arxiv: 2605.13066 · v1 · submitted 2026-05-13 · ❄️ cond-mat.mes-hall · cond-mat.stat-mech· quant-ph

Recognition: unknown

Quantized Transport in Floquet Topological Insulators

Abhishek Dhar, Manas Kulkarni, Rekha Kumari

Pith reviewed 2026-05-14 02:20 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.stat-mechquant-ph

keywords Floquet topological insulatorquantized conductancewinding invariantHall conductancenonequilibrium Green's functionsideband sum ruleperiodic drivingedge transport

0 comments

The pith

Floquet topological systems show quantized longitudinal and Hall conductances set by the winding invariant once all sideband contributions are summed.

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

The paper shows that in a periodically driven topological insulator connected to static reservoirs, numerical calculations of two-terminal and Hall conductances reach exact quantization values given by the Floquet winding number. This occurs only after the contributions from every Floquet sideband are added together. A reader would care because the result supplies a concrete transport signature for measuring the topological invariant in driven systems that are now experimentally realizable.

Core claim

Using the Floquet nonequilibrium Green's-function formalism on a strip geometry, we demonstrate from exact numerics that the longitudinal conductance quantizes to |W_ε| e²/h and the Hall conductance to W_ε e²/h, where W_ε is the Floquet winding invariant tied to the quasienergy gap at ε = 0 or ε = Ω/2. Quantization is achieved only after summing over all Floquet sidebands. In the weak-coupling limit an analytic argument shows that the sideband contributions, including the signs of the edge-mode velocities, add to produce the exact quantized value predicted by the winding number.

What carries the argument

The Floquet winding invariant W_ε for a chosen quasienergy gap, which fixes the total conductance after the sideband sum is performed.

If this is right

Longitudinal conductance reaches exactly |W_ε| times e²/h.
Hall conductance reaches exactly W_ε times e²/h.
The sum rule holds for both gaps at ε = 0 and ε = Ω/2.
Convergence occurs rapidly over a wide range of parameters, making the quantization observable.
An analytic proof of the Hall sum rule exists in the weak-reservoir-coupling limit.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The sideband-sum requirement distinguishes Floquet transport from its static counterpart and may apply to other non-equilibrium topological settings.
The result points to a practical route for extracting winding numbers from mesoscopic conductance measurements in driven devices.
Similar sum rules could be tested in multi-terminal or higher-dimensional Floquet geometries.

Load-bearing premise

The quantization requires adding the conductance contributions from every Floquet sideband.

What would settle it

A numerical evaluation of the strip conductance that leaves out some sidebands and yields a value different from |W_ε| e²/h or W_ε e²/h would falsify the sum-rule claim.

Figures

Figures reproduced from arXiv: 2605.13066 by Abhishek Dhar, Manas Kulkarni, Rekha Kumari.

**Figure 2.** Figure 2: FIG. 2. Schematic diagram of the cylindrical setup. The [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Quasienergy spectrum (in units of Ω) of the Hamilto [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Schematic of the two-terminal transport setup in a [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. (a–c) Individual Floquet sideband contributions [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Zero-bias conductance as a function of the system–reservoir coupling [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗

**Figure 7.** Figure 7: summarizes the bulk and spatially resolved conductance properties obtained within the Floquet–NEGF formalism. Panel (a) shows the bulk longitudinal and transverse conductances as functions of the unbiased chemical potential µF for the Floquet topological phase characterized by (W0, Wπ) = (1, 1). We observe that both the longitudinal conductance G2,nL+nx (µF ) ≈ |Wϵ| and the transverse (Hall) conductance G… view at source ↗

**Figure 8.** Figure 8: FIG. 8. System setup: The system described by Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. (a) Comparison of the exact Floquet–NEGF Hall conductance (solid lines) with the weak-coupling (WC) approximation [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗

read the original abstract

We study quantum transport in a periodically driven (Floquet) topological system coupled to static fermionic reservoirs. Using the Floquet nonequilibrium Green's-function (NEGF) formalism we show, from exact numerics for a strip geometry, that the two-terminal (longitudinal) conductance is quantized as $|W_{\varepsilon}|\,e^2/h$, while the Hall (transverse) conductance is quantized as $W_{\varepsilon}\,e^2/h$, where $W_{\varepsilon}$ is the Floquet winding invariant associated with the quasienergy gap at $\varepsilon = 0$ or $\varepsilon = \Omega/2$. Quantization is achieved only after summing over the contribution of all Floquet sidebands. We provide an analytic understanding of this Floquet conductance sum rule, by considering the Hall conductance in the weak coupling limit. In that limit, we show that the Floquet Hall conductance gets contributions from the Floquet sidebands, which includes the signs of the velocities of the edge modes. Their sum yields exact quantization, as predicted by the Floquet sum rule. We find that in a wide range of parameter regime, the convergence is fast, making observation of the sum rule and Floquet winding numbers accessible to experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper shows that summing all Floquet sidebands restores exact quantization of both longitudinal and Hall conductances to the winding number, with solid numerics and a clean weak-coupling analytic explanation.

read the letter

The central result is that two-terminal conductance quantizes to |W_ε| e²/h and Hall conductance to W_ε e²/h once every sideband is included. The numerics on the strip geometry via Floquet NEGF make this concrete and show fast convergence over a wide parameter range. The analytic derivation for the Hall case in the weak-coupling limit explains why the sum works: each sideband contributes according to the sign of its edge-mode velocity, and they add to the exact quantized value predicted by the winding invariant. That part is straightforward and matches the numerics without extra fitting. The winding number itself is defined from the quasienergy gap in the usual way, independent of the transport calculation. The main soft spot is that the analytic sum rule is shown only in the weak-coupling regime; the numerics are presented as covering stronger coupling, but there is no general analytic proof supplied. No internal contradictions appear in the setup or the reported data. The citation pattern is standard for the subfield and does not rely on self-reinforcement. This work is aimed at people studying driven topological systems who need a measurable transport signature. Experimentalists should find the fast convergence useful. It is worth sending to peer review because the numerics are direct and the sum-rule claim is new relative to static cases.

Referee Report

0 major / 2 minor

Summary. The paper studies quantum transport in a periodically driven Floquet topological insulator coupled to static reservoirs. Using the Floquet NEGF formalism, exact numerics on a strip geometry demonstrate that the longitudinal two-terminal conductance is quantized as |W_ε| e²/h and the transverse Hall conductance as W_ε e²/h, with W_ε the Floquet winding invariant of the quasienergy gap at ε = 0 or ε = Ω/2. Quantization requires summing all Floquet sideband contributions; an analytic derivation of the Hall sum rule is given in the weak-coupling limit, showing that edge-mode velocity signs yield exact quantization, with numerics indicating rapid convergence in a broad parameter range.

Significance. If the central claims hold, the work supplies direct numerical evidence that Floquet winding numbers control measurable conductances once all sidebands are included, together with a clean analytic confirmation of the sum rule in the weak-coupling regime. The combination of exact strip-geometry numerics and parameter-free analytic insight strengthens the link between Floquet topology and transport observables and indicates experimental accessibility given the reported fast convergence.

minor comments (2)

[Abstract] The abstract states that quantization holds 'only after summing over the contribution of all Floquet sidebands'; a brief sentence in the introduction or §2 clarifying why single-sideband conductances deviate from quantization would improve readability for readers unfamiliar with Floquet transport.
[Weak-coupling analytic derivation] In the weak-coupling analytic section, the statement that 'their sum yields exact quantization' would benefit from an explicit reference to the velocity-sign contribution (e.g., Eq. (X) or the paragraph immediately following the derivation) to make the cancellation transparent.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive report, which accurately summarizes our results on quantized transport in Floquet topological insulators, and for recommending acceptance of the manuscript.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The central result follows from direct numerical evaluation of the Floquet NEGF conductance formulas on a finite strip, summed over all sidebands, and is compared to the independently defined winding number W_ε extracted from the bulk quasienergy spectrum. The analytic weak-coupling Hall derivation uses only the standard Landauer-Büttiker structure plus the velocity signs of the edge modes; neither step defines W_ε in terms of the conductance nor fits parameters to the target quantization. No self-citation is load-bearing for the quantization claim, and the winding invariant is introduced via its standard topological definition rather than by ansatz or renaming.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the validity of the Floquet NEGF formalism for open driven systems and on the independent definition of the winding invariant W_ε from the quasienergy spectrum.

axioms (1)

domain assumption Floquet NEGF formalism correctly captures transport in periodically driven systems coupled to static reservoirs
Invoked throughout the numerical and analytic sections as the computational framework.

pith-pipeline@v0.9.0 · 5526 in / 1285 out tokens · 45391 ms · 2026-05-14T02:20:48.064348+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages

[1]

We show that, in certain parameter regimes, the sum rule is even satisfied on including a small number of Floquet sidebands

We first consider the strip geometry and using the Floquet nonequilibrium Green’s function (NEGF) formalism [48], we demonstrate quantization of the two terminal conductance using the Floquet sum rules. We show that, in certain parameter regimes, the sum rule is even satisfied on including a small number of Floquet sidebands

work page
[2]

We show, again for the strip geometry, that the spatially resolved bond currents (summed over the Floquet sidebands) can be used to compute, in ad- dition to the two-terminal conductance, also the Hall conductance which encodes both the magni- tude and the sign of the Floquet winding invari- ants

work page
[3]

This result is valid both for the strip and cylindrical geometries

We analyze the dependence of both the two ter- minal and Hall conductance quantization on sys- tem size and system–reservoir coupling strength, and show that quantization emerges in the weak- coupling limit when the transverse system size is sufficiently large. This result is valid both for the strip and cylindrical geometries

work page
[4]

In the cylindrical geometry and in the weak cou- pling limit, we provide a microscopic interpretation of the Floquet sum rule and an analytic proof of the Hall conductance quantization. We show that sum- ming over Floquet sidebands in the weak-coupling steady state reconstructs the full spectral weight of chiral Floquet edge modes distributed over Floquet...

work page
[5]

Floquet sum rules

Two-terminal conductance For the transport setup described above, the steady- state current can be expressed in terms of Floquet Green’s functions using the equation of motion approach for the periodically driven system and reservoir operators (see Appendix D for details). Following standard NEGF methods, the current (recalling that we are using units wit...

work page
[6]

4), in addition to the two-terminal conductance, we now compute the lo- cal bond currents along the longitudinal (x) and trans- verse (y) directions of the lattice

Longitudinal and transverse bond currents In the strip geometry (recall Fig. 4), in addition to the two-terminal conductance, we now compute the lo- cal bond currents along the longitudinal (x) and trans- verse (y) directions of the lattice. This will help to bet- ter characterize the spatial structure of transport. For a time-periodic Hamiltonian satisfy...

work page
[7]

In this case only the two chiral modes, localized in the left and right ends, contribute to theαsum

First consider the case whenµ F is in a topologi- cal gap. In this case only the two chiral modes, localized in the left and right ends, contribute to theαsum. For the left mode,|ϕ (n) α (xL)|2 is signif- icant while|ϕ (n) α (xR)|2 is small and vice-versa for the right edge mode. Hencew (n) α is negligible for 12 the right edge mode. For the left mode the...

work page
[8]

We note that in addition to the quantization of the summed conductance our weak-coupling approach also allows us to compute the contribution of each side-band to the total conductance and this is given by Eq. (65)

work page
[9]

In this case the weights,|ϕ α(Xλ)|2, at both left and right ends are small but comparable and so we getw (n) α <1

Next we consider the case whereµ F lies in the bulk bands. In this case the weights,|ϕ α(Xλ)|2, at both left and right ends are small but comparable and so we getw (n) α <1. Secondly there are a large number ofαmodes which will contribute to the sum and hence we do not get any quantization. This completes our proof of the Floquet sum rule and quantization...

work page 2022
[10]

Bukov, L

M. Bukov, L. D’Alessio, and A. Polkovnikov, Universal high-frequency behavior of periodically driven systems, Advances in Physics64, 139 (2015)

work page 2015
[11]

Goldman and J

N. Goldman and J. Dalibard, Periodically driven quan- tum systems: Effective hamiltonians and engineered gauge fields, Phys. Rev. X4, 031027 (2014)

work page 2014
[12]

Eckardt, Atomic quantum gases in periodically driven optical lattices, Rev

A. Eckardt, Atomic quantum gases in periodically driven optical lattices, Rev. Mod. Phys.89, 011004 (2017)

work page 2017
[13]

Harper, R

F. Harper, R. Roy, M. S. Rudner, and S. L. Sondhi, Topology and broken symmetry in floquet systems, An- nual Review of Condensed Matter Physics11, 345 (2020)

work page 2020
[14]

Oka and S

T. Oka and S. Kitamura, Floquet engineering of quantum materials, Annual Review of Condensed Matter Physics 10, 387 (2019)

work page 2019
[15]

Cayssol, B

J. Cayssol, B. D´ ora, F. Simon, and R. Moessner, Flo- quet topological insulators, physica status solidi (RRL) – Rapid Research Letters7, 101 (2013)

work page 2013
[16]

Rodriguez-Vega, A

M. Rodriguez-Vega, A. Kumar, and B. Seradjeh, Higher- order floquet topological phases with corner and bulk bound states, Phys. Rev. B100, 085138 (2019)

work page 2019
[17]

Morimoto, H

T. Morimoto, H. C. Po, and A. Vishwanath, Floquet topological phases protected by time glide symmetry, Phys. Rev. B95, 195155 (2017)

work page 2017
[18]

Chaudhary, A

S. Chaudhary, A. Haim, Y. Peng, and G. Refael, Phonon- induced floquet topological phases protected by space- time symmetries, Phys. Rev. Res.2, 043431 (2020)

work page 2020
[19]

Jangjan, L

M. Jangjan, L. E. F. Foa Torres, and M. V. Hosseini, Floquet topological phase transitions in a periodically quenched dimer, Phys. Rev. B106, 224306 (2022)

work page 2022
[20]

Kundu, H

A. Kundu, H. A. Fertig, and B. Seradjeh, Effective theory of floquet topological transitions, Phys. Rev. Lett.113, 236803 (2014)

work page 2014
[21]

Potirniche, A

I.-D. Potirniche, A. C. Potter, M. Schleier-Smith, A. Vishwanath, and N. Y. Yao, Floquet symmetry- protected topological phases in cold-atom systems, Phys. Rev. Lett.119, 123601 (2017)

work page 2017
[22]

Bukov, L

M. Bukov, L. D’Alessio, and A. Polkovnikov, Universal high-frequency behavior of periodically driven systems: from dynamical stabilization to floquet engineering, Ad- vances in Physics64, 139 (2015)

work page 2015
[23]

Kumari, G

R. Kumari, G. Dixit, and A. Kundu, Valley filtering and valley valves in irradiated pristine graphene, Phys. Rev. B111, 155421 (2025)

work page 2025
[24]

Kumari, B

R. Kumari, B. Seradjeh, and A. Kundu, Josephson- current signatures of unpaired floquet majorana fermions, Phys. Rev. Lett.133, 196601 (2024)

work page 2024
[25]

Mondal, R

D. Mondal, R. Kumari, T. Nag, and A. Saha, Transport signatures of single and multiple floquet majorana modes in a one-dimensional rashba nanowire and shiba chain, Phys. Rev. B111, 235441 (2025)

work page 2025
[26]

K. Roy, L. Kalita, B. Tanatar, and S. Basu, Floquet gen- eration of hybrid-order topology andZ 2-like bipolar lo- calization (2026), arXiv:2603.21954 [cond-mat.mes-hall]

work page arXiv 2026
[27]

L. Du, P. D. Schnase, A. D. Barr, A. R. Barr, and G. A. Fiete, Floquet topological transitions in extended kane- mele models with disorder, Phys. Rev. B98, 054203 (2018)

work page 2018
[28]

A. Raj, S. Chaudhary, M. Rodriguez-Vega, M. G. Vergniory, R. Ilan, and G. A. Fiete, Light-induced pseudomagnetic fields in three-dimensional topological semimetals, Phys. Rev. B113, 155117 (2026)

work page 2026
[29]

M. S. Rudner, N. H. Lindner, E. Berg, and M. Levin, Anomalous edge states and the bulk-edge correspondence for periodically driven two-dimensional systems, Phys. Rev. X3, 031005 (2013)

work page 2013
[30]

F. N. ¨Unal, A. Eckardt, and R.-J. Slager, Hopf character- ization of two-dimensional floquet topological insulators, Physical Review Research1, 022003 (2019)

work page 2019
[31]

Nathan and M

F. Nathan and M. S. Rudner, Topological singularities and the general classification of floquet–bloch systems, New J. Phys.17, 125014 (2015)

work page 2015
[32]

Titum, E

P. Titum, E. Berg, M. S. Rudner, G. Refael, and N. H. Lindner, Anomalous floquet–anderson insulator as a nonadiabatic quantized charge pump, Phys. Rev. X6, 021013 (2016)

work page 2016
[33]

Quelle, C

A. Quelle, C. Weitenberg, K. Sengstock, and C. M. Smith, Driving protocol for a floquet topological phase without static counterpart, New Journal of Physics19, 113010 (2017)

work page 2017
[34]

M. S. Rudner and N. H. Lindner, Band structure engi- neering and non-equilibrium dynamics in floquet topo- logical insulators, Nat. Rev. Phys.2, 229 (2020)

work page 2020
[35]

Titum, N

P. Titum, N. H. Lindner, M. C. Rechtsman, and G. Refael, Disorder-induced floquet topological insula- tors, Phys. Rev. Lett.114, 056801 (2015)

work page 2015
[36]

Mukherjee, A

S. Mukherjee, A. Spracklen, M. Valiente, E. Andersson, P. ¨Ohberg, N. Goldman, and R. R. Thomson, Experimen- tal observation of anomalous topological edge modes in a slowly driven photonic lattice, Nature Communications 8, 13918 (2017)

work page 2017
[37]

Ozawa, H

T. Ozawa, H. M. Price, A. Amo, N. Goldman, M. Hafezi, L. Lu, M. C. Rechtsman, D. Schuster, J. Simon, O. Zil- berberg, and I. Carusotto, Topological photonics, Rev. Mod. Phys.91, 015006 (2019)

work page 2019
[38]

F. N. ¨Unal, A. Eckardt, and R.-J. Slager, Hopf character- ization of two-dimensional floquet topological insulators, Phys. Rev. Res.1, 022003 (2019)

work page 2019
[39]

von Klitzing, G

K. von Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure con- stant based on quantized hall resistance, Phys. Rev. Lett. 45, 494 (1980)

work page 1980
[40]

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized hall conductance in a two- dimensional periodic potential, Phys. Rev. Lett.49, 405 (1982)

work page 1982
[41]

B¨ uttiker, Absence of backscattering in the quantum hall effect in multiprobe conductors, Phys

M. B¨ uttiker, Absence of backscattering in the quantum hall effect in multiprobe conductors, Phys. Rev. B38, 9375 (1988)

work page 1988
[42]

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

work page 2010
[43]

B. A. Bernevig and S.-C. Zhang, Quantum spin hall ef- fect, Phys. Rev. Lett.96, 106802 (2006)

work page 2006
[44]

K¨ onig, S

M. K¨ onig, S. Wiedmann, C. Br¨ une, and et al., Quantum spin hall insulator state in hgte quantum wells, Science 318, 766 (2007)

work page 2007
[45]

Ozawa and B

T. Ozawa and B. Mera, Relations between topology and the quantum metric for chern insulators, Phys. Rev. B 104, 045103 (2021)

work page 2021
[46]

B. Mera, K. Sacha, and Y. Omar, Topologically protected quantization of work, Phys. Rev. Lett.123, 020601 (2019). 20

work page 2019
[47]

Sinha, R

S. Sinha, R. Kumari, J. M. Bhat, A. Dhar, and R. Shankar, Proximity effects and a topological invari- ant in a chern insulator connected to leads (2025), arXiv:2512.12746 [cond-mat.mes-hall]

work page arXiv 2025
[48]

Majeed Bhat, R

J. Majeed Bhat, R. Shankar, and A. Dhar, Quantized two terminal conductance, edge states and current patterns in an open geometry 2-dimensional chern insulator, Journal of Physics: Condensed Matter37, 275601 (2025)

work page 2025
[49]

Kundu and B

A. Kundu and B. Seradjeh, Transport signatures of flo- quet majorana fermions in driven topological supercon- ductors, Phys. Rev. Lett.111, 136402 (2013)

work page 2013
[50]

L. E. F. Foa Torres, P. M. Perez-Piskunow, C. A. Bal- seiro, and G. Usaj, Multiterminal conductance of a flo- quet topological insulator, Phys. Rev. Lett.113, 266801 (2014)

work page 2014
[51]

I. Esin, M. S. Rudner, G. Refael, and N. H. Lindner, Quantized transport and steady states of floquet topo- logical insulators, Phys. Rev. B97, 245401 (2018)

work page 2018
[52]

Dehghani, T

H. Dehghani, T. Oka, and A. Mitra, Out-of-equilibrium electrons and the hall conductance of a floquet topologi- cal insulator, Phys. Rev. B91, 155422 (2015)

work page 2015
[53]

Farrell and T

A. Farrell and T. Pereg-Barnea, Edge-state transport in floquet topological insulators, Phys. Rev. B93, 045121 (2016)

work page 2016
[54]

H. H. Yap, L. Zhou, J.-S. Wang, and J. Gong, Com- putational study of the two-terminal transport of floquet quantum hall insulators, Phys. Rev. B96, 165443 (2017)

work page 2017
[55]

Bajpai, M

U. Bajpai, M. J. H. Ku, and B. K. Nikoli´ c, Robustness of quantized transport through edge states of finite length, Phys. Rev. Res.2, 033438 (2020)

work page 2020
[56]

Zhang, F

R. Zhang, F. Nathan, N. H. Lindner, and M. S. Rud- ner, Achieving quantized transport in floquet topological insulators via energy filters, Phys. Rev. B110, 075428 (2024)

work page 2024
[57]

Kohler, J

S. Kohler, J. Lehmann, and P. H¨ anggi, Driven quantum transport on the nanoscale, Phys. Rep.406, 379 (2005)

work page 2005
[58]

Iadecola, T

T. Iadecola, T. Neupert, and C. Chamon, Occupation of topological floquet bands in open systems, Phys. Rev. B 91, 235133 (2015)

work page 2015
[59]

Matsyshyn, J

O. Matsyshyn, J. C. W. Song, I. Sodemann Villadiego, and L.-k. Shi, Fermi-dirac staircase occupation of flo- quet bands and current rectification, Phys. Rev. B107, 195135 (2023)

work page 2023
[60]

Peralta Gavensky, G

L. Peralta Gavensky, G. Usaj, and N. Goldman, Stˇ reda formula for floquet systems: Topological invariants and quantized anomalies from ces` aro summation, Phys. Rev. X15, 031067 (2025)

work page 2025
[61]

Seshadri and D

R. Seshadri and D. Sen, Floquet topological phases and bulk–boundary correspondence in periodically driven systems, Phys. Rev. B106, 245401 (2022)

work page 2022
[62]

M. S. Rudner and N. H. Lindner, Floquet topo- logical insulators: from band structure engineering to novel non-equilibrium quantum phenomena (2019), arXiv:1909.02008 [cond-mat.mes-hall]

work page arXiv 2019
[63]

Mondal, R

D. Mondal, R. Kumari, T. Nag, and A. Saha, Transport signatures of single and multiple floquet majorana modes in a rashba nanowire and shiba chain, Phys. Rev. B111, 235441 (2025)

work page 2025
[64]

L.-k. Shi, O. Matsyshyn, J. C. W. Song, and I. Sode- mann Villadiego, Floquet fermi liquid, Phys. Rev. Lett. 132, 146402 (2024)

work page 2024
[65]

Rodriguez-Vega, M

M. Rodriguez-Vega, M. Lentz, and B. Seradjeh, Flo- quet perturbation theory: formalism and application to low-frequency limit, New Journal of Physics20, 093022 (2018)

work page 2018
[66]

Sambe, Steady states and quasienergies of a quantum- mechanical system in an oscillating field, Phys

H. Sambe, Steady states and quasienergies of a quantum- mechanical system in an oscillating field, Phys. Rev. A 7, 2203 (1973)

work page 1973
[67]

Privitera, A

L. Privitera, A. Russomanno, R. Citro, and G. E. San- toro, Nonadiabatic breaking of topological pumping, Phys. Rev. Lett.120, 106601 (2018)

work page 2018
[68]

Shih and Q

W.-K. Shih and Q. Niu, Nonadiabatic particle transport in a one-dimensional electron system, Phys. Rev. B50, 11902 (1994)

work page 1994
[69]

Shtoff, Y

A. Shtoff, Y. Dmitriev, and M. R´ erat, Quasienergy derivative method for the optical susceptibilities of molecules in the floquet theory, Optics and Spectroscopy 99, 545 (2005)

work page 2005