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arxiv: 2604.28184 · v1 · submitted 2026-04-30 · ❄️ cond-mat.mes-hall

Recognition: unknown

Intrinsic anomalous thermal hall effect as a signature of quantum metric in d-wave altermagnets

Rishi G. Gopalakrishnan , Srimayi Korrapati , Sumanta Tewari
Authors on Pith no claims yet

Pith reviewed 2026-05-07 06:38 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords anomalous thermal Hall effectquantum metricaltermagnetsd-wave symmetryBerry connectionnonlinear transportintrinsic responsethermal Hall conductivity
0
0 comments X

The pith

Crystalline symmetry in d-wave altermagnets cancels linear and second-order anomalous thermal Hall currents, leaving a third-order response driven by the nonlinear thermal Berry-connection polarizability.

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

The paper establishes that d-wave altermagnets generate a transverse heat current from a longitudinal temperature gradient with no magnetic field applied. Crystalline symmetry eliminates the usual linear contribution from Berry curvature and the quadratic contribution from the thermal quantum metric. The leading intrinsic term is therefore cubic in the temperature gradient strength and is set by a new response function, the nonlinear thermal Berry-connection polarizability. This cubic term produces a distinctive angular pattern when the gradient direction is rotated relative to the crystal axes, together with characteristic temperature and chemical-potential dependences. These features supply experimentally testable signatures of quantum geometry in heat transport.

Core claim

In d-wave altermagnets the intrinsic Berry curvature-driven linear and the thermal quantum-metric-driven second-order anomalous thermal Hall currents both vanish as a consequence of crystalline symmetry. The first nonvanishing contribution to the transverse heat current therefore arises at third order in the temperature gradient and is governed by a nonlinear thermal Berry-connection polarizability, a quantity introduced in this work.

What carries the argument

Nonlinear thermal Berry-connection polarizability: the third-order response coefficient that encodes the leading intrinsic thermal Hall conductivity after symmetry cancellation of lower-order Berry-curvature and quantum-metric terms.

If this is right

  • The anomalous thermal Hall conductance exhibits a characteristic angular dependence as the thermal gradient is rotated with respect to the crystal axes.
  • Distinctive temperature and chemical-potential dependences appear in the third-order response that can be tested experimentally.
  • Altermagnets serve as a platform for exploring intrinsic, scattering-time-independent geometric transport phenomena.

Where Pith is reading between the lines

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

  • Similar third-order thermal responses should appear in other altermagnets whose symmetry likewise forbids linear and quadratic terms.
  • The approach of introducing a nonlinear polarizability can be applied to calculate higher-order geometric contributions in additional symmetry-protected systems.
  • Material-specific computations of the polarizability would allow quantitative comparison with transport measurements in candidate compounds.

Load-bearing premise

Crystalline symmetry exactly cancels the linear and second-order contributions to the anomalous thermal Hall current in these altermagnets.

What would settle it

A measurement that finds the transverse heat current scaling linearly or quadratically with temperature-gradient magnitude, or that shows an angular dependence inconsistent with the predicted third-order form, would falsify the dominance of the nonlinear polarizability.

Figures

Figures reproduced from arXiv: 2604.28184 by Rishi G. Gopalakrishnan, Srimayi Korrapati, Sumanta Tewari.

Figure 1
Figure 1. Figure 1: Variation of the factors F xx + Ω z + (top panel), F xy + Ω z + (bottom panel) in Eq. (16) over the kx − ky plane. We note that F xx T ,=Ω z is even in kx and ky which makes the BZ in￾tegral of this quantity finite, resulting in ηabcc ̸= 0. On the other hand, F xy T ,+Ω z + is odd in both kx and ky and accord￾ingly integrates to zero, resulting in vanishing ηabxy and ηabyx. These factors are concentrated a… view at source ↗
Figure 2
Figure 2. Figure 2: Variation of the third order thermal Hall conduc view at source ↗
Figure 3
Figure 3. Figure 3: Variation of the third order thermal Hall conductiv view at source ↗
read the original abstract

We investigate the intrinsic anomalous thermal Hall effect in d-wave altermagnets, where a transverse heat current is generated by a longitudinal temperature gradient in the absence of a magnetic field, with the leading response proportional to $(\nabla T)^3$. In these systems, the intrinsic Berry curvature-driven linear and thermal quantum-metric-driven second-order anomalous thermal Hall currents vanish as a consequence of crystalline symmetry. We show that the first nonvanishing contribution arises at third order in the temperature gradient and is governed by a nonlinear thermal Berry-connection polarizability, a quantity introduced in this work. Our analysis reveals a distinctive angular dependence of the anomalous thermal Hall conductance as the applied thermal gradient is rotated with respect to the crystal axes. We also find characteristic temperature and chemical-potential dependences that can be tested experimentally. These results identify unique quantum geometry-induced thermal responses and establish altermagnets as a promising platform for exploring intrinsic (i.e., scattering-time-independent) geometric transport phenomena.

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 / 2 minor

Summary. The manuscript examines the intrinsic anomalous thermal Hall effect (ATHE) in d-wave altermagnets. It asserts that crystalline symmetry forces the linear (Berry-curvature) and quadratic (quantum-metric) contributions to the transverse heat current to vanish identically, so that the leading intrinsic response appears at third order in the temperature gradient and is controlled by a newly defined nonlinear thermal Berry-connection polarizability. The work derives the angular dependence of the resulting ATHE conductance when the thermal gradient is rotated relative to the crystal axes and predicts characteristic temperature and chemical-potential scalings that could be tested experimentally.

Significance. If the symmetry cancellation and the third-order derivation are correct, the paper supplies a concrete, scattering-independent signature of quantum geometry in thermal transport that is unique to the altermagnetic point group. The predicted angular anisotropy and the explicit temperature/chemical-potential dependence constitute falsifiable predictions that could distinguish this mechanism from extrinsic or lower-order contributions. The introduction of the nonlinear thermal Berry-connection polarizability extends the existing toolkit of geometric response functions and may find use in other symmetry-constrained systems.

major comments (2)
  1. [Symmetry analysis (likely §2–3 or Appendix A)] The central claim that linear and second-order ATHE tensors vanish identically rests on symmetry. The abstract states this cancellation occurs “as a consequence of crystalline symmetry,” yet the manuscript does not appear to contain an explicit decomposition of the relevant Kubo or semiclassical response tensors under the d-wave altermagnet little group (typically D4h or a subgroup with alternating spin texture). Without a table or appendix listing the allowed components of the first-, second-, and third-rank thermal Hall tensors and showing that all entries permitted by the point group are zero for the lower orders, it remains possible that a nonzero component survives for generic orientations of ∇T. This tensor analysis is load-bearing for the assertion that the third-order term is the leading intrinsic contribution.
  2. [Definition of the polarizability and derivation of the third-order current (likely §4)] The nonlinear thermal Berry-connection polarizability is introduced as the quantity that governs the (∇T)^3 response. The manuscript should provide its explicit microscopic expression (in terms of Berry connections, quantum metric, or interband matrix elements) and demonstrate how it is obtained from the appropriate third-order Kubo correlator or semiclassical expansion. If this definition reduces to a combination of already-known geometric quantities, the novelty of the polarizability needs to be clarified; if it is genuinely new, its gauge invariance and symmetry properties under the altermagnetic group should be verified explicitly.
minor comments (2)
  1. [Figures 2–4] Figure captions and axis labels should explicitly state the crystal axes relative to which the thermal gradient is rotated, so that the reported angular dependence can be directly compared with experiment.
  2. [Numerical results section] The temperature and chemical-potential dependence plots would benefit from an overlay of the expected power-law or Fermi-surface scaling derived analytically, to make the connection between numerics and the analytic third-order formula transparent.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive comments on the symmetry analysis and the definition of the nonlinear thermal Berry-connection polarizability. We agree that both points can be strengthened with additional explicit details and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: The central claim that linear and second-order ATHE tensors vanish identically rests on symmetry. The abstract states this cancellation occurs “as a consequence of crystalline symmetry,” yet the manuscript does not appear to contain an explicit decomposition of the relevant Kubo or semiclassical response tensors under the d-wave altermagnet little group (typically D4h or a subgroup with alternating spin texture). Without a table or appendix listing the allowed components of the first-, second-, and third-rank thermal Hall tensors and showing that all entries permitted by the point group are zero for the lower orders, it remains possible that a nonzero component survives for generic orientations of ∇T. This tensor analysis is load-bearing for the assertion that the third-order term is the leading intrinsic contribution.

    Authors: We agree that an explicit tensor decomposition under the relevant point group would make the symmetry argument more transparent. In the revised manuscript we will add a new Appendix A that performs this analysis for the D4h little group appropriate to d-wave altermagnets (including the alternating spin texture). The appendix will tabulate the independent components of the rank-2 (linear), rank-3 (quadratic), and rank-4 (cubic) thermal Hall response tensors allowed by the point group and explicitly demonstrate that all components of the first two tensors are forced to zero while several components of the third-order tensor remain finite. This will also address possible generic orientations of ∇T. revision: yes

  2. Referee: The nonlinear thermal Berry-connection polarizability is introduced as the quantity that governs the (∇T)^3 response. The manuscript should provide its explicit microscopic expression (in terms of Berry connections, quantum metric, or interband matrix elements) and demonstrate how it is obtained from the appropriate third-order Kubo correlator or semiclassical expansion. If this definition reduces to a combination of already-known geometric quantities, the novelty of the polarizability needs to be clarified; if it is genuinely new, its gauge invariance and symmetry properties under the altermagnetic group should be verified explicitly.

    Authors: We thank the referee for this request. In the revised Section 4 we will derive the nonlinear thermal Berry-connection polarizability from the third-order semiclassical expansion of the heat current (equivalently, the third-order Kubo correlator). The explicit expression will be written in terms of interband Berry connections and the quantum metric; we will show that it is a distinct nonlinear combination that does not reduce to previously defined geometric quantities. Gauge invariance will be verified by expressing the polarizability through manifestly gauge-invariant combinations of matrix elements. We will also discuss its transformation properties under the altermagnetic symmetry group and confirm that the allowed components reproduce the angular dependence reported in the main text. revision: yes

Circularity Check

0 steps flagged

No circularity; new polarizability defined independently and symmetry cancellation treated as external input

full rationale

The paper introduces the nonlinear thermal Berry-connection polarizability as a new quantity in this work and states that linear and second-order terms vanish due to crystalline symmetry of d-wave altermagnets. No quoted equation or derivation reduces the third-order result to a fitted parameter, a self-referential definition, or a load-bearing self-citation chain. The symmetry argument is presented as a consequence of the point group rather than derived from the target response itself, keeping the central claim independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Review performed on abstract only; full list of assumptions, parameters, and derivations is unavailable. The ledger below records only the symmetry assumption explicitly mentioned in the abstract.

axioms (1)
  • domain assumption Crystalline symmetry of d-wave altermagnets forces the linear and second-order intrinsic anomalous thermal Hall currents to vanish.
    Stated directly in the abstract as the reason lower-order terms disappear.
invented entities (1)
  • nonlinear thermal Berry-connection polarizability no independent evidence
    purpose: To describe the third-order anomalous thermal Hall response and link it to the quantum metric
    Explicitly introduced in this work according to the abstract; no independent experimental evidence is provided.

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Reference graph

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