv:1611.05024 (2016)

    2016 arXiv

  116. [125]

    Controlling and characterizing Flo- quet prethermalization in a driven quantum system,

    K. Singh, K. M. Fujiwara, Z. A. Geiger, E. Q. Sim- mons, M. Lipatov, A. Cao, P. Dotti, S. V. Rajagopal, R. Senaratne, T. Shimasaki, M. Heyl, A. Eckardt, and D. M. Weld, “Controlling and characterizing Flo- quet prethermalization in a driven quantum system,” arXiv:1809.05554 (2018)

    2018 arXiv

  117. [126]

    Exponentially long lifetime of univer- sal quasi-steady states in topological Floquet pumps,

    Tobias Gulden, Erez Berg, Mark S. Rudner, and Ne- tanel H. Lindner, “Exponentially long lifetime of univer- sal quasi-steady states in topological Floquet pumps,” arXiv:1901.08385 (2019)

    2019 arXiv

  118. [127]

    Metal insulator transition in a weakly interacting many- electron system with localized single-particle states,

    D. M. Basko, I. L. Aleiner, and B. L. Altshuler, “Metal insulator transition in a weakly interacting many- electron system with localized single-particle states,” Ann. Phys. 321, 1126 (2006)

    2006

  119. [128]

    Localization of interacting fermions at high temperature,

    Vadim Oganesyan and David A. Huse, “Localization of interacting fermions at high temperature,” Phys. Rev. B 75, 155111 (2007)

    2007

  120. [129]

    Many-body localiza- tion phase transition,

    Arijeet Pal and David A. Huse, “Many-body localiza- tion phase transition,” Phys. Rev. B 82, 174411 (2010)

    2010

  121. [130]

    Many-body lo- calization and thermalization in quantum statistical me- chanics,

    Rahul Nandkishore and David A. Huse, “Many-body lo- calization and thermalization in quantum statistical me- chanics,” Annual Review of Condensed Matter Physics 6, 15 (2015)

    2015

  122. [131]

    Fate of Many-Body Localization Under Periodic Driving,

    Achilleas Lazarides, Arnab Das, and Roderich Moess- ner, “Fate of Many-Body Localization Under Periodic Driving,” Phys. Rev. Lett. 115, 030402 (2015)

    2015

  123. [132]

    Many-Body Localization in Peri- odically Driven Systems,

    Pedro Ponte, Z. Papi´ c, Fran¸ cois Huveneers, and Dmitry A. Abanin, “Many-Body Localization in Peri- odically Driven Systems,” Phys. Rev. Lett. 114, 140401 (2015)

    2015

  124. [133]

    Periodically driving a many-body localized quantum system,

    P. Bordia, H. Luschen, U. Schneider, M. Knap, and I. Bloch, “Periodically driving a many-body localized quantum system,” Nature Phys. 13, 460 (2017)

    2017

  125. [134]

    Quantum time crystals,

    Frank Wilczek, “Quantum time crystals,” Phys. Rev. Lett. 109, 160401 (2012)

    2012

  126. [135]

    Prethermal time crystals 17 in one-dimensional periodically driven Floquet system,

    T.-S. Zeng and D. N. Sheng, “Prethermal time crystals 17 in one-dimensional periodically driven Floquet system,” arXiv:1707.00404 (2017)

    2017 arXiv

  127. [136]

    Observa- tion of a discrete time crystal,

    J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I.-D. Potirniche, A. C. Potter, A. Vishwanath, N. Y. Yao, and C. Monroe, “Observa- tion of a discrete time crystal,” Nature 543, 217 (2017)

    2017

  128. [137]

    Observation of discrete time-crystalline order in a disordered dipolar many-body system,

    S. Choi, J. Choi, R. Landig, G. Kucsko, H. Zhou, J. Isoya, F. Jelezko, S. Onoda, H. Sumiya, V. Khemani, C. von Keyserlingk, N. Y. Yao, E. Demler, and M. D. Lukin, “Observation of discrete time-crystalline order in a disordered dipolar many-body system,” Nature 543, 221 (2017)

    2017

  129. [138]

    Interaction-induced time-symmetry break- ing in driven quantum oscillators,

    M. I. Dykman, Christoph Bruder, Niels L¨ orch, and Yax- ing Zhang, “Interaction-induced time-symmetry break- ing in driven quantum oscillators,” Phys. Rev. B 98, 195444 (2018)

    2018

  130. [139]

    Marginal Anderson localization and many-body delocalization,

    Rahul Nandkishore and Andrew C. Potter, “Marginal Anderson localization and many-body delocalization,” Phys. Rev. B 90, 195115 (2014)

    2014

  131. [140]

    Chiral Floquet Phases of Many-Body Localized Bosons,

    Hoi Chun Po, Lukasz Fidkowski, Takahiro Morimoto, Andrew C. Potter, and Ashvin Vishwanath, “Chiral Floquet Phases of Many-Body Localized Bosons,” Phys. Rev. X 6, 041070 (2016)

    2016

  132. [141]

    Radical chiral Floquet phases in a periodically driven Kitaev model and beyond,

    Hoi Chun Po, Lukasz Fidkowski, Ashvin Vishwanath, and Andrew C. Potter, “Radical chiral Floquet phases in a periodically driven Kitaev model and beyond,” Phys. Rev. B 96, 245116 (2017)

    2017

  133. [142]

    Anomalous Floquet Insulators,

    Frederik Nathan, Dmitry Abanin, Erez Berg, Netanel H. Lindner, and Mark S. Rudner, “Anomalous Floquet Insulators,” Phys. Rev. B 99, 195133 (2019)

    2019

  134. [143]

    Classification of the Floquet statistical distribution for time-periodic open systems,

    Dong E. Liu, “Classification of the Floquet statistical distribution for time-periodic open systems,” Phys. Rev. B 91, 144301 (2015)

    2015

  135. [144]

    Condition for emergence of the Floquet-Gibbs state in periodically driven open systems,

    T. Shirai, T. Mori, and S. Miyashita, “Condition for emergence of the Floquet-Gibbs state in periodically driven open systems,” Phys. Rev. E 91, 030101(R) (2015)

    2015

  136. [145]

    Effective Floquet-Gibbs states for dissipative quantum systems,

    T. Shirai, J. Thinga, T. Mori, S. Denisov, P. Hanggi, and S. Miyashita, “Effective Floquet-Gibbs states for dissipative quantum systems,” New J. Phys. 18, 053008 (2016)

    2016

  137. [146]

    Kubo formula for floquet states and photoconductivity oscillations in a two-dimensional electron gas,

    Manuel Torres and Alejandro Kunold, “Kubo formula for floquet states and photoconductivity oscillations in a two-dimensional electron gas,” Phys. Rev. B 71, 115313 (2005)

    2005

  138. [147]

    Periodic thermodynamics,

    Walter Kohn, “Periodic thermodynamics,” Journal of Statistical Physics 103, 417 (2001)

    2001

  139. [148]

    Time-dependent Floquet theory and absence of an adi- abatic limit,

    Daniel W. Hone, Roland Ketzmerick, and Walter Kohn, “Time-dependent Floquet theory and absence of an adi- abatic limit,” Phys. Rev. A 56, 4045 (1997)

    1997

  140. [149]

    Statistical mechanics of Floquet systems: The perva- sive problem of near degeneracies,

    Daniel W. Hone, Roland Ketzmerick, and Walter Kohn, “Statistical mechanics of Floquet systems: The perva- sive problem of near degeneracies,” Phys. Rev. E 79, 051129 (2009)

    2009

  141. [150]

    Out-of- equilibrium electrons and the Hall conductance of a Flo- quet topological insulator,

    H. Dehghani, T. Oka, and A. Mitra, “Out-of- equilibrium electrons and the Hall conductance of a Flo- quet topological insulator,” Phys. Rev. B 91, 155422 (2015)

    2015

  142. [151]

    Floquet- Boltzmann equation for periodically driven Fermi sys- tems,

    Maximilian Genske and Achim Rosch, “Floquet- Boltzmann equation for periodically driven Fermi sys- tems,” Phys. Rev. A 92, 062108 (2015)

    2015

  143. [152]

    Quantized transport and steady states of Flo- quet topological insulators,

    Iliya Esin, Mark S. Rudner, Gil Refael, and Netanel H. Lindner, “Quantized transport and steady states of Flo- quet topological insulators,” Phys. Rev. B 97, 245401 (2018)

    2018

  144. [153]

    Occupation of topological Floquet bands in open systems,

    Thomas Iadecola, Titus Neupert, and Claudio Cha- mon, “Occupation of topological Floquet bands in open systems,” Phys. Rev. B 91, 235133 (2015)

    2015

  145. [154]

    Thermalization of the Electron-Hole Plasma in GaAs,

    E. O. Goebel and O. Hildebrand, “Thermalization of the Electron-Hole Plasma in GaAs,” Phys. Stat. Sol. (b)88, 685 (1978)

    1978

  146. [155]

    Resonant excitation of carriers in a sem- inconductor by a high-power laser pulse,

    L. I. Glazman, “Resonant excitation of carriers in a sem- inconductor by a high-power laser pulse,” Sov. Phys. JETP 53, 178–181 (1981)

    1981

  147. [156]

    Kinetics of electrons and holes in di- rect gap seminconductors photoexcited by high inten- sity pulses,

    L. I. Glazman, “Kinetics of electrons and holes in di- rect gap seminconductors photoexcited by high inten- sity pulses,” Sov. Phys. Semi. 17, 494–498 (1983)

    1983

  148. [157]

    Chow and Stephan W

    Weng W. Chow and Stephan W. Koch, Semiconductor- Laser Fundamentals (Springer, 1999)

    1999

  149. [158]

    Room- Temperature Ultraviolet Nanowire Nanolasers,

    Michael H. Huang, Samuel Mao, Henning Feick, Hao- quan Yan, Yiying Wu, Hannes Kind, Eicke We- ber, Richard Russo, and Peidong Yang, “Room- Temperature Ultraviolet Nanowire Nanolasers,” Science 292, 1897 (2001)

    2001

  150. [159]

    Continuous wave nanowire lasing,

    Robert R¨ oder, Marcel Wille, Sebastian Geburt, Jura Rensberg, Mengyao Zhang, Jia Grace Lu, Federico Ca- passo, Robert Buschlinger, Ulf Peshcel, and Carsten Ronning, “Continuous wave nanowire lasing,” Nano Letters 13, 3602 (2013)

    2013

  151. [160]

    Dissipative Flo- quet topological systems,

    H. Dehghani, T. Oka, and A. Mitra, “Dissipative Flo- quet topological systems,” Phys. Rev. B 90, 195429 (2014)

    2014

  152. [161]

    Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths,

    K. I. Seetharam, C.-E. Bardyn, N. H. Lindner, M. S. Rudner, and G. Refael, “Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths,” Phys. Rev. X 5, 041050 (2015)

    2015

  153. [162]

    On the level of a theoretical model, the single resonance condition can be imposed by taking a system with nar- row bands separated by a large gap

  154. [163]

    Quan- tum heating of a parametrically modulated oscillator: Spectral signatures,

    M. I. Dykman, M. Marthaler, and V. Peano, “Quan- tum heating of a parametrically modulated oscillator: Spectral signatures,” Phys. Rev. A 83, 052115 (2011)

    2011

  155. [164]

    Electric and Magnetic Properties of a Semiconductor in the Field of a Strong Electromagnetic Wave,

    V. M. Galitskii, S. P. Goreslavskii, and V. F. Elesin, “Electric and Magnetic Properties of a Semiconductor in the Field of a Strong Electromagnetic Wave,” Sov. Phys. JETP 30, 117 (1970)

    1970

  156. [165]

    Microscopic theory for the light-induced anomalous Hall effect in graphene,

    S. A. Sato, J. W. McIver, M. Nuske, P. Tang, G. Jotzu, B. Schulte, H. H¨ ubener, U. De Giovannini, L. Mathey, M. A. Sentef, A. Cavalleri, and A. Rubio, “Microscopic theory for the light-induced anomalous Hall effect in graphene,” Phys. Rev. B 99, 214302 (2019)

    2019

  157. [166]

    Time evolution of a quantum many- body system: Transition from integrability to ergodicity in the thermodynamic limit,

    Tomaˇ z Prosen, “Time evolution of a quantum many- body system: Transition from integrability to ergodicity in the thermodynamic limit,” Phys. Rev. Lett. 80, 1808 (1998)

    1998

  158. [167]

    Corner transfer ma- trices for 2D strongly coupled many-body Floquet sys- tems,

    Ivan Kukuljan and Tomaz Prosen, “Corner transfer ma- trices for 2D strongly coupled many-body Floquet sys- tems,” J. Stat.Mech. 2016, 043305 (2016)

    2016

  159. [168]

    Dynamical stability of a many-body Kapitza pendulum,

    Roberta Citro, Emanuele G. Dalla Torre, Luca D’Alessio, Anatoli Polkovnikov, Mehrtash Berbadi, Takashi Oka, and Eugene Demler, “Dynamical stability of a many-body Kapitza pendulum,” Annals of Physics 360, 694 (2015)

    2015

  160. [169]

    Interaction- stabilized steady states in the driven O(N) model,

    Anushya Chandran and S. L. Sondhi, “Interaction- stabilized steady states in the driven O(N) model,” Phys. Rev. B 93, 174305 (2016)

    2016

  161. [170]

    On- set of Floquet thermalization,

    Asmi Haldar, Roderich Moessner, and Arnab Das, “On- set of Floquet thermalization,” Phys. Rev. B97, 245122 18 (2018)

    2018

  162. [171]

    Absence of thermalization in finite iso- lated interacting Floquet systems,

    Karthik Seetharam, Paraj Titum, Michael Kolodrubetz, and Gil Refael, “Absence of thermalization in finite iso- lated interacting Floquet systems,” Phys. Rev. B 97, 014311 (2018)

    2018

  163. [172]

    Henrik Bruus and Karsten Felnsberg, Many-Body Quantum Theory in Condensed Matter Physics: An In- troduction (Oxford University Press, 2004)

    2004

  164. [173]

    Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism,

    Naoto Tsuji, Takashi Oka, and Hideo Aoki, “Correlated electron systems periodically driven out of equilibrium: Floquet + DMFT formalism,” Phys. Rev. B 78, 235124 (2008)

    2008

  165. [174]

    Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study,

    Tao Qin and Walter Hofstetter, “Spectral functions of a time-periodically driven Falicov-Kimball model: Real-space Floquet dynamical mean-field theory study,” Phys. Rev. B 96, 075134 (2017)

    2017

  166. [175]

    Emergence of Floquet behavior for lattice fermions driven by light pulses,

    Mona H. Kalthoff, G¨ otz S. Uhrig, and J. K. Freericks, “Emergence of Floquet behavior for lattice fermions driven by light pulses,” Phys. Rev. B98, 035138 (2018)

    2018

  167. [176]

    Mahan, Many-particle physics (Springer, 2000)

    Gerald D. Mahan, Many-particle physics (Springer, 2000)

    2000

  168. [177]

    Insulator, metal, or superconductor: The cri- teria,

    Douglas J. Scalapino, Steven R. White, and Shoucheng Zhang, “Insulator, metal, or superconductor: The cri- teria,” Phys. Rev. B 47, 7995–8007 (1993). Supplementary material for “Floquet topological insulators: from band structure engineering to novel non-equilibrium quantum ph...

    1993

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