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arxiv: 2505.16999 · v2 · submitted 2025-05-22 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Nonlinear thermal and thermoelectric transport from quantum geometry

Yuan Fang , Shouvik Sur , Yonglong Xie , Qimiao Si This is my paper

Pith reviewed 2026-05-22 01:19 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords quantum geometrynonlinear transportthermal transportthermoelectric responseBerry curvature dipolequantum metric dipoleWiedemann-Franz relationMott relation
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0 comments X

The pith

Nonlinear thermal and thermoelectric transport is controlled by quantum geometry through relations parallel to the Wiedemann-Franz and Mott laws.

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 responses in heat and electric current carry direct signatures of quantum geometry, specifically through Berry curvature dipole and quantum metric dipole. These signatures produce a set of interconnected relations among the nonlinear conductivities that mirror the classic Wiedemann-Franz relation between thermal and electrical conductivity and the Mott relation between thermoelectric and electrical response. A reader would care because the result supplies new experimental routes to measure quantum geometry in time-reversal-invariant, inversion-broken systems and in systems with broken time-reversal symmetry, with direct relevance to materials such as Weyl-Kondo semimetals and Bernal bilayer graphene.

Core claim

Nonlinear thermal and thermoelectric transport coefficients are generated by quantum geometry contributions (Berry curvature dipole with time-reversal symmetry and quantum metric dipole when time-reversal is broken) and these coefficients obey a network of exact relations that parallel the standard Wiedemann-Franz and Mott relations.

What carries the argument

Berry curvature dipole and quantum metric dipole, which enter the nonlinear response functions and enforce the geometric identities that link the various thermal, thermoelectric, and electrical conductivities.

If this is right

  • The same geometric identities allow thermal measurements to extract the magnitude of Berry curvature dipole and quantum metric dipole.
  • The relations extend the diagnostic power of nonlinear transport to systems where time-reversal symmetry is present or absent.
  • Explicit predictions exist for the nonlinear responses in Weyl-Kondo semimetals and Bernal bilayer graphene.
  • The framework supplies additional constraints that any microscopic theory of these materials must satisfy.

Where Pith is reading between the lines

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

  • If the relations hold, temperature-dependent nonlinear transport could become a standard tool for mapping quantum geometry across a wider class of topological semimetals.
  • The parallel to linear Wiedemann-Franz and Mott laws suggests that quantum geometry may impose universal constraints on higher-order responses in other correlated systems.
  • Experimental verification would motivate searches for analogous geometric relations in nonlinear responses involving spin or valley degrees of freedom.

Load-bearing premise

The nonlinear thermal and thermoelectric responses are dominated by quantum geometry contributions without significant interference from scattering or other band-structure effects.

What would settle it

A measurement in Bernal bilayer graphene or a Weyl-Kondo semimetal in which the ratio of nonlinear thermal to nonlinear electrical conductivity deviates from the predicted geometric value at low temperature would falsify the central claim.

Figures

Figures reproduced from arXiv: 2505.16999 by Qimiao Si, Shouvik Sur, Yonglong Xie, Yuan Fang.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Relations for linear order longitudinal responses. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Berry curvature dipole at [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

Quantum geometry may enable the development of quantum phases ranging from superconductivity to correlated topological states. One powerful probe of quantum geometry is the nonlinear Hall response which detects Berry curvature dipole in systems with time-reversal invariance and broken inversion symmetry. With broken time-reversal symmetry, this response is also associated with quantum metric dipole. Here we investigate nonlinear thermal and thermoelectric responses, which provide a wealth of new information about quantum geometry. In particular, we uncover a web of connections between these quantities that parallel the standard Wiedemann-Franz and Mott relations. Implications for the studies of a variety of topological systems, including Weyl-Kondo semimetals and Bernal bilayer graphene, are discussed.

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

1 major / 1 minor

Summary. The manuscript investigates nonlinear thermal and thermoelectric transport in systems with nontrivial quantum geometry. It derives a set of algebraic relations among the nonlinear thermal conductivity, thermoelectric current, and related response tensors that parallel the linear Wiedemann-Franz and Mott relations; these relations are expressed in terms of the Berry-curvature dipole and quantum-metric dipole. Implications for Weyl-Kondo semimetals and Bernal bilayer graphene are discussed.

Significance. If the reported relations survive in the full transport coefficients, the work would furnish additional experimental handles on quantum geometry beyond the nonlinear Hall effect. The semiclassical Boltzmann derivation supplies a concrete, falsifiable framework that could be tested in existing materials.

major comments (1)
  1. [Nonlinear thermal and thermoelectric response derivations] The parallel relations are obtained after projecting onto the isolated quantum-geometry dipole terms. The manuscript does not demonstrate that the same algebraic relations continue to hold once conventional velocity-matrix-element contributions and energy-dependent scattering are restored (see the Boltzmann-equation treatment of the nonlinear thermal conductivity). This projection is load-bearing for the claim that the relations are experimentally accessible.
minor comments (1)
  1. [Abstract] The abstract states the existence of the parallels but supplies neither the explicit form of the relations nor the key approximations; a short sentence listing the main relations would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive major comment. We appreciate the recognition that our work provides a semiclassical framework for nonlinear thermal and thermoelectric responses tied to quantum geometry. We address the concern below and have revised the manuscript to strengthen the generality of the reported relations.

read point-by-point responses

  1. Referee: The parallel relations are obtained after projecting onto the isolated quantum-geometry dipole terms. The manuscript does not demonstrate that the same algebraic relations continue to hold once conventional velocity-matrix-element contributions and energy-dependent scattering are restored (see the Boltzmann-equation treatment of the nonlinear thermal conductivity). This projection is load-bearing for the claim that the relations are experimentally accessible.

    Authors: We thank the referee for highlighting this important point. In the original derivation we isolated the quantum-geometry dipole contributions to emphasize the novel connections to Berry curvature and quantum metric dipoles. To address the concern, the revised manuscript now includes an extended Boltzmann-equation analysis (new subsection in Sec. III) that restores the full velocity-matrix-element terms and allows for energy-dependent scattering rates. Under the assumption of momentum-independent scattering (or scattering that preserves the relevant symmetries), we explicitly verify that the algebraic relations among the nonlinear thermal conductivity, thermoelectric current, and related tensors continue to hold. We have added a discussion of the regime in which conventional contributions remain subdominant, thereby clarifying the conditions for experimental accessibility. These additions directly respond to the load-bearing character of the projection while preserving the focus on quantum-geometry effects. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper derives expressions for nonlinear thermal and thermoelectric conductivities in terms of Berry curvature dipole and quantum metric dipole within the semiclassical Boltzmann framework, then identifies algebraic relations among those dipole contributions that mirror the linear Wiedemann-Franz and Mott forms. These relations follow directly from the structure of the integrals over the dipoles and the assumed energy-independent relaxation time; they are not obtained by fitting parameters to data and then relabeling the fit as a prediction, nor by importing a uniqueness theorem from prior self-citation. The central claim is therefore an explicit calculation rather than a tautology, and the paper states its approximations openly rather than smuggling them in via citation. No load-bearing step reduces to its own input by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the central claim rests on the domain assumption that quantum geometry controls the listed nonlinear responses in the cited material classes.

axioms (1)
  • domain assumption Quantum geometry (Berry curvature dipole and quantum metric dipole) determines the leading nonlinear thermal and thermoelectric responses in the systems of interest.
    Invoked when the abstract states that these responses 'provide a wealth of new information about quantum geometry' and parallel standard relations.

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    Drude”, “anomalous

    Useful formulas We find the transport coefficients can all be expressed in terms of the following integrals: In(Φk)≡ Z ∞ −∞ ∂ ∂µ n f0 Θ(ϵ−ϵ k)Φkdϵ ,(S32) Jn(Φk)≡ Z ∞ −∞ (ϵ−µ) ∂ ∂µ n f0 Θ(ϵ−ϵ k)Φkdϵ .(S33) whereΦ k is a function ofk,Θ(ϵ−ϵ k)is the Heaviside step function andf0 is the Fermi-Dirac distribution function. This motivates us the summarize the re...

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