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arxiv: 2604.20592 · v1 · submitted 2026-04-22 · ❄️ cond-mat.mes-hall

Disorder induced time-reversal-odd nonlinear spin and orbital Hall effects

Ruda Guo , Yi Liu , Cong Xiao , Zhe Yuan This is my paper

Pith reviewed 2026-05-09 23:05 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords nonlinear Hall effecttime-reversal odd transportspin Hall effectorbital Hall effectdisorder scatteringside-jump mechanismskew scatteringBerry curvature dipole
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0 comments X

The pith

Disorder generates second-order time-reversal-odd nonlinear spin and orbital Hall currents, with the orbital part often larger than the spin part.

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

The paper builds a theory for second-order T-odd angular-momentum currents that include both spin and orbital pieces. These currents arise from Berry curvature dipoles but also from several disorder mechanisms: coordinate shift, side-jump currents, anomalous scattering, and skew scattering. A single scaling relation is derived that lets some of these contributions be separated experimentally. Model calculations show the orbital component can match or exceed the spin component. The work supplies a framework for understanding T-odd nonlinear transport in real materials.

Core claim

We develop a theory for the second-order time-reversal-odd (T-odd) angular-momentum current, incorporating both spin and orbital components. We reveal that besides spin and orbital Berry curvature dipoles, T-odd nonlinear angular-momentum current can originate from disorder-induced mechanisms including coordinate shift, side-jump spin and orbital currents, anomalous scattering amplitude, and skew scattering. A general scaling relation is derived to help distinguish some of these contributions in experiments. Model calculations demonstrate that the orbital component can be comparable to and much larger than the spin component.

What carries the argument

Disorder-induced mechanisms (coordinate shift, side-jump spin and orbital currents, anomalous scattering amplitude, skew scattering) together with a derived scaling relation that separates their contributions to the second-order T-odd angular-momentum current.

If this is right

  • Nonlinear T-odd transport measurements can separate disorder contributions using the scaling relation.
  • Orbital angular-momentum currents must be included when modeling nonlinear Hall responses, as they can dominate the spin part.
  • The theory applies to both spin and orbital degrees of freedom in the same formal framework.
  • Clean-limit Berry-curvature-dipole contributions can be isolated from disorder terms by varying sample quality.

Where Pith is reading between the lines

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

  • Device geometries that rely on nonlinear angular-momentum injection could be tuned by controlling disorder type and density.
  • The same mechanisms may appear in other second-order responses such as nonlinear thermal or thermoelectric transport.
  • Extension to three-dimensional systems or interfaces would require checking whether the scaling relation remains material-independent.

Load-bearing premise

The listed disorder mechanisms act additively and can be separated by a single scaling relation without material-specific mixing or higher-order corrections.

What would settle it

An experiment on a disordered sample in which the measured second-order T-odd Hall conductivity fails to follow the predicted scaling with impurity density or scattering strength would falsify the separability of the mechanisms.

Figures

Figures reproduced from arXiv: 2604.20592 by Cong Xiao, Ruda Guo, Yi Liu, Zhe Yuan.

Figure 1
Figure 1. Figure 1: FIG. 1. Results obtained from the tilted four-band Dirac model in Eq. ( [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

We develop a theory for the second-order time-reversal-odd ($\mathcal{T}$-odd) angular-momentum current, incorporating both spin and orbital components. We reveal that besides spin and orbital Berry curvature dipoles, $\mathcal{T}$-odd nonlinear angular-momentum current can originate from disorder-induced mechanisms including coordinate shift, side-jump spin and orbital currents, anomalous scattering amplitude, and skew scattering. A general scaling relation is derived to help distinguish some of these contributions in experiments. Model calculations demonstrate that the orbital component can be comparable to and much larger than the spin component. Our theory lays the groundwork for $\mathcal{T}$-odd nonlinear spin and orbital 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 / 2 minor

Summary. The paper develops a theory for second-order time-reversal-odd (T-odd) angular-momentum currents that includes both spin and orbital components. It identifies contributions from spin and orbital Berry curvature dipoles as well as disorder-induced mechanisms (coordinate shift, side-jump spin/orbital currents, anomalous scattering amplitude, and skew scattering). A general scaling relation is derived to distinguish some of these contributions experimentally, and model calculations are presented showing that the orbital component can be comparable to or much larger than the spin component. The work aims to lay groundwork for T-odd nonlinear spin and orbital transport.

Significance. If the scaling relation and model results hold without unaccounted mixing terms, the paper would provide a useful framework for interpreting and separating disorder contributions to nonlinear angular-momentum transport, extending prior work on nonlinear Hall effects to include orbital degrees of freedom. The explicit comparison of orbital versus spin magnitudes in models is a positive feature that could guide future experiments in mesoscopic systems.

major comments (2)
  1. [§3] §3 (scaling relation derivation): The central scaling relation that separates coordinate shift, side-jump, anomalous scattering, and skew scattering assumes these mechanisms remain additive and produce distinct power-law dependencies on disorder strength or relaxation time. The derivation does not explicitly include or bound interference/cross terms (e.g., products of side-jump and skew amplitudes) that appear at the same perturbative order in multi-band systems; if such terms alter the effective exponents, both the experimental separability claim and the relative-magnitude conclusion are weakened.
  2. [Model calculations] Model calculations section (near Eq. (scaling) and numerical results): The demonstration that orbital contributions exceed spin ones relies on specific tight-binding or continuum models. The manuscript does not show that the orbital dominance survives when band-structure details or higher-order scattering are varied, nor does it provide a general condition under which the orbital term is parametrically larger; this is load-bearing for the claim that orbital effects can be 'much larger'.
minor comments (2)
  1. [Introduction] Notation for the T-odd angular-momentum current (J_L) and its spin/orbital decomposition is introduced without a clear comparison table to the conventional nonlinear Hall current; adding such a table would improve readability.
  2. [Introduction] The abstract and introduction cite prior nonlinear Hall literature but omit explicit references to recent orbital Hall effect papers (e.g., works on orbital Berry curvature in 2D materials); a short additional paragraph would strengthen context.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help clarify the scope and limitations of our results. We address each major comment below and will revise the manuscript to incorporate the suggested improvements.

read point-by-point responses

  1. Referee: §3 (scaling relation derivation): The central scaling relation that separates coordinate shift, side-jump, anomalous scattering, and skew scattering assumes these mechanisms remain additive and produce distinct power-law dependencies on disorder strength or relaxation time. The derivation does not explicitly include or bound interference/cross terms (e.g., products of side-jump and skew amplitudes) that appear at the same perturbative order in multi-band systems; if such terms alter the effective exponents, both the experimental separability claim and the relative-magnitude conclusion are weakened.

    Authors: We appreciate the referee pointing out the need to address possible cross terms explicitly. Our scaling relation is derived within the semiclassical Boltzmann framework by isolating the leading-order contributions of each mechanism in the dilute-disorder limit, where the T-odd nonlinear response is linear in the impurity concentration for skew scattering and quadratic for side-jump and coordinate-shift terms. Products of distinct scattering amplitudes (e.g., side-jump × skew) enter only at higher perturbative orders due to the additional momentum relaxation factors and the time-reversal-odd symmetry constraints; they therefore do not modify the leading power-law exponents. To make this bound transparent, we will add a short paragraph in the revised §3 that enumerates the perturbative orders and shows why interference terms remain sub-leading for the quantities of interest. revision: yes

  2. Referee: Model calculations section (near Eq. (scaling) and numerical results): The demonstration that orbital contributions exceed spin ones relies on specific tight-binding or continuum models. The manuscript does not show that the orbital dominance survives when band-structure details or higher-order scattering are varied, nor does it provide a general condition under which the orbital term is parametrically larger; this is load-bearing for the claim that orbital effects can be 'much larger'.

    Authors: We agree that robustness checks strengthen the claim. The orbital dominance observed in our calculations originates from the parametrically larger orbital magnetic moments and interband matrix elements relative to their spin counterparts, a feature generic to systems with strong atomic spin-orbit coupling and multi-orbital character. In the revised manuscript we will (i) present additional numerical results for varied Rashba strengths, lattice constants, and impurity potentials, confirming that the orbital-to-spin ratio remains greater than unity over a broad parameter window, and (ii) derive a simple analytic estimate showing that the orbital term is larger whenever the orbital Berry curvature dipole exceeds the spin one by a factor set by the ratio of orbital to spin angular-momentum matrix elements. These additions will make the generality of the conclusion explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity; scaling relation and model results are derived from transport equations rather than imposed by definition or self-citation

full rationale

The paper derives a general scaling relation from perturbative transport theory to separate coordinate-shift, side-jump, anomalous-scattering, and skew-scattering contributions to the T-odd nonlinear angular-momentum current. Model calculations then evaluate the relative size of orbital versus spin components under that relation. No equation is shown to reduce to its own input by construction, no fitted parameter is relabeled as a prediction, and no load-bearing uniqueness claim rests solely on prior self-citation. The derivation remains self-contained against external benchmarks once the stated assumptions (additivity at the considered perturbative order) are granted; any concern about missing higher-order mixing terms is a question of completeness, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard semiclassical transport theory extended to nonlinear T-odd responses; no new free parameters, invented particles, or ad-hoc entities are introduced in the abstract.

axioms (2)
  • standard math Semiclassical Boltzmann transport framework applies to second-order nonlinear responses
    Used to derive currents from scattering and Berry curvature terms.
  • domain assumption Disorder scattering can be classified into coordinate shift, side-jump, anomalous, and skew channels
    Invoked to generate the T-odd nonlinear angular-momentum current.

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