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REVIEW 4 major objections 4 minor 66 references

Transport signatures of a Floquet topological transition at the helical edge

T0 review · 4 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A periodically driven quantum point contact between helical edge states undergoes a topological phase transition when the drive amplitude crosses the Zeeman field, and the transition is visible in the conductance.

desk verdict A concrete proposal for a Floquet topological transition in a driven helical-edge QPC, with a transport signature that is well worked out; the missing topological invariant leaves the central claim underdetermined. read the letter →

arxiv 1908.11719 v2 pith:QEAPIUAF submitted 2019-08-30 cond-mat.mes-hall

C. Fleckenstein , N. Traverso Ziani , L. Privitera , M. Sassetti , B. Trauzettel This is my paper · ORCID
classification cond-mat.mes-hall
keywords helicaledgestatesFloquettopologicalphasetransitionquantumpointcontactphoton-assistedtransportspinHallinsulatorquasi-energyspectrumbound
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 paper predicts that a quantum point contact between the helical edge states of a two-dimensional topological insulator, when driven by a time-periodic electric field, undergoes a Floquet topological phase transition as the drive amplitude $eA$ is tuned through the Zeeman field $B_z$. The transition appears as a closing and reopening of the quasi-energy gap at half the driving frequency, $\omega/2$, and is accompanied by localized topological bound states at the ends of the point contact. The authors show that the transition can be detected through photon-assisted conductance measurements in both two-terminal and four-terminal setups, so the effect does not require direct access to wavefunctions. This matters because it offers a concrete solid-state platform in which a Floquet topological transition and its associated boundary states could be observed.

What carries the argument

The central object is the quasi-energy operator $Q = H(t) - i\partial_t$ acting on the extended Floquet-Hilbert space. Projecting $Q$ onto the zero- and one-photon sectors (Shirley-Floquet theory to lowest order in the drive) yields a four-by-four effective Hamiltonian $\mathcal{H}_{\mathrm{eff}}$ whose eigenvalues are quasi-energies. The drive enters through matrix elements $\Delta_0(k) \propto eA$, while the Zeeman field enters through $B_0(k) \propto B_z$; the transition occurs where these two couplings balance. For resonant frequency $\omega = 2\sqrt{\gamma_c^2+\gamma_0^2}$, the gap closes at $k=0$ and at quasi-energy $\omega/2$ when $eA = B_z$, reopening with a different character on each side. For off-resonant driving with imbalance $\delta\omega$, the phase boundary shifts to $B_z = \sqrt{(eA)^2 + (\delta\omega)^2(1+(\gamma_c/\gamma_0)^2)}$.

What would settle it

Evaluate a Floquet topological invariant, such as a winding number of the effective quasi-energy Hamiltonian, as a function of $eA/B_z$; if the invariant does not change at $eA = B_z$, the claimed topological transition is refuted, while the conductance features would remain as ordinary spectral effects.

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Extended reading notes

Core claim

The central claim is that a periodically driven QPC between helical edges exhibits a Floquet topological phase transition as the dimensionless ratio $eA/B_z$ crosses unity. At resonant driving, $\omega = 2\sqrt{\gamma_c^2+\gamma_0^2}$, the effective quasi-energy operator projects onto zero- and one-photon sectors and its spectrum shows a gap-closing and reopening at quasi-energy $\epsilon = \omega/2$ exactly at $eA = B_z$. In the topological phase, $0 < eA/B_z < 1$, bound states localized at the ends of the QPC appear at $\omega/2$, with a dominant spin component perpendicular to the helical spin axis. These bound states act as a ferromagnetic barrier, enabling backscattering into the same channel, which breaks the perfect $e^2/h$ quantization of the four-terminal conductance and leaves distinctive resonances in the two-terminal conductance of a weakly coupled QPC. The paper thus establishes the QPC as a feasible platform for detecting a Floquet topological transition via transport alone.

Load-bearing premise

The paper's identification of the transition as topological rests on observing gap closing and reopening at a symmetric quasi-energy together with localized boundary states, without computing a full topological invariant; if the two sides were found to be topologically equivalent, the central claim would fail.

Editorial extensions

If this is right

  • At resonance, the QPC is in a topological Floquet phase for $0 < eA/B_z < 1$ and a trivial phase for $eA/B_z > 1$, with the phase boundary at $eA = B_z$.
  • The topological phase hosts bound states at quasi-energy $\omega/2$ localized at the QPC ends, with spin polarization perpendicular to the helical quantization axis.
  • In a four-terminal measurement, the trivial phase has conductance quantized at $e^2/h$ per channel; this quantization is lost in the topological phase because the bound state backscatters same-channel electrons.
  • In a two-terminal measurement with weak coupling to the leads, the topological bound states appear as sharp resonances at $\omega/2$ in the conductance.
  • Off-resonant driving shifts the transition but leaves the same qualitative transport signatures, with the boundary given by the generalized condition $B_z = \sqrt{(eA)^2 + (\delta\omega)^2(1+(\gamma_c/\gamma_0)^2)}$.

Reading between the lines

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

  • The mechanism is generic: any one-dimensional junction with a charge-conjugation symmetry and a Zeeman gap could show the same Floquet transition, so similar signatures may be sought in other helical or spin-orbit coupled systems.
  • The spin-polarized bound state could be used as an electrically controlled spin flipper or spin filter, since tunneling into it flips the spin and produces same-channel reflection.
  • The paper never computes a bulk topological invariant for the Floquet bands; if a future calculation showed the two phases have the same invariant, the 'topological' designation would be wrong, though the conductance features would remain as spectral signatures.
  • A direct extension would be to study the interacting case: with electron-electron interactions along the helical edges, the bound-state spin texture might give rise to correlation effects detectable in noise measurements.
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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

4 major / 4 minor

Summary. The paper proposes a quantum point contact (QPC) between helical edge states of a two-dimensional topological insulator, subjected to a static Zeeman field B_z and a periodic drive of amplitude eA and frequency ω. Using Shirley-Floquet theory in a one-photon rotating-wave approximation, the authors derive an effective quasi-energy Hamiltonian (Eq. (6)) and identify a gap closing and reopening at quasi-energy ω/2 when eA = B_z; they interpret this as a Floquet topological phase transition. They then solve a Floquet scattering problem with a transfer matrix and compute two-terminal and four-terminal conductances, showing that the four-terminal conductance changes across the transition and that a localized bound state appears at the QPC ends. The central claim is that this transition and its bound states can be detected unambiguously by photon-assisted transport.

Significance. If established, the result would provide a solid-state, experimentally accessible platform for a Floquet topological phase transition with transport signatures in a device whose undriven version has already been realized in the lab. The main strengths are that the effective Hamiltonian is derived from a microscopic model, the transport calculation is performed from first principles without fitting experimental data, and the predicted transition condition eA = B_z is falsifiable within the model. The main weaknesses are that no topological invariant is computed and the bound-state criterion is not a topological diagnostic; these issues undermine the central 'topological' classification as stated, although they do not invalidate the transport calculation itself.

major comments (4)
  1. [Model and Bound state (Eq. (6), Fig. 1(d)-(f))] The paper identifies the transition by a gap closing and reopening at quasi-energy ϵ = ω/2 together with localized states at the QPC ends, but it never computes a bulk Floquet topological invariant for H_eff(k) in Eq. (6), nor a scattering-matrix invariant from the Floquet scattering amplitudes in the Transport section. In a one-dimensional Floquet system with charge-conjugation symmetry, a gap closing at a particle-hole symmetric point is necessary but not sufficient for a topological transition: a trivial band inversion can close and reopen the gap without changing any invariant. Since the central claim is that the system undergoes a Floquet topological phase transition, the presented evidence does not rule out a non-topological band inversion. I request an invariant calculation (for example, a winding number of the effective Hamiltonian or the Floquet scattering matrix invariant) or an explicit restriction of the claims to a gap-closing transition with boundary states.
  2. [Bound state, Eq. (13) and Fig. 5(a)] The criterion used to identify a topological bound state is that a local maximum in the probability density grows as the gap-inducing parameters are increased. This is a resonance criterion, not a topological criterion. A non-topological interface state in an open system would behave in the same way, so the existence of such a local maximum does not establish that the state is protected. Please add a diagnostic that ties the state to the claimed topology, such as pinning at quasi-energy ϵ = ω/2, exponential localization controlled by |eA − B_z|, appearance in pairs at the two QPC ends, or robustness against symmetry-preserving disorder.
  3. [Supplementary Material A, Eqs. (19)-(20)] The effective Hamiltonian in Eq. (6) is not fully specified: B_0(k) is left implicit in the main text, and B_0(k), B_1(k), B_2(k) in Eq. (19) of the Supplementary Material are declared 'too lengthy to be presented'. Because Eq. (6) is the basis of the transition condition in Eq. (14) and of all subsequent transport predictions, the omitted matrix elements are load-bearing for the central derivation. They should be supplied explicitly, or at least in a systematically defined form, so that the gap-closing condition and the conductance curves can be independently verified.
  4. [Model and Supplementary Material A] The rotating-wave/one-photon approximation is introduced with the condition eA, B_z ≪ ω, but the manuscript does not estimate the error from neglected multi-photon processes. Since the transition occurs at eA = B_z and transport is computed with a photon cutoff m, the one-photon effective Hamiltonian could receive quantitative corrections near the transition. Please provide a perturbative estimate of the leading neglected terms or a convergence check in the photon cutoff that demonstrates the transition condition in Eq. (14) is stable.
minor comments (4)
  1. [Transport, Eqs. (10) and (13)] In Eqs. (10) and (13), the symbol m is used both as the truncation order and as the summation/running photon index; please use different letters (for example, n for the running index and M for the cutoff).
  2. [Fig. 2 caption] The red line in Fig. 2 is referenced as Eq. (14), but that equation appears only in footnote 57; it should be promoted to a numbered equation in the main text.
  3. [Abstract and Introduction] The abstract and introduction claim that the transition can be 'unambiguously detected' by transport, but the two-terminal conductance in Fig. 2(a) is stated not to distinguish the topological and trivial regimes; please qualify the claim to the four-terminal measurement or provide a quantitative criterion.
  4. [Fig. 4 caption] The caption says 'driven electro-magnetic vector field eA', but Eq. (5) describes a periodic scalar-type coupling eA cos(ωt) τ_z σ_z; please unify the terminology.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted transition and conductance signatures are derived from the stated Hamiltonian, with no fitted inputs and no load-bearing self-citation.

full rationale

The paper's central claim is that a driven QPC between helical edges undergoes a Floquet topological phase transition as eA crosses B_z. The effective quasi-energy operator in Eq. (6) is derived directly from the model Hamiltonian, Eqs. (1)-(5), using Shirley-Floquet theory in the supplementary material, and the transition condition eA = B_z follows from the explicit Hamiltonian parameters rather than from data fitting or from a pre-assigned prediction. The conductance curves in Figs. 2 and 4 are obtained by solving the Floquet scattering problem defined by Eqs. (7)-(11), with no experimental data and no parameter tuned to force the claimed signatures. The bound-state evidence is likewise presented as explicit probability densities and spin densities computed from the same scattering formalism. Self-citations appear in the paper (e.g., the QPC model and the prior work defining a bound-state diagnostic), but they serve as background or as a naming convention; the load-bearing derivations do not reduce to an assertion from these citations. The reader's concern that no bulk Floquet topological invariant is computed is a completeness and correctness issue, not a circularity issue: the absence of an invariant does not mean the prediction is equivalent to an input. Overall, the derivation is self-contained and the predicted transport signatures are consequences of the stated model.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the low-energy non-interacting edge model, the rotating-wave Floquet approximation, and the identification of gap closing and bound states with a topological transition. No external data are fitted, but several matrix elements are left implicit and no bulk topological invariant is calculated. The bound state is a derived consequence of the model, not an ad hoc new entity.

free parameters (6)
  • Driving amplitude eA = Control parameter; transition predicted at eA = B_z
    Not fitted to data; it is the central knob whose variation drives the predicted topological transition.
  • Zeeman field B_z = Control parameter; sets transition scale
    Input magnetic field that breaks time-reversal symmetry and sets the scale for the transition condition.
  • Static coupling strengths gamma_0 and gamma_c = Chosen equal in numerics (gamma_0 = gamma_c)
    Device parameters of the QPC; the transition condition depends on their ratio, but no data are fitted.
  • Drive frequency omega = Resonant value omega = 2 sqrt(gamma_0^2 + gamma_c^2), with detuning delta_omega
    Set to couple degenerate levels in the quasi-energy spectrum; detuning shifts the transition slightly.
  • QPC length L = Examples: L = 27 v_F/gamma_0 and L = 120 v_F/gamma_0
    Used in numerical conductance and bound-state plots; it does not enter the analytic transition condition.
  • Photon cutoff m = m = 10 or m = 5
    Truncation of Floquet harmonics in the transfer-matrix calculation; no convergence analysis is shown.
assumptions (6)
  • domain assumption Low-energy helical edge theory with four Fermi fields and linear dispersion is valid when all energy scales are below the bulk gap.
    Used to write H_p in Eq. (1); standard for quantum spin Hall edges but not justified for all gate regimes.
  • domain assumption Electron-electron interactions and other symmetry-breaking perturbations are neglected in the QPC and leads.
    The model is non-interacting; helical edges are generally interacting, which could alter the predicted transport signatures.
  • ad hoc to paper Rotating-wave or one-photon Floquet approximation with eA, B_z much smaller than omega is sufficient to capture the topological transition.
    Used to derive the effective Hamiltonian Eq. (6); higher harmonics and off-resonant couplings are neglected in the analytic criterion.
  • domain assumption Gap closing and reopening at charge-conjugation-symmetric quasi-energies, plus localized bound states, identifies a topological phase transition.
    No explicit topological invariant is computed; the paper relies on this criterion to call the transition topological.
  • ad hoc to paper Step-function QPC potentials with lambda_F much smaller than L_s much smaller than L describe the device.
    Assumed for the scattering calculation in footnote 58; real QPC potentials have finite smoothness.
  • standard math Floquet scattering theory with independent Fermi distributions in each lead applies to the driven open system.
    Used for the current formula Eq. (9); standard but assumes no drive-induced heating or dephasing in the leads.

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Cite this review

Pith. "Pith review of Transport signatures of a Floquet topological transition at the helical edge." pith.science (2026). https://pith.science/paper/QEAPIUAF

@misc{pith2026190811719,
  author       = {Pith},
  title        = {Pith review of: Transport signatures of a Floquet topological transition at the helical edge},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QEAPIUAF}},
  note         = {Machine review of arXiv:1908.11719}
}
read the original abstract

The manipulation of the helical edge states of two-dimensional topological insulators is crucial for the development of technological applications. Recently, an important step forward, namely, the experimental realization of a quantum point contact between helical edges, has been accomplished. We theoretically predict that such a quantum point contact, in the presence of a time periodic applied electric field, is characterized by a topological quantum phase transition in the Floquet spectrum. Moreover, we show that it is possible to detect this dynamical topological quantum phase transition by a bare conductance measurements.

Figures

Figures reproduced from arXiv: 1908.11719 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of the system: QPC based on a QSHI [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Two terminal conductance evaluated from Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Schematic of a QPC with barriers. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a-b) Two terminal and (c-d) four terminal conduc [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. ( [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Probability density according to Eq.13 of the main [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

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Works this paper leans on

66 extracted references · 48 canonical work pages

  1. [1]

    author author C. L. \ Kane \ and\ author E. J. \ Mele ,\ 10.1103/PhysRevLett.95.146802 journal journal Phys. Rev. Lett. \ volume 95 ,\ pages 146802 ( year 2005 ) NoStop

    doi:10.1103/physrevlett.95.146802 2005

  2. [2]

    author author B. A. \ Bernevig , author T. L. \ Hughes , \ and\ author S.-C. \ Zhang ,\ @noop journal journal Science \ volume 314 ,\ pages 1757 ( year 2006 ) NoStop

    work page 2006

  3. [3]

    o nig , author S. Wiedmann , author C. Br \

    author author M. K \"o nig , author S. Wiedmann , author C. Br \"u ne , author A. Roth , author H. Buhmann , author L. W. \ Molenkamp , author X.-L. \ Qi , \ and\ author S.-C. \ Zhang ,\ @noop journal journal Science \ volume 318 ,\ pages 766 ( year 2007 ) NoStop

    work page 2007

  4. [4]

    Nadj-Perge , author I

    author author S. Nadj-Perge , author I. K. \ Drozdov , author J. Li , author H. Chen , author S. Jeon , author J. Seo , author A. H. \ MacDonald , author B. A. \ Bernevig , \ and\ author A. Yazdani ,\ 10.1126/science.1259327 journal journal Science \ volume 346 ,\ pages 602 ( year 2014 ) NoStop

    doi:10.1126/science.1259327

  5. [5]

    Michetti \ and\ author B

    author author P. Michetti \ and\ author B. Trauzettel ,\ 10.1063/1.4792275 journal journal Appl. Phys. Lett. \ volume 102 ,\ pages 063503 ( year 2013 ) NoStop

    work page doi:10.1063/1.4792275 2013

  6. [6]

    Linder \ and\ author J

    author author J. Linder \ and\ author J. W. A. \ Robinson ,\ https://doi.org/10.1038/nphys3242 journal journal Nat. Phys. \ volume 11 ,\ pages 307 ( year 2015 ) NoStop

    doi:10.1038/nphys3242 2015

  7. [7]

    Breunig , author P

    author author D. Breunig , author P. Burset , \ and\ author B. Trauzettel ,\ 10.1103/PhysRevLett.120.037701 journal journal Phys. Rev. Lett. \ volume 120 ,\ pages 037701 ( year 2018 ) NoStop

    work page doi:10.1103/physrevlett.120.037701 2018

  8. [8]

    author author R. S. K. \ Mong , author D. J. \ Clarke , author J. Alicea , author N. H. \ Lindner , author P. Fendley , author C. Nayak , author Y. Oreg , author A. Stern , author E. Berg , author K. Shtengel , \ and\ author M. P. A. \ Fisher ,\ 10.1103/PhysRevX.4.011036 journal journal Phys. Rev. X \ volume 4 ,\ pages 011036 ( year 2014 ) NoStop

    doi:10.1103/physrevx.4.011036

Show all 66 references
  1. [9]

    Klinovaja \ and\ author D

    author author J. Klinovaja \ and\ author D. Loss ,\ 10.1103/PhysRevLett.112.246403 journal journal Phys. Rev. Lett. \ volume 112 ,\ pages 246403 ( year 2014 ) NoStop

    2014 doi

  2. [10]

    Wiedenmann , author E

    author author J. Wiedenmann , author E. Bocquillon , author R. S. \ Deacon , author S. Hartinger , author O. Herrmann , author T. M. \ Klapwijk , author L. Maier , author C. Ames , author C. Bruene , author C. Gould , author A. Oiwa , author K. Ishibashi , author S. Tarucha , ...

    2016 doi

  3. [11]

    Maciejko , author C

    author author J. Maciejko , author C. Liu , author Y. Oreg , author X.-L. \ Qi , author C. Wu , \ and\ author S.-C. \ Zhang ,\ 10.1103/PhysRevLett.102.256803 journal journal Phys. Rev. Lett. \ volume 102 ,\ pages 256803 ( year 2009 ) NoStop

    doi

  4. [12]

    Traverso Ziani , author F

    author author N. Traverso Ziani , author F. Cr\'epin , \ and\ author B. Trauzettel ,\ 10.1103/PhysRevLett.115.206402 journal journal Phys. Rev. Lett. \ volume 115 ,\ pages 206402 ( year 2015 ) NoStop

    2015 doi

  5. [13]

    Zhang \ and\ author C

    author author F. Zhang \ and\ author C. L. \ Kane ,\ 10.1103/PhysRevLett.113.036401 journal journal Phys. Rev. Lett. \ volume 113 ,\ pages 036401 ( year 2014 ) NoStop

    2014 doi

  6. [14]

    author author C. P. \ Orth , author R. P. \ Tiwari , author T. Meng , \ and\ author T. L. \ Schmidt ,\ 10.1103/PhysRevB.91.081406 journal journal Phys. Rev. B \ volume 91 ,\ pages 081406 ( year 2015 ) NoStop

    2015 doi

  7. [15]

    C. Y. J. Teo and C. L. Kane, https://doi.org/10.1103/PhysRevB.79.235321 Phys. Rev. B 79, 235321(2009)

    2009 doi

  8. [16]

    Asano, Y

    Y. Asano, Y. Tanaka, and N. Nagaosa, https://doi.org/10.1103/PhysRevLett.105.056402 Phys. Rev. Lett. 105, 056402 (2010)

    2010 doi

  9. [17]

    Strunz, J

    J. Strunz, J. Wiedenmann, C. Fleckenstein, L. Lunczer, W. Beugeling, V. L M\"uller, P. Shekhar, N. Traverso Ziani, S. Shamim, J. Kleinlein, H. Buhmann, B. Trauzettel, L. W. Molenkamp, Nat. Phys. 16, 83 (2020)

    2020

  10. [18]

    \ Liu , author J

    journal author author C.-X. \ Liu , author J. C. \ Budich , author P. Recher , \ and\ author B. Trauzettel ,\ 10.1103/PhysRevB.83.035407 journal journal Phys. Rev. B \ volume 83 ,\ pages 035407 ( year 2011 ) NoStop

    2011 doi

  11. [19]

    Dolcini ,\ 10.1103/PhysRevB.83.165304 journal journal Phys

    author author F. Dolcini ,\ 10.1103/PhysRevB.83.165304 journal journal Phys. Rev. B \ volume 83 ,\ pages 165304 ( year 2011 ) NoStop

    2011 doi

  12. [20]

    Ferraro , author G

    author author D. Ferraro , author G. Dolcetto , author R. Citro , author F. Romeo , \ and\ author M. Sassetti ,\ 10.1103/PhysRevB.87.245419 journal journal Phys. Rev. B \ volume 87 ,\ pages 245419 ( year 2013 ) NoStop

    2013 doi

  13. [21]

    Klinovaja , author A

    author author J. Klinovaja , author A. Yacoby , \ and\ author D. Loss ,\ 10.1103/PhysRevB.90.155447 journal journal Phys. Rev. B \ volume 90 ,\ pages 155447 ( year 2014 ) NoStop

    2014 doi

  14. [22]

    Fleckenstein , author N

    author author C. Fleckenstein , author N. Traverso Ziani , \ and\ author B. Trauzettel ,\ 10.1103/PhysRevB.97.134523 journal journal Phys. Rev. B \ volume 97 ,\ pages 134523 ( year 2018 a ) NoStop

    2018 doi

  15. [23]

    Li , author W

    author author J. Li , author W. Pan , author B. A. \ Bernevig , \ and\ author R. M. \ Lutchyn ,\ 10.1103/PhysRevLett.117.046804 journal journal Phys. Rev. Lett. \ volume 117 ,\ pages 046804 ( year 2016 ) NoStop

    2016 doi

  16. [24]

    Fleckenstein , author N

    author author C. Fleckenstein , author N. Traverso Ziani , \ and\ author B. Trauzettel ,\ 10.1103/PhysRevLett.122.066801 journal journal Phys. Rev. Lett. \ volume 122 ,\ pages 066801 ( year 2019 ) NoStop

    2019 doi

  17. [25]

    Yao , author A

    author author W. Yao , author A. H. \ MacDonald , \ and\ author Q. Niu ,\ 10.1103/PhysRevLett.99.047401 journal journal Phys. Rev. Lett. \ volume 99 ,\ pages 047401 ( year 2007 ) NoStop

    2007 doi

  18. [26]

    Liu , author H

    author author M. Liu , author H. Y. \ Hwang , author H. Tao , author A. C. \ Strikwerda , author K. Fan , author G. R. \ Keiser , author A. J. \ Sternbach , author K. G. \ West , author S. Kittiwatanakul , author J. Lu , author S. A. \ Wolf , author F. G. \ Omenetto , author X...

    doi

  19. [27]

    author author E. J. \ Sie , author J. W. \ McIver , author Y.-H. \ Lee , author L. Fu , author J. Kong , \ and\ author N. Gedik ,\ https://doi.org/10.1038/nmat4156 journal journal Nat. Mater. \ volume 14 ,\ pages 290 ( year 2014 ) NoStop

    doi

  20. [28]

    Klinovaja and D

    J. Klinovaja and D. Loss, http://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.121410 Phys. Rev. B 92 121410(R) (2015)

    2015 doi

  21. [29]

    Thakurathi , author D

    author author M. Thakurathi , author D. Loss , \ and\ author J. Klinovaja ,\ 10.1103/PhysRevB.95.155407 journal journal Phys. Rev. B \ volume 95 ,\ pages 155407 ( year 2017 ) NoStop

    2017 doi

  22. [30]

    Cavalleri ,\ 10.1080/00107514.2017.1406623 journal journal Contemporary Physics \ volume 59 ,\ pages 31 ( year 2018 ) NoStop

    author author A. Cavalleri ,\ 10.1080/00107514.2017.1406623 journal journal Contemporary Physics \ volume 59 ,\ pages 31 ( year 2018 ) NoStop

    2017

  23. [31]

    Oka \ and\ author S

    author author T. Oka \ and\ author S. Kitamura ,\ 10.1146/annurev-conmatphys-031218-013423 journal journal Annual Review of Condensed Matter Physics \ volume 10 ,\ pages 387 ( year 2019 ) NoStop

    2019 doi

  24. [32]

    Rudner and J

    M. Rudner and J. C. Song, Nat. Phys. 15, 1017 (2019)

    2019

  25. [33]

    McIver , author B

    author author J. McIver , author B. Schulte , author F.-U. \ Stein , author T. Matsuyama , author G. Jotzu , author G. Meier , \ and\ author A. Cavalleri ,\ @noop journal journal preprint arXiv:1811.03522 \ ( year 2018 ) NoStop

    2018 arXiv

  26. [34]

    Oka \ and\ author H

    author author T. Oka \ and\ author H. Aoki ,\ @noop journal journal Phys. Rev. B \ volume 79 ,\ pages 081406 ( year 2009 ) NoStop

    2009

  27. [35]

    Kitagawa , author E

    author author T. Kitagawa , author E. Berg , author M. Rudner , \ and\ author E. Demler ,\ @noop journal journal Phys. Rev. B \ volume 82 ,\ pages 235114 ( year 2010 ) NoStop

    2010

  28. [36]

    author author N. H. \ Lindner , author G. Refael , \ and\ author V. Galitski ,\ @noop journal journal Nat. Phys. \ volume 7 ,\ pages 490 ( year 2011 ) NoStop

    2011

  29. [37]

    Kitagawa , author T

    author author T. Kitagawa , author T. Oka , author A. Brataas , author L. Fu , \ and\ author E. Demler ,\ @noop journal journal Phys. Rev. B \ volume 84 ,\ pages 235108 ( year 2011 ) NoStop

    2011

  30. [38]

    Gu , author H

    author author Z. Gu , author H. Fertig , author D. P. \ Arovas , \ and\ author A. Auerbach ,\ @noop journal journal Phys. Rev. Lett. \ volume 107 ,\ pages 216601 ( year 2011 ) NoStop

    2011

  31. [39]

    author author D. E. \ Liu , author A. Levchenko , \ and\ author H. U. \ Baranger ,\ @noop journal journal Phys. Rev. Lett. \ volume 111 ,\ pages 047002 ( year 2013 ) NoStop

    2013

  32. [40]

    Kundu and B

    A. Kundu and B. Seradjeh Phys. Rev. Lett. 111, 136402 (2013)

    2013

  33. [41]

    Ezawa ,\ 10.1103/PhysRevLett.110.026603 journal journal Phys

    author author M. Ezawa ,\ 10.1103/PhysRevLett.110.026603 journal journal Phys. Rev. Lett. \ volume 110 ,\ pages 026603 ( year 2013 ) NoStop

    2013 doi

  34. [42]

    Wang , author B

    author author R. Wang , author B. Wang , author R. Shen , author L. Sheng , \ and\ author D. Y. \ Xing ,\ http://stacks.iop.org/0295-5075/105/i=1/a=17004 journal journal EPL (Europhysics Letters) \ volume 105 ,\ pages 17004 ( year 2014 ) NoStop

    2014

  35. [43]

    author author L. E. F. Foa Torres , author P. M. Perez-Piskunow , author C. A. Balseiro , \ and\ author G. Usaj ,\ https://link.aps.org/doi/10.1103/PhysRevLett.113.266801 journal journal Phys. Rev. Lett. \ volume 113 ,\ pages 266801 ( year 2014 ) NoStop

    doi

  36. [44]

    L. E. F. Foa Torres, P. M. Perez-Piskunow, C. A. Balseiro, and Gonzalo Usaj, Phys

  37. [45]

    Sentef , author M

    author author M. Sentef , author M. Claassen , author A. Kemper , author B. Moritz , author T. Oka , author J. Freericks , \ and\ author T. Devereaux ,\ @noop journal journal Nature Communications \ volume 6 ( year 2015 ) NoStop

    2015

  38. [46]

    Farrell and T

    A. Farrell and T. Pereg-Barnea, Phys. Rev. Lett. 115, 106403 (2015)

    2015

  39. [47]

    Farrell and T

    A. Farrell and T. Pereg-Barnea, Phys. Rev. B 93, 045121 (2016)

    2016

  40. [48]

    Privitera \ and\ author G

    author author L. Privitera \ and\ author G. E. \ Santoro ,\ 10.1103/PhysRevB.93.241406 journal journal Phys. Rev. B \ volume 93 ,\ pages 241406 ( year 2016 ) NoStop

    2016 doi

  41. [49]

    Yan \ and\ author Z

    author author Z. Yan \ and\ author Z. Wang ,\ 10.1103/PhysRevLett.117.087402 journal journal Phys. Rev. Lett. \ volume 117 ,\ pages 087402 ( year 2016 ) NoStop

    2016 doi

  42. [50]

    H \"u bener , author M

    author author H. H \"u bener , author M. A. \ Sentef , author U. De Giovannini , author A. F. \ Kemper , \ and\ author A. Rubio ,\ https://doi.org/10.1038/ncomms13940 journal journal Nature Communications \ volume 8 ,\ pages 13940 ( year 2017 ) NoStop

    doi

  43. [51]

    Ezawa ,\ @noop journal journal Physical Review B \ volume 96 ,\ pages 041205 ( year 2017 ) NoStop

    author author M. Ezawa ,\ @noop journal journal Physical Review B \ volume 96 ,\ pages 041205 ( year 2017 ) NoStop

    2017

  44. [52]

    Rodriguez-Vega, H

    M. Rodriguez-Vega, H. A. Fertig, and B. Seradjeh, Phys. Rev. B 98, 041113(R) (2018)

    2018

  45. [53]

    Rodriguez-Vega , author A

    author author M. Rodriguez-Vega , author A. Kumar , \ and\ author B. Seradjeh ,\ 10.1103/PhysRevB.100.085138 journal journal Phys. Rev. B \ volume 100 ,\ pages 085138 ( year 2019 ) NoStop

    2019 doi

  46. [54]

    D. M. Kennes, N. Muller, M. Pletyukhov, C. Weber, C. Bruder, F. Hassler, J. Klinovaja, D. Loss, and H. Schoeller, https://journals.aps.org/prb/abstract/10.1103/PhysRevB.100.041103 Phys. Rev. B 100, 041103(R) (2019)

    2019 doi

  47. [55]

    Jotzu , author M

    author author G. Jotzu , author M. Messer , author R. Desbuquois , author M. Lebrat , author T. Uehlinger , author D. Greif , \ and\ author T. Esslinger ,\ @noop journal journal Nature \ volume 515 ,\ pages 237 ( year 2014 ) NoStop

    2014

  48. [56]

    Asteria , author D

    author author L. Asteria , author D. T. \ Tran , author T. Ozawa , author M. Tarnowski , author B. S. \ Rem , author N. Fl \"a schner , author K. Sengstock , author N. Goldman , \ and\ author C. Weitenberg ,\ 10.1038/s41567-019-0417-8 journal journal Nat. Phys. \ volume 15 ,\ ...

    doi

  49. [57]

    U nal , author N. Fl \

    author author M. Tarnowski , author F. N. \ \"U nal , author N. Fl \"a schner , author B. S. \ Rem , author A. Eckardt , author K. Sengstock , \ and\ author C. Weitenberg ,\ 10.1038/s41467-019-09668-y journal journal Nat. Commun. \ volume 10 ,\ pages 1728 ( year 2019 ) NoStop

    doi

  50. [58]

    ( Eq:Heff ), we obtain a gap closing-reopening transition at k=0 for eqnarray Eq:GapClosing B_z= (eA)^2+( )^2(1+( _c/ _0)^2)

    Generalizing the above discussion to a driving frequency =2( _0^2+ _c^2 - ) , with an imbalance , from Eq. ( Eq:Heff ), we obtain a gap closing-reopening transition at k=0 for eqnarray Eq:GapClosing B_z= (eA)^2+( )^2(1+( _c/ _0)^2) . eqnarray

  51. [59]

    Hence, we require _F L_s L

    This assumption is valid, provided the Fermi wave length _F is much smaller than the smoothening length L_s that describes the build-up of the QPC potentials which itself should be smaller than L . Hence, we require _F L_s L

  52. [60]

    P. K. Tien and J. P. Gordon Phys. Rev. 129, 647 (1963)

    1963

  53. [61]

    author author M. V. \ Moskalets ,\ @noop title Scattering matrix approach to non - stationary quantum transport \ ( publisher World Scientific ,\ year 2012 ) NoStop

    2012

  54. [62]

    Moskalets \ and\ author M

    author author M. Moskalets \ and\ author M. B\"uttiker ,\ 10.1103/PhysRevB.66.205320 journal journal Phys. Rev. B \ volume 66 ,\ pages 205320 ( year 2002 ) NoStop

    2002 doi

  55. [63]

    Atteia , author J

    author author J. Atteia , author J. H. Bardarson ,\ and\ author J. Cayssol ,\ 10.1103/PhysRevB.96.245404 journal journal Phys. Rev. B \ volume 96 ,\ pages 245404 ( year 2017 b ) NoStop

    2017 doi

  56. [64]

    The sum is due to the fact that an incoming electron can be reflected with the absorption of, generically, m photons

  57. [65]

    Fleckenstein , author F

    author author C. Fleckenstein , author F. Keidel , author B. Trauzettel , \ and\ author N. Traverso Ziani ,\ 10.1140/epjst/e2018-800093-5 journal journal Eur. Phys. J. Special Topics \ volume 227 ,\ pages 1377 ( year 2018 b ) NoStop

    2018 doi

  58. [66]

    Klinovaja , \ and\ author D

    author author J. Klinovaja , \ and\ author D. Loss ,\ https://doi.org/10.1103/PhysRevB.86.085408 journal journal Phys. Rev. B \ volume 86 ,\ pages 085408 ( year 2012 b ) NoStop

    2012 doi

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