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REVIEW 1 major objections 6 minor 136 references

Valley Gapless Semiconductor: Models and Applications

T0 review · 1 major / 6 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read This paper proposes the valley gapless semiconductor, a phase that locks the carrier type to the valley index, and shows that a single gate voltage can switch a valley filter between fully valley-polarized electron and hole transmission.

desk verdict The VGS phase and its honeycomb realization are worth taking seriously, but the paper's headline transport claim—the sharp P flip at Ug=0—is an unstated energy-convention artifact and needs to be re-examined before publication. read the letter →

arxiv 2502.02057 v3 pith:O7BONGEC submitted 2025-02-04 cond-mat.mes-hall

Kok Wai Lee , Pei-Hao Fu , Jun-Feng Liu , Ching Hua Lee , Yee Sin Ang This is my paper · ORCID
classification cond-mat.mes-hall
keywords valleygaplesssemiconductorvalleytronicspolarizationHaldanemodelmodifiedfilterDiracHamiltonianhoneycomblattice
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

The paper introduces and studies the valley gapless semiconductor (VGS), a phase in which the conduction-band edge of one valley touches the valence-band edge of the other valley at the Fermi level. In this phase the carrier type and the valley index are locked together: electrons are supplied by one valley and holes by the other, so a gate voltage that selects electrons or holes also selects a valley. The authors show that in a two-band Dirac model this locking occurs at the ratio $\Delta_1/\Delta_2 = 1$, and in a honeycomb lattice when the Haldane and modified Haldane hopping strengths are equal, $t_H = t_{MH}$. For a gate-controlled device they compute the valley-resolved conductance and find that the valley polarization efficiency takes $P = +1$ for positive gate voltage and $P = -1$ for negative gate voltage, flipping sharply at $U_g = 0$. The proposal matters because it offers an all-electrical route to valley-polarized currents, without magnetic fields or optical pumping.

What carries the argument

The central object is the two-band Dirac Hamiltonian $H_\eta(k) = \eta\hbar v_{Fx} k_x \tau_x + \hbar v_{Fy} k_y \tau_y + \Delta_1 \tau_z - \eta \Delta_2 \tau_0$, whose two competing terms set the phase. The mechanism is the competition between $\Delta_1$, which opens the same-sign gap in both valleys, and $\Delta_2$, which shifts the Dirac points of the two valleys in opposite energy directions; when the two are equal, the conduction band of one valley meets the valence band of the other at the Fermi level, making the carrier type valley-locked. In the honeycomb lattice the same competition is carried by the Haldane term (time-reversal breaking, $t_H$) and the modified Haldane term (inversion- and time-reversal breaking, $t_{MH}$), with $t_H = t_{MH}$ the VGS condition. The transport calculation then uses wavefunction matching of the Dirac spinors across the lead, gated VGS, and drain regions to obtain the valley-dependent transmission amplitude $t_\eta$ and conductance $G_\eta$.

What would settle it

Measure the valley polarization efficiency $P$ of a gate-controlled VGS device as a function of $U_g$ at low temperature: the central claim predicts a sharp transition from $P = -1$ to $P = +1$ at $U_g = 0$ with $|P| = 1$ on both sides, so a rounded step, plateaus with $|P| < 1$, or a window where both valleys transmit would contradict it. In parallel, a scattering calculation that includes a short-range impurity potential coupling $K$ and $K'$ should show how much intervalley scattering is required to destroy the polarization flip.

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Extended reading notes

Core claim

At the heart of the paper is the two-band valley-dependent Dirac Hamiltonian $H_\eta(k) = \eta\hbar v_{Fx} k_x \tau_x + \hbar v_{Fy} k_y \tau_y + \Delta_1 \tau_z - \eta \Delta_2 \tau_0$, where $\Delta_1$ is a Dirac mass that opens an intravalley gap and $\Delta_2$ is a valley-dependent scalar potential that shifts the two Dirac cones in opposite directions. The VGS is the critical line $\Delta_1/\Delta_2 = 1$ (and the mirror line $-1$ for the opposite sign of $\Delta_2$), where the intervalley gap $\Delta_{\mathrm{inter}} = 2(|\Delta_1| - \eta \Delta_2)$ vanishes while the intravalley gap $2|\Delta_1|$ remains nonzero. In the honeycomb realization the same phase appears when $t_H = t_{MH}$, with $t_H$ the Haldane next-nearest-neighbour hopping and $t_{MH}$ the modified Haldane term. The paper's central transport claim is that in a source-VGS-drain junction with a top gate, the valley-dependent transmission $T_\eta$ vanishes inside a gate-voltage window that is valley-dependent, so for $U_g < 0$ only the $\eta = -1$ valley transmits and for $U_g > 0$ only the $\eta = +1$ valley transmits; the valley polarization efficiency $P = (G_+ - G_-)/(G_+ + G_-)$ therefore takes the values $-1$ and $+1$ and flips sharply at $U_g = 0$.

Load-bearing premise

The load-bearing premise is that electrons never scatter between the two valleys while passing through the device, so the valley index is conserved and the two valley conductances can simply be added; the paper supports this with the large momentum separation between valleys and smooth gate potentials, but gives no quantitative disorder estimate, so any appreciable intervalley scattering would wash out the perfect filtering and the sharp polarization flip at zero gate voltage.

Editorial extensions

If this is right

  • A single gate voltage can switch a device between fully valley-polarized electron transport and fully valley-polarized hole transport, with the sign of the polarization set by the sign of the gate voltage.
  • The VGS phase can be realized in a honeycomb lattice by tuning the modified Haldane hopping to equal the Haldane hopping, a condition already within reach of optical-lattice, photonic-crystal, and topolectrical-circuit realizations.
  • In TMDC monolayers with spin-orbit coupling of strength $\lambda_{\mathrm{SOC}}$, the VGS appears in one spin subband when the Semenoff mass vanishes, because both $\Delta_1$ and $\Delta_2$ equal $\lambda_{\mathrm{SOC}}/2$.
  • The predicted $P = \pm 1$ plateaus can be probed by helicity-resolved photoluminescence, which the paper identifies as the direct experimental signature.

Reading between the lines

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

  • Editorial inference: the same ratio condition $\Delta_1/\Delta_2 = 1$ suggests that any knob that tunes the two terms independently, such as strain, Floquet driving, or layer stacking, could sweep the system through the VGS line and act as an electrically controllable valve, since the sharp polarization flip appears only at the ratio.
  • Editorial inference: the perfect $P = \pm 1$ result is computed from independent valley conductances, so in a real sample short-range disorder or atomically sharp gate edges, which couple valleys, would likely round the plateaus unless the interfaces are made smooth on the lattice scale; quantifying this rounding is a natural next calculation.
  • Editorial inference: the sharp sign flip at $U_g = 0$ could be used as a binary valley switch for logic or memory, but the paper does not quantify temperature, noise, or power dissipation, which would determine whether the effect survives in a practical device.
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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 / 6 minor

Summary. The paper proposes and analyzes the 'valley gapless semiconductor' (VGS), defined in the two-band Dirac Hamiltonian of Eq. (1) by the condition Δ1/Δ2 = ±1, where the Dirac mass Δ1 and a valley-dependent scalar potential Δ2 align the conduction-band edge of one valley with the valence-band edge of the other. The eigenvalues (Eq. (3)) give a clean Δ1–Δ2 phase diagram: indirect-gap semiconductor for |Δ1/Δ2| > 1, metal for |Δ1/Δ2| < 1, and VGS at |Δ1/Δ2| = 1, with valley-polarized carriers in an energy window of width 4|Δ1| centered on the touching point. Section III realizes the VGS in a honeycomb lattice with competing Haldane (tH) and modified Haldane (tMH) hoppings, with the VGS at tMH = tH, and the transport section (Sec. IV) studies a gate-controlled barrier between normal leads, computing valley-resolved transmission, conductance, and polarization P = (G+ − G−)/(G+ + G−) by closed-form mode matching (Appendices A–C). The central claim is that the VGS-based filter produces full valley polarization that flips sharply from P = −1 to P = +1 at Ug = 0, enabling all-electrical valley control.

Significance. The two-band analysis is sound and self-contained: the phase diagram and the VGS condition follow directly from the eigenvalues with no fitting, the honeycomb realization maps onto the continuum model with a single tunable ratio tMH/tH, and the closed-form scattering coefficients in Appendix C make the predicted P = ±1 windows analytically checkable and falsifiable. The conceptual message — that a VGS couples carrier type to valley index and thereby allows electrical switching of valley polarization — is well grounded in the band structure and is of genuine interest for valleytronics, and the paper appropriately distinguishes its proposal from the experimentally observed valley-polarized quantum Hall phase of Pb1−xSnxSe. The main weakness is that the transport section's headline result (the flip at Ug = 0) is tied to an unstated energy reference; once that is fixed, the device prediction is meaningful. The contribution is incremental relative to the authors' earlier VGS proposal (ref. [76]) but supplies a concrete lattice model and a device-level analysis that the earlier work lacked.

major comments (1)
  1. [Sec. IV (Eqs. (12)–(15)) and Appendix B (Eq. (B2))] The central device claim—full valley polarization with a sharp flip of P at Ug = 0 for the VGS—rests on an energy reference that is never stated. From Z±(x) = E + U(x) + ηΔ2(x) ± Δ1(x) (main text, paragraph containing Eqs. (12)–(13); Appendix B, Eq. (B2)), valley η has a propagating mode in the central region only when |E + Ug + ηΔ2| > Δ1, so the blocking windows are −(E + ηΔ2 + Δ1) < Ug < −(E + ηΔ2 − Δ1). The text instead states them as −(ηΔ2 + Δ1) < Ug < −(ηΔ2 − Δ1), and later quotes P = −1 (+1) for −(Δ2 + Δ1) < Ug < Δ1 − Δ2 (Δ2 − Δ1 < Ug < Δ2 + Δ1), with the flip at Ug = 0; all of these omit E and are correct only for E = 0. Since Sec. IV fixes EF = Ul + E = 1, the choice E = 0 corresponds to the unstated lead potential Ul = 1. With the equally natural choice Ul = 0 (E = EF = 1) and the stated Δ1 = Δ2 = 0.5EF, the same condition gives windows −2 < Ug < −1 (η = + blocked) and −1 < Ug < 0 (η = − blocked), i.e., full polarization of the opposite sign, located at negative Ug, and no fully polarized window for Ug > 0. The headline 'sharp flip at Ug = 0' is therefore a consequence of the chosen zero of energy rather than a gauge-invariant prediction; in general the flip occurs at E + Ug = 0 (equivalently Ug = Ul − EF), the point at which carriers in the barrier switch between electron- and hole-like. This affects the abstract, the mechanism statement in Fig. 3(b) ('For a positive (negative) gate voltage, only the electrons (holes) in the η = +1 (−1) valley are transmitted'), and the conclusion. The revision should state E (or Ul) explicitly, write the windows with E included, and rephrase the flipping condition accordingly.
minor comments (6)
  1. [Sec. III (Eq. (9) paragraph)] The sentence stating that 'in TMDC monolayers such as MoS2, the VGS is expected in one of the spin subbands' overstates the case: Eq. (9) realizes the VGS only for mS = 0, whereas monolayer MoS2 has a large Semenoff mass (mS ≈ 0.8 eV) that puts Δ1/Δ2 ≈ 1 ± 2mS/λSOC, far from the VGS condition; the claim should be reframed as an engineering scenario (tuning mS toward zero) rather than an expectation for intrinsic MoS2.
  2. [Sec. IV (Eq. (13) area)] The incident-angle definition is garbled: the text reads θ0 = arcsin(ℏvF ky / E_F^{1/2}), whereas Appendix C (Eq. (C4) and its context) implies sin θ0 = ℏvFy ky / EF; the formula should be corrected.
  3. [Sec. IV (Eq. (10))] The potential profile U(x) = UlΘ(−x) + UgΘ(dx − x²) + UlΘ(x − d) and the analogous Θ(dx − x²) in Δ1,2(x) use a factor that appears to be a typo for the rectangular-barrier form Θ(x)Θ(d − x); as written the barrier region is not clearly defined and the setup is not reproducible.
  4. [Sec. IV (intervalley-scattering paragraph)] The assumption that intervalley scattering is negligible is supported only by a qualitative momentum-separation argument and a reference to smoother-potential results in ref. [74]; a quantitative estimate (e.g., the intervalley scattering amplitude or mean free path relative to the valley-selective window width Δ1 and the device length d) would substantially strengthen the device claim.
  5. [Sec. IV (parameter paragraph)] The statements that the results are 'qualitatively similar for different combinations of the parameters' and 'remain valid under the anisotropic case' are asserted without demonstration; a supporting example or argument would make the robustness claim checkable.
  6. [Sec. IV (P-window text after Eq. (15))] For the semiconducting phase (Δ2 < Δ1), the stated full-polarization windows −(Δ2+Δ1) < Ug < Δ1−Δ2 (P = −1) and Δ2−Δ1 < Ug < Δ2+Δ1 (P = +1) include the interval |Ug| < Δ1 − Δ2 in which both valleys are blocked (G = 0) and P is ill-defined, as the red dashed line in Fig. 3(e) itself indicates; the windows should be restricted to −(Δ2+Δ1) < Ug < −(Δ1−Δ2) and Δ1−Δ2 < Ug < Δ2+Δ1.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the VGS condition and the transport P=±1 response are derived from the model Hamiltonian rather than fitted or defined into existence; the only self-reference is background attribution.

full rationale

The derivation chain is self-contained. The VGS phase condition Δ1/Δ2=1 is obtained algebraically from the eigenvalues E_{η,±}(k)=−ηΔ2±sqrt((ℏvF|k|)^2+Δ1^2) and the definition Δ_inter=2(|Δ1|−ηΔ2); setting Δ_inter=0 gives the VGS condition, so the phase boundary is a consequence of the model, not an input. The honeycomb-lattice realization maps Δ1=tH sinφ and Δ2=tMH sinφ′ and then derives tH=tMH from the same eigenvalue condition; no parameter is fitted to the target phase. The transport calculation is equally direct: valley-dependent transmission Tη, conductance Gη, and polarization P are obtained by wavefunction matching in Appendices A–C, with Z±(x)=E+U(x)+ηΔ2(x)±Δ1(x). The reported blocking windows and the P=+1/−1 response follow from the band structure and the gate potential, not from any fitted quantity. The paper does cite its own earlier VGS concept paper (ref. [76], with overlapping authorship), but that citation is background attribution rather than load-bearing evidence: none of the derivations in Sections II–IV require a theorem or result imported from [76]. The intervalley-scattering-negligible assumption is a stated physical approximation supported by the large momentum separation between valleys and by prior smoother-potential studies; even if it is a weakness, it is an assumption, not a circular reduction. A separate correctness concern is that the blocking windows in Sec. IV omit the incident energy E, so the sharp flip at Ug=0 corresponds to E=0 (i.e., Ul=EF); with Ul=0 the flip would move to Ug=−EF. This is an energy-reference ambiguity and a correctness risk, but it is not circularity because no prediction is being made equal to its own input by construction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central derivation uses a two-band Dirac Hamiltonian with a valley-dependent scalar potential, adds no new particle or force, and has no fitted data. The load-bearing assumptions are the neglect of intervalley scattering, the smooth-interface condition, a specific energy-scale convention for the transport setup, and the mapping to TMDC monolayers with mS=0. These are the places where the device claim could fail.

free parameters (4)
  • Δ1 (Dirac mass in the device) = 0.5 EF
    Chosen for the transport calculation; the paper asserts the qualitative results are parameter-independent but shows no sweep.
  • Δ2/Δ1 ratio = 0.5, 1.0, 1.5 (three phases)
    These represent the indirect-gap semiconductor, VGS, and metal phases; only the ratio matters analytically.
  • kF d (central region length) = 20
    Sets the barrier length and controls Fabry-Perot oscillations in the conductance; fixed in all device results.
  • tH/t (Haldane hopping in honeycomb band plots) = 0.1
    Energy unit for the illustrative band structures in Fig. 2; the phase boundaries do not depend on it.
assumptions (5)
  • domain assumption Intervalley interaction is negligible, so the Hamiltonian is block-diagonal in valley index.
    Stated in Sec. II after Eq. (1): 'Here, we assume that the intervalley interaction is negligible.' Load-bearing for the independent valley conductances in Sec. IV.
  • domain assumption Interfaces are smooth on the atomic scale, so intervalley scattering at the potential steps is negligible.
    Sec. IV uses the de Broglie wavelength argument (about 100 nm versus a 2.46 Å lattice constant) and cites ref. [74] for smoother potentials; no quantitative disorder or interface calculation is given.
  • domain assumption The leads are described by the same massless Dirac Hamiltonian with a constant potential Ul, and the incident energy E is measured relative to the Fermi level such that E=0 and EF=Ul.
    Sec. IV and Appendix A; the paper never states Ul, but the gap windows in the text and the symmetry of Fig. 3(e) only follow from the E=0 convention.
  • domain assumption The TMDC low-energy model of ref. [38] is valid, including Δ1=Δ2 for each spin subband.
    Sec. III, Eq. (9); the VGS-in-one-spin-subband statement requires mS=0, which is not stated when the text mentions MoS2.
  • domain assumption The two-band Dirac description captures the band structure near the valley points.
    Secs. II and III; standard low-energy approximation that ignores trigonal warping and higher-order terms.

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Cite this review

Pith. "Pith review of Valley Gapless Semiconductor: Models and Applications." pith.science (2026). https://pith.science/paper/O7BONGEC

@misc{pith2026250202057,
  author       = {Pith},
  title        = {Pith review of: Valley Gapless Semiconductor: Models and Applications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O7BONGEC}},
  note         = {Machine review of arXiv:2502.02057}
}
read the original abstract

The emerging field of valleytronics harnesses the valley degree of freedom of electrons, akin to how electronic and spintronic devices utilize the charge and spin degrees of freedom of electrons respectively. The engineering of valleytronic devices typically relies on the coupling between valley and other degrees of freedom such as spin, giving rise to valley-spintronics where an external magnetic field manipulates the information stored in valleys. Here, the valley gapless semiconductor is proposed as a potential electrically controlled valleytronic platform because the valley degree of freedom is coupled to the carrier type, i.e., electrons and holes. The valley degree of freedom can be electrically controlled by tuning the carrier type via the device gate voltage. We demonstrate the proposal for realizing a valley gapless semiconductor in the honeycomb lattice with the Haldane and modified Haldane models. The system's valley-carrier coupling is further studied for its transport properties in an all-electrically controlled valley filter device setting. Our work highlights the significance of the valley gapless semiconductor for valleytronic devices.

Figures

Figures reproduced from arXiv: 2502.02057 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic phase diagram of the system in the ∆ [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Schematic of the Haldane ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Schematic of the gate-controlled VGS-based valley filter where the gate voltage, [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

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Works this paper leans on

136 extracted references · 71 canonical work pages

  1. [76]

    Rycerz, J

    A. Rycerz, J. Tworzyd lo, and C. Beenakker, Valley filter and valley valve in graphene, Nature Phys3, 172 (2007)

    work page 2007

  2. [1]

    When ∆ 1 ̸= 0, the Dirac points are destroyed and the band structures illustrated in Fig

    (3) For ∆1 = ∆2 = 0, the system is gapless which is known as a Dirac semimetal, supporting two Dirac points lo- calized at the same energy. When ∆ 1 ̸= 0, the Dirac points are destroyed and the band structures illustrated in Fig. 1 reveal an intravalley gap, denoted as ∆ intra, which represents the energy difference between the con- duction and valence ba...

  3. [2]

    Y. Liu, Y. Gao, S. Zhang, J. He, J. Yu, and Z. Liu, Val- leytronics in transition metal dichalcogenides materials, Nano Res. 12, 2695 (2019)

    2019

  4. [3]

    Zheng, Y.-F

    J.-D. Zheng, Y.-F. Zhao, Y.-F. Tan, Z. Guan, N. Zhong, F.-Y. Yue, P.-H. Xiang, and C.-G. Duan, Coupling of ferroelectric and valley properties in 2D materials, J. Appl. Phys. 132, 120902 (2022)

    2022

  5. [4]

    H. Yu, X. Cui, X. Xu, and W. Yao, Valley excitons in two-dimensional semiconductors, Natl. Sci. Rev. 2, 57 (2015)

    2015

  6. [5]

    J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Valleytronics in 2D materials, Nat Rev Mater 1, 16055 (2016)

    2016

  7. [6]

    C. Luo, Z. Huang, H. Qiao, X. Qi, and X. Peng, Val- leytronics in two-dimensional magnetic materials, J. Phys. Mater. 7, 022006 (2024)

    2024

  8. [7]

    X. Xu, W. Yao, D. Xiao, and T. F. Heinz, Spin and pseudospins in layered transition metal dichalcogenides, Nature Phys 10, 343 (2014)

    2014

Show all 136 references
  1. [8]

    Tyulnev, ´A

    I. Tyulnev, ´A. Jim´ enez-Gal´ an, J. Poborska, L. Vamos, P. S. J. Russell, F. Tani, O. Smirnova, M. Ivanov, R. E. Silva, and J. Biegert, Valleytronics in bulk MoS2 with a topologic optical field, Nature 628, 746 (2024)

    2024

  2. [9]

    S. Yang, H. Long, W. Chen, B. Sa, Z. Guo, J. Zheng, J. Pei, H. Zhan, and Y. Lu, Valleytronics Meets Strain- tronics: Valley Fine Structure Engineering of 2D Tran- sition Metal Dichalcogenides, Adv. Opt. Mater. 12, 2302900 (2024)

    2024

  3. [10]

    Huang, K

    K. Huang, K. Samanta, D.-F. Shao, and E. Y. Tsymbal, Two-Dimensional Nonvolatile Valley Spin Valve, ACS Nano 19, 3448 (2025)

    2025

  4. [11]

    A. R. Nirjhar and S. Ahmed, Magnetic Proximity- Induced Colossal Valley Splitting in WTe 2 for Room Temperature Valleytronics, ACS Appl. Electron. Mater. 7, 2012 (2025)

    2025

  5. [12]

    S.-D. Guo, P. Li, and G. Wang, First-principles calcu- lations study of valley polarization in antiferromagnetic bilayer systems, Phys. Rev. B 111, L140404 (2025)

    2025

  6. [13]

    Jiang, Y

    H. Jiang, Y. Zhang, L. An, Q. Tan, X. Dai, Y. Chen, W. Chen, H. Cai, J. Fu, J. Z´ u˜ niga-P´ erez,et al., Chi- ral light detection with centrosymmetric-metamaterial- assisted valleytronics, Nat. Mater. , 1 (2025)

    2025

  7. [14]

    Shen, J.-D

    Y.-H. Shen, J.-D. Zheng, W.-Y. Tong, Z.-Q. Bao, X.-G. Wan, and C.-G. Duan, Twist-induced quantum valley Hall states in bilayer germanene, Phys. Rev. B 111, 075421 (2025)

    2025

  8. [15]

    A. M. Shirai, Y. Murotani, T. Fujimoto, N. Kanda, J. Yoshinobu, and R. Matsunaga, Valley polarization dynamics of photoinjected carriers at the band edge in room-temperature silicon studied by terahertz po- larimetry, Phys. Rev. B 111, L121201 (2025)

    2025

  9. [16]

    R. Wang, K. Chang, W. Duan, Y. Xu, and P. Tang, Twist-Angle-Dependent Valley Polarization of In- tralayer Moir´ e Excitons in van der Waals Superlattices, 10 Phys. Rev. Lett. 134, 026904 (2025)

    2025

  10. [17]

    Herrmann, S

    P. Herrmann, S. Klimmer, T. Lettau, T. Weickhardt, A. Papavasileiou, K. Mosina, Z. Sofer, I. Paradisanos, D. Kartashov, J. Wilhelm, et al., Nonlinear valley selec- tion rules and all-optical probe of broken time-reversal symmetry in monolayer WSe 2, Nat. Photon. 19, 300 (2025)

    2025

  11. [18]

    Jiang, L.-Y

    X.-C. Jiang, L.-Y. Qiao, and Y.-Z. Zhang, Anomalous valley Hall effect in monolayer chromium-based triple-Q magnets, Phys. Rev. B 111, L140416 (2025)

    2025

  12. [19]

    Zhang, J

    W. Zhang, J. Zhou, and S. Cheng, Valley transport in breathing kagome lattices with chiral spin textures, Phys. Rev. B 111, 165307 (2025)

    2025

  13. [20]

    Gunawan, Y

    O. Gunawan, Y. P. Shkolnikov, K. Vakili, T. Gokmen, E. P. De Poortere, and M. Shayegan, Valley Susceptibil- ity of an Interacting Two-Dimensional Electron System, Phys. Rev. Lett. 97, 186404 (2006)

    2006

  14. [21]

    ˇZuti´ c, J

    I. ˇZuti´ c, J. Fabian, and S. Das Sarma, Spintronics: Fun- damentals and applications, Rev. Mod. Phys. 76, 323 (2004)

    2004

  15. [22]

    M. A. Mueed, M. S. Hossain, I. Jo, L. N. Pfeiffer, K. W. West, K. W. Baldwin, and M. Shayegan, Realization of a Valley Superlattice, Phys. Rev. Lett. 121, 036802 (2018)

    2018

  16. [23]

    Gokmen, M

    T. Gokmen, M. Padmanabhan, O. Gunawan, Y. P. Shkolnikov, K. Vakili, E. P. De Poortere, and M. Shayegan, Parallel magnetic-field tuning of valley splitting in AlAs two-dimensional electrons, Phys. Rev. B 78, 233306 (2008)

    2008

  17. [24]

    Shen, W.-Y

    X.-W. Shen, W.-Y. Tong, S.-J. Gong, and C.-G. Duan, Electrically tunable polarizer based on 2D orthorhombic ferrovalley materials, 2D Mater. 5, 011001 (2017)

    2017

  18. [25]

    Tong, S.-J

    W.-Y. Tong, S.-J. Gong, X. Wan, and C.-G. Duan, Con- cepts of ferrovalley material and anomalous valley Hall effect, Nat Commun 7, 13612 (2016)

    2016

  19. [26]

    Hu, W.-Y

    H. Hu, W.-Y. Tong, Y.-H. Shen, X. Wan, and C.-G. Duan, Concepts of the half-valley-metal and quantum anomalous valley Hall effect, npj Comput Mater 6, 129 (2020)

    2020

  20. [27]

    Y. Lai, Z. Song, Y. Wan, M. Xue, C. Wang, Y. Ye, L. Dai, Z. Zhang, W. Yang, H. Du, et al. , Two- dimensional ferromagnetism and driven ferroelectricity in van der Waals CuCrP2S6, Nanoscale 11, 5163 (2019)

    2019

  21. [28]

    T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, B. Liu, et al., Valley-selective circu- lar dichroism of monolayer molybdenum disulphide, Nat Commun 3, 887 (2012)

    2012

  22. [29]

    Z. Wan, W. Zhou, G. Zheng, H. Duan, Y. Chen, and F. Ouyang, Tuning the Magnetization Direction and Valley Splitting of Monolayer Ferrovalley CrISe: Impli- cations for Spintronics and Valleytronics Devices, ACS Appl. Nano Mater. 8, 2466 (2025)

    2025

  23. [30]

    A. M. Jones, H. Yu, N. J. Ghimire, S. Wu, G. Aivazian, J. S. Ross, B. Zhao, J. Yan, D. G. Mandrus, D. Xiao, et al., Optical generation of excitonic valley coherence in monolayer WSe2, Nature Nanotech 8, 634 (2013)

    2013

  24. [31]

    H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, Valley polarization in MoS 2 monolayers by optical pumping, Nature Nanotech 7, 490 (2012)

    2012

  25. [32]

    Aivazian, Z

    G. Aivazian, Z. Gong, A. M. Jones, R.-L. Chu, J. Yan, D. G. Mandrus, C. Zhang, D. Cobden, W. Yao, and X. Xu, Magnetic control of valley pseudospin in mono- layer WSe2, Nature Phys 11, 148 (2015)

    2015

  26. [33]

    Suzuki, M

    R. Suzuki, M. Sakano, Y. Zhang, R. Akashi, D. Morikawa, A. Harasawa, K. Yaji, K. Kuroda, K. Miyamoto, T. Okuda, et al., Valley-dependent spin polarization in bulk MoS 2 with broken inversion sym- metry, Nature Nanotech 9, 611 (2014)

    2014

  27. [34]

    Zhong, K

    D. Zhong, K. L. Seyler, X. Linpeng, R. Cheng, N. Sivadas, B. Huang, E. Schmidgall, T. Taniguchi, K. Watanabe, M. A. McGuire, W. Yao, D. Xiao, K.- M. C. Fu, and X. Xu, Van der Waals engineering of ferromagnetic semiconductor heterostructures for spin and valleytronics, Sci. Adv...

    2017

  28. [35]

    Z. Wang, J. Shan, and K. F. Mak, Valley-and spin- polarized Landau levels in monolayer WSe 2, Nature Nanotech 12, 144 (2017)

    2017

  29. [36]

    Z. Wu, B. T. Zhou, X. Cai, P. Cheung, G.-B. Liu, M. Huang, J. Lin, T. Han, L. An, Y. Wang, et al., In- trinsic valley Hall transport in atomically thin MoS 2, Nat Commun 10, 611 (2019)

    2019

  30. [37]

    P. Dey, L. Yang, C. Robert, G. Wang, B. Urbaszek, X. Marie, and S. A. Crooker, Gate-Controlled Spin- Valley Locking of Resident Carriers in WSe 2 Monolay- ers, Phys. Rev. Lett. 119, 137401 (2017)

    2017

  31. [38]

    Xiao, G.-B

    D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Cou- pled Spin and Valley Physics in Monolayers of MoS 2 and Other Group-VI Dichalcogenides, Phys. Rev. Lett. 108, 196802 (2012)

    2012

  32. [39]

    L. Li, L. Shao, X. Liu, A. Gao, H. Wang, B. Zheng, G. Hou, K. Shehzad, L. Yu, F. Miao, et al., Room- temperature valleytronic transistor, Nat. Nanotechnol. 15, 743 (2020)

    2020

  33. [40]

    Gong, G.-B

    Z. Gong, G.-B. Liu, H. Yu, D. Xiao, X. Cui, X. Xu, and W. Yao, Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers, Nat Commun 4, 2053 (2013)

    2013

  34. [41]

    R. Xu, Z. Zhang, J. Liang, and H. Zhu, Valleytronics: Fundamental Challenges and Materials Beyond Transi- tion Metal Chalcogenides, Small , 2402139 (2024)

    2024

  35. [42]

    A. M. Jones, H. Yu, J. S. Ross, P. Klement, N. J. Ghimire, J. Yan, D. G. Mandrus, W. Yao, and X. Xu, Spin–layer locking effects in optical orientation of exci- ton spin in bilayer WSe 2, Nature Phys 10, 130 (2014)

    2014

  36. [43]

    S. Wu, J. S. Ross, G.-B. Liu, G. Aivazian, A. Jones, Z. Fei, W. Zhu, D. Xiao, W. Yao, D. Cobden, et al., Electrical tuning of valley magnetic moment through symmetry control in bilayer MoS 2, Nature Phys 9, 149 (2013)

    2013

  37. [44]

    Shimazaki, M

    Y. Shimazaki, M. Yamamoto, I. V. Borzenets, K. Watanabe, T. Taniguchi, and S. Tarucha, Generation and detection of pure valley current by electrically in- duced Berry curvature in bilayer graphene, Nature Phys 11, 1032 (2015)

    2015

  38. [45]

    M. Sui, G. Chen, L. Ma, W.-Y. Shan, D. Tian, K. Watanabe, T. Taniguchi, X. Jin, W. Yao, D. Xiao, et al., Gate-tunable topological valley transport in bi- layer graphene, Nature Phys 11, 1027 (2015)

    2015

  39. [46]

    Scuri, T

    G. Scuri, T. I. Andersen, Y. Zhou, D. S. Wild, J. Sung, R. J. Gelly, D. B´ erub´ e, H. Heo, L. Shao, A. Y. Joe, A. M. Mier Valdivia, T. Taniguchi, K. Watanabe, M. Lonˇ car, P. Kim, M. D. Lukin, and H. Park, Electrically Tun- able Valley Dynamics in Twisted WSe2/WSe2 Bilayers, ...

    2020

  40. [47]

    J. Lee, K. F. Mak, and J. Shan, Electrical control of the valley Hall effect in bilayer MoS 2 transistors, Nature Nanotech 11, 421 (2016)

    2016

  41. [48]

    Zhang, X

    T. Zhang, X. Xu, B. Huang, Y. Dai, L. Kou, and Y. Ma, Layer-polarized anomalous Hall effects in valleytronic van der Waals bilayers, Mater. Horiz. 10, 483 (2023). 11

    2023

  42. [49]

    Z.-M. Yu, S. Guan, X.-L. Sheng, W. Gao, and S. A. Yang, Valley-Layer Coupling: A New Design Principle for Valleytronics, Phys. Rev. Lett. 124, 037701 (2020)

    2020

  43. [50]

    S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, L. A. Ponomarenko, D. Jiang, and A. K. Geim, Strong Suppression of Weak Localization in Graphene, Phys. Rev. Lett. 97, 016801 (2006)

    2006

  44. [51]

    McCann, K

    E. McCann, K. Kechedzhi, V. I. Fal’ko, H. Suzuura, T. Ando, and B. L. Altshuler, Weak-Localization Mag- netoresistance and Valley Symmetry in Graphene, Phys. Rev. Lett. 97, 146805 (2006)

    2006

  45. [52]

    Y. S. Ang, S. A. Yang, C. Zhang, Z. Ma, and L. K. Ang, Valleytronics in merging Dirac cones: All-electric- controlled valley filter, valve, and universal reversible logic gate, Phys. Rev. B 96, 245410 (2017)

    2017

  46. [53]

    A. F. Morpurgo and F. Guinea, Intervalley Scatter- ing, Long-Range Disorder, and Effective Time-Reversal Symmetry Breaking in Graphene, Phys. Rev. Lett. 97, 196804 (2006)

    2006

  47. [54]

    J. Xin, Y. Tang, Y. Liu, X. Zhao, H. Pan, and T. Zhu, Valleytronics in thermoelectric materials, npj Quant Mater 3, 9 (2018)

    2018

  48. [55]

    J. Chen, Y. Zhou, J. Yan, J. Liu, L. Xu, J. Wang, T. Wan, Y. He, W. Zhang, and Y. Chai, Room- temperature valley transistors for low-power neuromor- phic computing, Nat Commun 13, 7758 (2022)

    2022

  49. [56]

    C. W. J. Beenakker, N. V. Gnezdilov, E. Dresselhaus, V. P. Ostroukh, Y. Herasymenko, i. d. I. Adagideli, and J. Tworzyd lo, Valley switch in a graphene super- lattice due to pseudo-Andreev reflection, Phys. Rev. B 97, 241403 (2018)

    2018

  50. [57]

    Y.-M. Xie, D. K. Efetov, and K. T. Law, φ0-Josephson junction in twisted bilayer graphene induced by a valley- polarized state, Phys. Rev. Res. 5, 023029 (2023)

    2023

  51. [58]

    The key challenge to designing valleytronic devices in- volves generating and manipulating valley-polarized car- riers

    and other novel devices [59–65]. The key challenge to designing valleytronic devices in- volves generating and manipulating valley-polarized car- riers. The degeneracy of the two valleys, protected by both the time-reversal and inversion symmetries, lim- its their direct appli...

    2025 arXiv

  52. [59]

    J. J. Wang, S. Liu, J. Wang, and J.-F. Liu, Valley su- percurrent in the Kekul´ e graphene superlattice hetero- junction, Phys. Rev. B 101, 245428 (2020)

    2020

  53. [60]

    X. Wu, H. Meng, F. Kong, H. Zhang, Y. Bai, and N. Xu, Tunable nonlocal valley-entangled Cooper pair splitter realized in bilayer-graphene van der Waals spin valves, Phys. Rev. B 101, 125406 (2020)

    2020

  54. [61]

    X. Chen, L. Zhang, and H. Guo, Valley caloritronics and its realization by graphene nanoribbons, Phys. Rev. B 92, 155427 (2015)

    2015

  55. [62]

    X.-T. An, J. Xiao, M. W.-Y. Tu, H. Yu, V. I. Fal’ko, and W. Yao, Realization of Valley and Spin Pumps by Scattering at Nonmagnetic Disorders, Phys. Rev. Lett. 118, 096602 (2017)

    2017

  56. [63]

    Z. Wu, F. Zhai, F. M. Peeters, H. Q. Xu, and K. Chang, Valley-Dependent Brewster Angles and Goos-H¨ anchen Effect in Strained Graphene, Phys. Rev. Lett. 106, 176802 (2011)

    2011

  57. [64]

    X. Qiu, Q. Lv, and Z. Cao, A high-quality spin and val- ley beam splitter in WSe 2 tunnelling junction through the Goos–H¨ anchen shift, J. Phys.: Condens. Matter31, 225303 (2019)

    2019

  58. [65]

    R. Liu, Y. Zhang, Y. Zhou, J. Nie, L. Li, and Y. Zhang, Polarization-driven high Rabi frequency of piezotronic valley transistors, Nano Energy 113, 108550 (2023)

    2023

  59. [66]

    S. Lai, Z. Zhang, N. Wang, A. Rasmita, Y. Deng, Z. Liu, and W.-b. Gao, Dual-Gate All-Electrical Valleytronic Transistors, Nano Lett. 23, 192 (2023)

    2023

  60. [67]

    K. Shao, H. Geng, E. Liu, J. L. Lado, W. Chen, and D. Y. Xing, Non-Hermitian Moir´ e Valley Filter, Phys. Rev. Lett. 132, 156301 (2024)

    2024

  61. [68]

    D. Xiao, W. Yao, and Q. Niu, Valley-Contrasting Physics in Graphene: Magnetic Moment and Topologi- cal Transport, Phys. Rev. Lett. 99, 236809 (2007)

    2007

  62. [69]

    K. Das, K. Ghorai, D. Culcer, and A. Agarwal, Non- linear Valley Hall Effect, Phys. Rev. Lett. 132, 096302 (2024)

    2024

  63. [70]

    Ghadimi, C

    R. Ghadimi, C. Mondal, S. Kim, and B.-J. Yang, Quan- tum Valley Hall Effect without Berry Curvature, Phys. Rev. Lett. 133, 196603 (2024)

    2024

  64. [71]

    Zhang, D.-F

    S.-H. Zhang, D.-F. Shao, Z.-A. Wang, J. Yang, W. Yang, and E. Y. Tsymbal, Tunneling Valley Hall Effect Driven by Tilted Dirac Fermions, Phys. Rev. Lett. 131, 246301 (2023)

    2023

  65. [72]

    J. Zhou, Q. Sun, and P. Jena, Valley-Polarized Quan- tum Anomalous Hall Effect in Ferrimagnetic Honey- comb Lattices, Phys. Rev. Lett. 119, 046403 (2017)

    2017

  66. [73]

    H. Pan, Z. Li, C.-C. Liu, G. Zhu, Z. Qiao, and Y. Yao, Valley-Polarized Quantum Anomalous Hall Effect in Sil- icene, Phys. Rev. Lett. 112, 106802 (2014)

    2014

  67. [74]

    H. Pan, X. Li, F. Zhang, and S. A. Yang, Perfect valley filter in a topological domain wall, Phys. Rev. B 92, 041404 (2015)

    2015

  68. [75]

    H. Pan, X. Li, H. Jiang, Y. Yao, and S. A. Yang, Valley- polarized quantum anomalous Hall phase and disorder- induced valley-filtered chiral edge channels, Phys. Rev. B 91, 045404 (2015)

    2015

  69. [77]

    X. L. Wang, Proposal for a New Class of Materials: Spin Gapless Semiconductors, Phys. Rev. Lett. 100, 156404 (2008)

    2008

  70. [78]

    Guo, Y.-L

    S.-D. Guo, Y.-L. Tao, G. Wang, S. Chen, D. Huang, and Y. S. Ang, Proposal for valleytronic materials: Fer- rovalley metal and valley gapless semiconductor, Front. Phys. 19, 23302 (2024)

    2024

  71. [79]

    Krizman, J

    G. Krizman, J. Bermejo-Ortiz, T. Zakusylo, M. Ha- jlaoui, T. Takashiro, M. Rosmus, N. Olszowska, J. J. Ko lodziej, G. Bauer, Y. Guldner, G. Springholz, and L.- A. de Vaulchier, Valley-Polarized Quantum Hall Phase in a Strain-Controlled Dirac System, Phys. Rev. Lett. 132, 166601 (2024)

    2024

  72. [80]

    F. D. M. Haldane, Model for a Quantum Hall Effect without Landau Levels: Condensed-Matter Realization of the ”Parity Anomaly”, Phys. Rev. Lett. 61, 2015 (1988)

    1988

  73. [81]

    Colom´ es and M

    E. Colom´ es and M. Franz, Antichiral Edge States in a Modified Haldane Nanoribbon, Phys. Rev. Lett. 120, 086603 (2018)

    2018

  74. [82]

    Qi, Y.-S

    X.-L. Qi, Y.-S. Wu, and S.-C. Zhang, Topological quan- tization of the spin Hall effect in two-dimensional para- magnetic semiconductors, Phys. Rev. B 74, 085308 (2006)

    2006

  75. [83]

    Ezawa, Spin valleytronics in silicene: Quantum spin Hall–quantum anomalous Hall insulators and single- valley semimetals, Phys

    M. Ezawa, Spin valleytronics in silicene: Quantum spin Hall–quantum anomalous Hall insulators and single- valley semimetals, Phys. Rev. B 87, 155415 (2013)

    2013

  76. [84]

    Jotzu, M

    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

  77. [85]

    J. W. McIver, B. Schulte, F.-U. Stein, T. Matsuyama, G. Jotzu, G. Meier, and A. Cavalleri, Light-induced anomalous Hall effect in graphene, Nat. Phys. 16, 38 (2020)

    2020

  78. [86]

    T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. Devakul, K. Watanabe, T. Taniguchi, L. Fu, et al., Quantum anomalous Hall effect from intertwined moir´ e 12 bands, Nature 600, 641 (2021)

    2021

  79. [87]

    Zhou, G.-G

    P. Zhou, G.-G. Liu, Y. Yang, Y.-H. Hu, S. Ma, H. Xue, Q. Wang, L. Deng, and B. Zhang, Observation of Pho- tonic Antichiral Edge States, Phys. Rev. Lett. 125, 263603 (2020)

    2020

  80. [88]

    Y. Yang, D. Zhu, Z. Hang, and Y. Chong, Observation of antichiral edge states in a circuit lattice, Sci. China Phys. Mech. Astron. 64, 1 (2021)

    2021

  81. [89]

    M. Vila, N. T. Hung, S. Roche, and R. Saito, Tunable circular dichroism and valley polarization in the modi- fied Haldane model, Phys. Rev. B 99, 161404 (2019)

    2019

  82. [90]

    Ezawa, Photoinduced Topological Phase Transition and a Single Dirac-Cone State in Silicene, Phys

    M. Ezawa, Photoinduced Topological Phase Transition and a Single Dirac-Cone State in Silicene, Phys. Rev. Lett. 110, 026603 (2013)

    2013

  83. [91]

    W. Zhao, K. Kang, Y. Zhang, P. Kn¨ uppel, Z. Tao, L. Li, C. L. Tschirhart, E. Redekop, K. Watanabe, T. Taniguchi, et al., Realization of the Haldane Chern insulator in a moir´ e lattice, Nat. Phys.20, 275 (2024)

    2024

  84. [92]

    Mitra, ´A

    S. Mitra, ´A. Jim´ enez-Gal´ an, M. Aulich, M. Neuhaus, R. E. Silva, V. Pervak, M. F. Kling, and S. Biswas, Light-wave-controlled Haldane model in monolayer hexagonal boron nitride, Nature , 1 (2024)

    2024

  85. [93]

    Oka and H

    T. Oka and H. Aoki, Photovoltaic Hall effect in graphene, Phys. Rev. B 79, 081406 (2009)

    2009

  86. [94]

    Hofmann, T

    T. Hofmann, T. Helbig, C. H. Lee, M. Greiter, and R. Thomale, Chiral Voltage Propagation and Calibra- tion in a Topolectrical Chern Circuit, Phys. Rev. Lett. 122, 247702 (2019)

    2019

  87. [95]

    Liu, F.-L

    J.-W. Liu, F.-L. Shi, K. Shen, X.-D. Chen, K. Chen, W.- J. Chen, and J.-W. Dong, Antichiral surface states in time-reversal-invariant photonic semimetals, Nat Com- mun 14, 2027 (2023)

    2023

  88. [96]

    X. Xi, B. Yan, L. Yang, Y. Meng, Z.-X. Zhu, J.-M. Chen, Z. Wang, P. Zhou, P. P. Shum, Y. Yang, et al., Topological antichiral surface states in a magnetic Weyl photonic crystal, Nat Commun 14, 1991 (2023)

    2023

  89. [97]

    H. Yuan, M. S. Bahramy, K. Morimoto, S. Wu, K. No- mura, B.-J. Yang, H. Shimotani, R. Suzuki, M. Toh, C. Kloc, et al., Zeeman-type spin splitting controlled by an electric field, Nature Phys 9, 563 (2013)

    2013

  90. [98]

    B. Yang, E. Molina, J. Kim, D. Barroso, M. Lohmann, Y. Liu, Y. Xu, R. Wu, L. Bartels, K. Watan- abe, T. Taniguchi, and J. Shi, Effect of Distance on Photoluminescence Quenching and Proximity-Induced Spin–Orbit Coupling in Graphene/WSe 2 Heterostruc- tures, Nano Lett. 18, 3580 (2018)

    2018

  91. [99]

    Cheiwchanchamnangij, W

    T. Cheiwchanchamnangij, W. R. L. Lambrecht, Y. Song, and H. Dery, Strain effects on the spin-orbit- induced band structure splittings in monolayer MoS 2 and graphene, Phys. Rev. B 88, 155404 (2013)

    2013

  92. [100]

    Fujita, M

    T. Fujita, M. B. A. Jalil, and S. G. Tan, Valley filter in strain engineered graphene, Appl. Phys. Lett. 97, 043508 (2010)

    2010

  93. [101]

    M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Chiral tunnelling and the Klein paradox in graphene, Nature Phys 2, 620 (2006)

    2006

  94. [102]

    Ozawa, A

    T. Ozawa, A. Amo, J. Bloch, and I. Carusotto, Klein tunneling in driven-dissipative photonic graphene, Phys. Rev. A 96, 013813 (2017)

    2017

  95. [103]

    C. W. J. Beenakker, Colloquium: Andreev reflection and Klein tunneling in graphene, Rev. Mod. Phys. 80, 1337 (2008)

    2008

  96. [104]

    A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009)

    2009

  97. [105]

    P. E. Allain and J.-N. Fuchs, Klein tunneling in graphene: optics with massless electrons, Eur. Phys. J. B 83, 301 (2011)

    2011

  98. [106]

    A. R. Myers, D. B. Sulas-Kern, R. Fei, D. Ghoshal, M. A. Hermosilla-Palacios, and J. L. Blackburn, Quanti- fying carrier density in monolayer MoS2 by optical spec- troscopy, J. Chem. Phys. 161, 044706 (2024)

    2024

  99. [107]

    Y. Yin, Z. Cheng, L. Wang, K. Jin, and W. Wang, Graphene, a material for high temperature devices– intrinsic carrier density, carrier drift velocity and lattice energy, Sci Rep 4, 5758 (2014)

    2014

  100. [108]

    Friesen, S

    M. Friesen, S. Chutia, C. Tahan, and S. N. Coppersmith, Valley splitting theory of SiGe /Si/SiGe quantum wells, Phys. Rev. B 75, 115318 (2007)

    2007

  101. [109]

    N. H. Shon and T. Ando, Quantum transport in two- dimensional graphite system, J. Phys. Soc. Jpn. 67, 2421 (1998)

    1998

  102. [110]

    K. F. Mak, K. He, J. Shan, and T. F. Heinz, Control of valley polarization in monolayer MoS 2 by optical helic- ity, Nature Nanotech 7, 494 (2012)

    2012

  103. [111]

    J. M. Koh, T. Tai, and C. H. Lee, Simulation of Interaction-Induced Chiral Topological Dynamics on a Digital Quantum Computer, Phys. Rev. Lett. 129, 140502 (2022)

    2022

  104. [112]

    J. Wang, S. Valligatla, Y. Yin, L. Schwarz, M. Medina- S´ anchez, S. Baunack, C. H. Lee, R. Thomale, S. Li, V. M. Fomin, et al., Experimental observation of Berry phases in optical M¨ obius-strip microcavities, Nat. Pho- ton. 17, 120 (2023)

    2023

  105. [113]

    S. A. Vitale, D. Nezich, J. O. Varghese, P. Kim, N. Gedik, P. Jarillo-Herrero, D. Xiao, and M. Roth- schild, Valleytronics: Opportunities, Challenges, and Paths Forward, Small 14, 1801483 (2018)

    2018

  106. [114]

    C. H. Lee and X.-L. Qi, Lattice construction of pseu- dopotential Hamiltonians for fractional Chern insula- tors, Phys. Rev. B 90, 085103 (2014)

    2014

  107. [115]

    T. D. Stanescu, V. Galitski, and S. Das Sarma, Topo- logical states in two-dimensional optical lattices, Phys. Rev. A 82, 013608 (2010)

    2010

  108. [116]

    Raoux, M

    A. Raoux, M. Morigi, J.-N. Fuchs, F. Pi´ echon, and G. Montambaux, From Dia- to Paramagnetic Orbital Susceptibility of Massless Fermions, Phys. Rev. Lett. 112, 026402 (2014)

    2014

  109. [117]

    K. W. Lee, P.-H. Fu, and Y. S. Ang, Interplay between Haldane and modified Haldane models in α−T3 lattice: Band structures, phase diagrams, and edge states, Phys. Rev. B 109, 235105 (2024)

    2024

  110. [118]

    Vidal, R

    J. Vidal, R. Mosseri, and B. Dou¸ cot, Aharonov-Bohm Cages in Two-Dimensional Structures, Phys. Rev. Lett. 81, 5888 (1998)

    1998

  111. [119]

    Vidal, P

    J. Vidal, P. Butaud, B. Dou¸ cot, and R. Mosseri, Dis- order and interactions in Aharonov-Bohm cages, Phys. Rev. B 64, 155306 (2001)

    2001

  112. [120]

    Oka and S

    T. Oka and S. Kitamura, Floquet Engineering of Quan- tum Materials, Annu. Rev. Condens. Matter Phys. 10, 387 (2019)

    2019

  113. [121]

    K. W. Lee, M. J. A. Calderon, X.-L. Yu, C. H. Lee, Y. S. Ang, and P.-H. Fu, Floquet engineering of topological phase transitions in a quantum spin Hall α−T3 system, Phys. Rev. B 111, 045406 (2025). 13

    2025

  114. [122]

    Goldman and J

    N. Goldman and J. Dalibard, Periodically Driven Quan- tum Systems: Effective Hamiltonians and Engineered Gauge Fields, Phys. Rev. X 4, 031027 (2014)

    2014

  115. [123]

    Rahav, I

    S. Rahav, I. Gilary, and S. Fishman, Effective Hamilto- nians for periodically driven systems, Phys. Rev. A 68, 013820 (2003)

    2003

  116. [124]

    Plekhanov, G

    K. Plekhanov, G. Roux, and K. Le Hur, Floquet engi- neering of Haldane Chern insulators and chiral bosonic phase transitions, Phys. Rev. B 95, 045102 (2017)

    2017

  117. [125]

    C. H. Lee, W. W. Ho, B. Yang, J. Gong, and Z. Papi´ c, Floquet Mechanism for Non-Abelian Fractional Quan- tum Hall States, Phys. Rev. Lett. 121, 237401 (2018)

    2018

  118. [126]

    F. Qin, C. H. Lee, and R. Chen, Light-induced phase crossovers in a quantum spin Hall system, Phys. Rev. B 106, 235405 (2022)

    2022

  119. [127]

    F. Qin, R. Chen, and C. H. Lee, Light-enhanced non- linear Hall effect, Commun Phys 7, 368 (2024)

    2024

  120. [128]

    Stegmaier, A

    A. Stegmaier, A. Fritzsche, R. Sorbello, M. Greiter, H. Brand, C. Barko, M. Hofer, U. Schwingenschl¨ ogl, R. Moessner, C. H. Lee, A. Szameit, A. Alu, T. Kießling, and R. Thomale, Topological Edge State Nucleation in Frequency Space and its Realization with Floquet Elec- trical...

    2024 arXiv

  121. [129]

    Li, P.-H

    R. Li, P.-H. Fu, J.-F. Liu, and J. Wang, Armchair edge states in shear-strained graphene: Magnetic properties and quantum valley Hall edge states, Phys. Rev. B 109, 045403 (2024)

    2024

  122. [130]

    S.-D. Guo, Y. Liu, J. Yu, and C.-C. Liu, Valley polar- ization in twisted altermagnetism, Phys. Rev. B 110, L220402 (2024)

    2024

  123. [131]

    C.-C. Liu, H. Jiang, and Y. Yao, Low-energy effec- tive Hamiltonian involving spin-orbit coupling in sil- icene and two-dimensional germanium and tin, Phys. Rev. B 84, 195430 (2011)

    2011

  124. [132]

    L¨ u, Y.-C

    X.-L. L¨ u, Y.-C. Zhang, P.-H. Fu, and J.-F. Liu, Phase diagrams and topological mixed edge states in silicene with intrinsic and extrinsic Rashba effects, Phys. Rev. Res. 6, 043108 (2024)

    2024

  125. [133]

    S.-Q. Lin, H. Tan, P.-H. Fu, and J.-F. Liu, Interaction- driven Chern insulating phases in the α-T3 lattice with Rashba spin-orbit coupling, iScience 26 (2023)

    2023

  126. [134]

    Dai, P.-H

    X. Dai, P.-H. Fu, Y. S. Ang, and Q. Chen, Two- dimensional Weyl nodal-line semimetal and antihelical edge states in a modified Kane-Mele model, Phys. Rev. B 110, 195409 (2024)

    2024

  127. [135]

    P. A. M. Dirac, The quantum theory of the electron, Proc. R. Soc. Lond. A 117, 610 (1928)

    1928

  128. [136]

    P. A. M. Dirac, The Principles of Quantum Mechanics (Clarendon Press, Oxford, 1930)

    1930

Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.