pith. sign in

arxiv: 2607.02100 · v1 · pith:2NQISWVSnew · submitted 2026-07-02 · ❄️ cond-mat.mes-hall

Quantum-geometric shift of quasiequilibrium: Origin of nonreciprocal current driven by quantum-metric dipole

Sota Kitamura , Takahiro Anan , Takahiro Morimoto This is my paper

Pith reviewed 2026-07-03 06:55 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords quantum metricnonreciprocal transportnonlinear conductivityquasiequilibriumadiabatic perturbationnonequilibrium Green function
0
0 comments X

The pith

A quantum correction to the electron distribution from wave-packet spreading under bias produces nonreciprocal current set by the quantum-metric dipole.

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

The paper establishes that nonlinear DC transport of quantum-metric origin stems from a shift in quasiequilibrium caused by the finite spatial spread of electron wave packets while they relax under an applied field. This produces a correction to the steady-state distribution function that semiclassical treatments omit. The result is a longitudinal nonreciprocal current controlled by the quantum-metric dipole. A reader would care because the mechanism supplies a concrete physical picture for how quantum geometry enters steady-state transport rather than acting only through instantaneous band properties.

Core claim

Applying the adiabatic perturbation theory combined with nonequilibrium Green functions, the work finds a longitudinal nonreciprocal current governed by the quantum-metric dipole. The essential ingredient is a quantum correction to the distribution function absent from semiclassical treatments. This correction is traced to the finite spread of an electron wave packet during relaxation under a bias field, identifying the shifted quasiequilibrium as the physical origin of quantum-metric nonreciprocal transport.

What carries the argument

Shifted quasiequilibrium arising from the finite spatial spread of the electron wave packet under a DC bias, obtained via the adiabatic-basis Hamiltonian.

If this is right

  • The nonreciprocal current appears already at linear order in the relaxation time and is longitudinal.
  • Semiclassical Boltzmann approaches miss the effect because they lack the quantum correction to the distribution function.
  • The same adiabatic formulation yields equivalent Hamiltonians in velocity and length gauges, allowing direct comparison of results.
  • The mechanism operates in the DC limit without requiring an AC-field zero-frequency extrapolation.

Where Pith is reading between the lines

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

  • Materials with large quantum metric but small Berry curvature could still exhibit measurable nonreciprocity if the distribution-shift channel dominates.
  • The same wave-packet-spread correction may appear in other nonlinear responses such as second-harmonic generation or photogalvanic effects.
  • Numerical simulations that retain the spatial extent of wave packets during scattering should reproduce the nonreciprocal term even without explicit geometric-phase tracking.

Load-bearing premise

The adiabatic ansatz can be used to treat a DC electric field directly in the velocity gauge and produces a Hamiltonian of the same form as in the length gauge.

What would settle it

A calculation or measurement showing that the nonreciprocal current disappears when the quantum-metric dipole is set to zero while all other geometric quantities remain finite.

Figures

Figures reproduced from arXiv: 2607.02100 by Sota Kitamura, Takahiro Anan, Takahiro Morimoto.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic picture for the adiabatic-basis representation. Each basis function depicted as a wave packet smoothly evolves along [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Electron occupation under the tilted chemical potential [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

We study nonlinear DC electric transport of quantum-metric origin by combining adiabatic perturbation theory with the nonequilibrium Green function approach. The adiabatic ansatz provides a basis for directly treating a DC electric field in the velocity gauge, rather than introducing it as the zero-frequency limit of an AC field. The resulting adiabatic-basis Hamiltonian takes the same form as in the length gauge, enabling a systematic comparison across different formulations. Applying this fully quantum formulation, we find a longitudinal nonreciprocal current governed by the quantum-metric dipole. The essential ingredient is a quantum correction to the distribution function that is absent in semiclassical treatments. We trace this correction to the finite spread of an electron wave packet during relaxation under a bias field, thereby identifying shifted quasiequilibrium as the physical origin of quantum-metric nonreciprocal transport.

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.

Referee Report

2 major / 1 minor

Summary. The manuscript develops a quantum formulation of nonlinear DC transport by combining adiabatic perturbation theory with the nonequilibrium Green's function (NEGF) method. It asserts that an adiabatic ansatz permits direct inclusion of a constant DC electric field in the velocity gauge, producing a Hamiltonian identical in form to the length-gauge case. This framework yields a longitudinal nonreciprocal current controlled by the quantum-metric dipole. The key element is a quantum correction to the nonequilibrium distribution function, absent from semiclassical treatments, which the authors trace to the finite spatial spread of electron wave packets during relaxation under bias; the resulting picture is termed a 'shifted quasiequilibrium.'

Significance. If the derivation is shown to be gauge-consistent and independent of the specific relaxation model, the work supplies a concrete physical mechanism (wave-packet spreading under bias) for quantum-metric dipole effects in nonreciprocal transport. This interpretation goes beyond semiclassical Boltzmann approaches and could inform both theory and experiment on geometric contributions to nonlinear conductivity in topological and flat-band materials.

major comments (2)
  1. [Theory section on adiabatic ansatz and velocity gauge] The adiabatic ansatz (theory section describing the velocity-gauge treatment of a time-independent DC field): the claim that this ansatz directly reproduces the distribution-function correction without taking the zero-frequency limit of an AC field is load-bearing for the central identification of 'shifted quasiequilibrium' as the origin. For a strictly constant field the adiabatic condition is not obviously satisfied in the same manner as for slowly ramped or AC fields; an explicit check that the lesser Green's function and resulting current remain unchanged under this choice (and match the AC limit) is required.
  2. [Section deriving the distribution correction and semiclassical comparison] Comparison to semiclassical limit (likely §4 or the discussion of the distribution correction): the manuscript states the quantum correction is absent in semiclassics, yet the precise manner in which the wave-packet spread enters the NEGF lesser component versus the semiclassical Boltzmann collision integral is not shown in sufficient detail to confirm the correction survives all gauge choices and relaxation models.
minor comments (1)
  1. [Throughout] Notation for the quantum-metric dipole and the shifted distribution should be defined once with an explicit equation number before being used in the current expression.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and the positive assessment of the work's potential significance. We address the two major comments point by point below, providing clarifications and committing to revisions that strengthen the manuscript without altering its central claims.

read point-by-point responses

  1. Referee: [Theory section on adiabatic ansatz and velocity gauge] The adiabatic ansatz (theory section describing the velocity-gauge treatment of a time-independent DC field): the claim that this ansatz directly reproduces the distribution-function correction without taking the zero-frequency limit of an AC field is load-bearing for the central identification of 'shifted quasiequilibrium' as the origin. For a strictly constant field the adiabatic condition is not obviously satisfied in the same manner as for slowly ramped or AC fields; an explicit check that the lesser Green's function and resulting current remain unchanged under this choice (and match the AC limit) is required.

    Authors: We agree that an explicit verification would reinforce the load-bearing claim. The adiabatic ansatz is motivated by the fact that a constant DC field can be incorporated via a time-dependent vector potential whose time derivative is constant, allowing the same perturbative expansion as in the AC case. In the revised manuscript we will add a dedicated appendix or subsection that computes the lesser Green's function under the direct DC adiabatic ansatz and demonstrates its equivalence (to leading order in the field) with the zero-frequency limit of the AC treatment, confirming that both the distribution correction and the longitudinal nonreciprocal current are unchanged. revision: yes

  2. Referee: [Section deriving the distribution correction and semiclassical comparison] Comparison to semiclassical limit (likely §4 or the discussion of the distribution correction): the manuscript states the quantum correction is absent in semiclassics, yet the precise manner in which the wave-packet spread enters the NEGF lesser component versus the semiclassical Boltzmann collision integral is not shown in sufficient detail to confirm the correction survives all gauge choices and relaxation models.

    Authors: We accept that the current presentation leaves the microscopic origin of the wave-packet-spread correction insufficiently contrasted with the semiclassical collision integral. The NEGF lesser component encodes the finite spatial extent of the wave packet through the off-diagonal elements of the adiabatic-basis density matrix, an effect absent from the local Boltzmann equation. In the revision we will expand the relevant section (and add a short supplementary note) with an explicit side-by-side expansion: we show how the first-order correction to the lesser function arises from the commutator structure in the Dyson equation under the adiabatic ansatz, why the corresponding term vanishes upon taking the semiclassical limit (ħ→0 while keeping the relaxation time fixed), and why the resulting nonreciprocal current remains gauge-independent for the relaxation models considered. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper derives the quantum correction to the distribution function by combining adiabatic perturbation theory with the NEGF formalism, then interprets the result as arising from finite wave-packet spread under bias. No step reduces by construction to a fitted parameter renamed as a prediction, nor does any central claim rest on a self-citation chain whose content is unverified outside the present work. The adiabatic ansatz is introduced as a methodological choice enabling direct DC treatment, but the resulting current expression and its physical tracing are not shown to be equivalent to the inputs by definition. The derivation therefore retains independent content relative to its assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the adiabatic ansatz and NEGF framework are standard but their precise implementation details are not stated.

pith-pipeline@v0.9.1-grok · 5679 in / 1178 out tokens · 17778 ms · 2026-07-03T06:55:47.594471+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages · 2 internal anchors

  1. [1]

    Xiao, M.-C

    D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on elec- tronic properties, Rev. Mod. Phys.82, 1959 (2010)

    work page 1959

  2. [2]

    Nagaosa, J

    N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Anomalous Hall effect, Rev. Mod. Phys.82, 1539 (2010)

    work page 2010

  3. [3]

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

    work page 2010

  4. [4]

    Qi and S.-C

    X.-L. Qi and S.-C. Zhang, Topological insulators and supercon- ductors, Rev. Mod. Phys.83, 1057 (2011)

    work page 2011

  5. [5]

    R. D. King-Smith and D. Vanderbilt, Theory of polarization of crystalline solids, Phys. Rev. B47, 1651(R) (1993)

    work page 1993

  6. [6]

    Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Rev

    R. Resta, Macroscopic polarization in crystalline dielectrics: the geometric phase approach, Rev. Mod. Phys.66, 899 (1994)

    work page 1994

  7. [7]

    M. V . Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. London A392, 45 (1984)

    work page 1984

  8. [8]

    Tokura and N

    Y . Tokura and N. Nagaosa, Nonreciprocal responses from non- centrosymmetric quantum materials, Nat. Commun.9, 3740 (2018)

    work page 2018

  9. [9]

    Morimoto, S

    T. Morimoto, S. Kitamura, and N. Nagaosa, Geometric As- pects of Nonlinear and Nonequilibrium Phenomena, J. Phys. Soc. Jpn.92, 072001 (2023)

    work page 2023

  10. [10]

    Nagaosa and Y

    N. Nagaosa and Y . Yanase, Nonreciprocal Transport and Op- tical Phenomena in Quantum Materials, Annu. Rev. Condens. 14 Matter Phys.15, 63 (2024)

    work page 2024

  11. [11]

    Su ´arez-Rodr´ıguez, F

    M. Su ´arez-Rodr´ıguez, F. de Juan, I. Souza, M. Gobbi, F. Casanova, and L. E. Hueso, Nonlinear transport in non- centrosymmetric systems, Nat. Mater.24, 1005 (2025)

    work page 2025

  12. [12]

    J. E. Sipe and A. I. Shkrebtii, Second-order optical response in semiconductors, Phys. Rev. B61, 5337 (2000)

    work page 2000

  13. [13]

    Morimoto and N

    T. Morimoto and N. Nagaosa, Topological nature of nonlinear optical effects in solids, Sci. Adv.2, e1501524 (2016)

    work page 2016

  14. [14]

    Aversa and J

    C. Aversa and J. E. Sipe, Nonlinear optical susceptibilities of semiconductors: Results with a length-gauge analysis, Phys. Rev. B52, 14636 (1995)

    work page 1995

  15. [15]

    Ghimire and D

    S. Ghimire and D. A. Reis, High-harmonic generation from solids, Nat. Phys.15, 10 (2019)

    work page 2019

  16. [16]

    Sodemann and L

    I. Sodemann and L. Fu, Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materi- als, Phys. Rev. Lett.115, 216806 (2015)

    work page 2015

  17. [17]

    Ma, S.-Y

    Q. Ma, S.-Y . Xu, H. Shen, D. MacNeill, V . Fatemi, T.-R. Chang, A. M. Mier Valdivia, S. Wu, Z. Du, C.-H. Hsu, S. Fang, Q. D. Gibson, K. Watanabe, T. Taniguchi, R. J. Cava, E. Kaxiras, H.- Z. Lu, H. Lin, L. Fu, N. Gedik, and P. Jarillo-Herrero, Observa- tion of the nonlinear Hall effect under time-reversal-symmetric conditions, Nature565, 337 (2019)

    work page 2019

  18. [18]

    K. Kang, T. Li, E. Sohn, J. Shan, and K. F. Mak, Nonlinear anomalous Hall effect in few-layer WTe2, Nat. Mater.18, 324 (2019)

    work page 2019

  19. [19]

    G. L. J. A. Rikken, J. F ¨olling, and P. Wyder, Electrical Magne- tochiral Anisotropy, Phys. Rev. Lett.87, 236602 (2001)

    work page 2001

  20. [20]

    Wakatsuki, Y

    R. Wakatsuki, Y . Saito, S. Hoshino, Y . M. Itahashi, T. Ideue, M. Ezawa, Y . Iwasa, and N. Nagaosa, Nonreciprocal charge transport in noncentrosymmetric superconductors, Sci. Adv.3, e1602390 (2017)

    work page 2017

  21. [21]

    Morimoto and N

    T. Morimoto and N. Nagaosa, Nonreciprocal current from elec- tron interactions in noncentrosymmetric crystals: roles of time reversal symmetry and dissipation, Sci. Rep.8, 2973 (2018)

    work page 2018

  22. [22]

    Kitamura, N

    S. Kitamura, N. Nagaosa, and T. Morimoto, Nonreciprocal Lan- dau–Zener tunneling, Commun. Phys.3, 63 (2020)

    work page 2020

  23. [23]

    J. P. Provost and G. Vallee, Riemannian structure on manifolds of quantum states, Commun. Math. Phys.76, 289 (1980)

    work page 1980

  24. [24]

    Liu, X.-B

    T. Liu, X.-B. Qiang, H.-Z. Lu, and X. C. Xie, Quantum geome- try in condensed matter, Natl. Sci. Rev.12, nwae334 (2025)

    work page 2025

  25. [25]

    J. Yu, B. A. Bernevig, R. Queiroz, E. Rossi, P. T¨orm¨a, and B.-J. Yang, Quantum geometry in quantum materials, npj Quantum Materials10, 101 (2025)

    work page 2025

  26. [26]

    Marzari and D

    N. Marzari and D. Vanderbilt, Maximally localized generalized Wannier functions for composite energy bands, Phys. Rev. B 56, 12847 (1997)

    work page 1997

  27. [27]

    Peotta and P

    S. Peotta and P. T¨orm¨a, Superfluidity in topologically nontrivial flat bands, Nat. Commun.6, 8944 (2015)

    work page 2015

  28. [28]

    Liang, T

    L. Liang, T. I. Vanhala, S. Peotta, T. Siro, A. Harju, and P. T ¨orm¨a, Band geometry, Berry curvature, and superfluid weight, Phys. Rev. B95, 024515 (2017)

    work page 2017

  29. [29]

    Roy, Band geometry of fractional topological insulators, Phys

    R. Roy, Band geometry of fractional topological insulators, Phys. Rev. B90, 165139 (2014)

    work page 2014

  30. [30]

    T. S. Jackson, G. M ¨oller, and R. Roy, Geometric stability of topological lattice phases, Nat. Commun.6, 8629 (2015)

    work page 2015

  31. [31]

    Onishi and L

    Y . Onishi and L. Fu, Fundamental bound on topological gap, Phys. Rev. X14, 011052 (2024)

    work page 2024

  32. [32]

    Onishi and L

    Y . Onishi and L. Fu, Topological Bound on the Structure Factor, Phys. Rev. Lett.133, 206602 (2024)

    work page 2024

  33. [33]

    Y . Gao, S. A. Yang, and Q. Niu, Field Induced Positional Shift of Bloch Electrons and Its Dynamical Implications, Phys. Rev. Lett.112, 166601 (2014)

    work page 2014

  34. [34]

    Watanabe and Y

    H. Watanabe and Y . Yanase, Nonlinear electric transport in odd- parity magnetic multipole systems: Application to Mn-based compounds, Phys. Rev. Res.2, 043081 (2020)

    work page 2020

  35. [35]

    Oiwa and H

    R. Oiwa and H. Kusunose, Systematic Analysis Method for Nonlinear Response Tensors, J. Phys. Soc. Jpn.91, 014701 (2022)

    work page 2022

  36. [36]

    Michishita and N

    Y . Michishita and N. Nagaosa, Dissipation and geometry in nonlinear quantum transports of multiband electronic systems, Phys. Rev. B106, 125114 (2022)

    work page 2022

  37. [37]

    K. Das, S. Lahiri, R. B. Atencia, D. Culcer, and A. Agarwal, In- trinsic nonlinear conductivities induced by the quantum metric, Phys. Rev. B108, L201405 (2023)

    work page 2023

  38. [38]

    Y . Wang, Z. Zhang, Z.-G. Zhu, and G. Su, Intrinsic nonlinear Ohmic current, Phys. Rev. B109, 085419 (2024)

    work page 2024

  39. [39]

    Kaplan, T

    D. Kaplan, T. Holder, and B. Yan, Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry, Phys. Rev. Lett.132, 026301 (2024)

    work page 2024

  40. [40]

    C. Xiao, J. Cao, Q. Niu, and S. A. Yang, Proper Definition of In- trinsic Nonlinear Current, Phys. Rev. Lett.135, 256306 (2025)

    work page 2025

  41. [41]

    Qiang, T

    X.-B. Qiang, T. Liu, Z.-X. Gao, H.-Z. Lu, and X. C. Xie, A Clarification on Quantum-Metric-Induced Nonlinear Transport, Adv. Sci.13, e14818 (2026)

    work page 2026

  42. [42]

    Absence of Quantum-Metric-Induced Intrinsic Longitudinal Response

    P. Tang, Absence of Quantum-Metric-Induced Intrinsic Longi- tudinal Response, arXiv:2605.02750 [cond-mat.mes-hall]

    work page internal anchor Pith review Pith/arXiv arXiv

  43. [43]

    Ulrich, J

    Y . Ulrich, J. Mitscherling, L. Classen, and A. P. Schnyder, Quantum geometric origin of the intrinsic nonlinear Hall effect, Phys. Rev. B113, L201107 (2026)

    work page 2026

  44. [44]

    Guo, X.-Y

    Z. Guo, X.-Y . Liu, H. Wang, L.-k. Shi, and K. Chang, Dissipation-Shaped Quantum Geometry in Nonlinear Trans- port, Phys. Rev. Lett.136, 206303 (2026)

    work page 2026

  45. [45]

    T. Anan, S. Kitamura, and T. Morimoto, Nonreciprocal cur- rent induced by dissipation in time-reversal symmetric systems, arXiv:2604.04520 [cond-mat.mes-hall]

    work page internal anchor Pith review Pith/arXiv arXiv

  46. [46]

    Rigolin, G

    G. Rigolin, G. Ortiz, and V . H. Ponce, Beyond the quantum adiabatic approximation: Adiabatic perturbation theory, Phys. Rev. A78, 052508 (2008)

    work page 2008

  47. [47]

    C. D. Grandi and A. Polkovnikov, Adiabatic Perturbation The- ory: From Landau–Zener Problem to Quenching Through a Quantum Critical Point, inQuantum Quenching, Annealing and Computation(Springer Berlin Heidelberg, 2010) pp. 75–114

    work page 2010

  48. [48]

    Kitamura, N

    S. Kitamura, N. Nagaosa, and T. Morimoto, Current response of nonequilibrium steady states in the Landau-Zener problem: Nonequilibrium Green’s function approach, Phys. Rev. B102, 245141 (2020)

    work page 2020

  49. [49]

    B ¨uttiker, Four-Terminal Phase-Coherent Conductance, Phys

    M. B ¨uttiker, Four-Terminal Phase-Coherent Conductance, Phys. Rev. Lett.57, 1761 (1986)

    work page 1986

  50. [50]

    Jauho, N

    A.-P. Jauho, N. S. Wingreen, and Y . Meir, Time-dependent transport in interacting and noninteracting resonant-tunneling systems, Phys. Rev. B50, 5528 (1994)

    work page 1994

  51. [51]

    Terada, S

    I. Terada, S. Kitamura, H. Watanabe, and H. Ikeda, Limita- tions and improvements of the relaxation time approximation in the quantum master equation: Linear conductivity in insulat- ing systems, Phys. Rev. B109, L180302 (2024)

    work page 2024

  52. [52]

    Terada, S

    I. Terada, S. Kitamura, H. Watanabe, and H. Ikeda, Problem of Nonlinear Conductivity within Relaxation Time Approxima- tion in Noncentrosymmetric Insulators, Phys. Status Solidi B 262, 2400533 (2025)

    work page 2025

  53. [53]

    D. J. Passos, G. B. Ventura, J. M. V . P. Lopes, J. M. B. L. d. Santos, and N. M. R. Peres, Nonlinear optical responses of crys- talline systems: Results from a velocity gauge analysis, Phys. Rev. B97, 235446 (2018)

    work page 2018

  54. [54]

    G. B. Ventura, D. J. Passos, J. M. B. Lopes dos Santos, J. M. Viana Parente Lopes, and N. M. R. Peres, Gauge covariances and nonlinear optical responses, Phys. Rev. B96, 035431 (2017)

    work page 2017