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arXiv:2604.11527

Semiclassical theory of frequency dependent linear magneto-optical transport in Weyl semimetals

Azaz Ahmad, Pankaj Bhalla, Snehasish Nandy, Tanay Nag

cond-mat.mes-hallquant-phSubmitted Apr 13, 2026• Announced Apr 14, 2026
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Abstract

We develop a semiclassical Boltzmann theory for frequency-dependent magneto-optical transport in Weyl semimetals (WSMs), incorporating momentum-dependent relaxation via a scattering matrix approach. The interplay of orbital magnetic moment, Weyl cone tilt, intervalley scattering, and electromagnetic driving is analyzed to obtain the full conductivity tensor in the presence of a static magnetic field. For untilted WSMs with orbital magnetic moment, strong intervalley scattering in the weak ac regime induces a sign reversal of the longitudinal magneto-optical conductivity (LMOC), thereby suppressing the chiral anomaly. In contrast, in the strong ac regime, intervalley scattering fails to neutralize the chiral imbalance within a driving cycle, and no sign reversal is observed. Orbital magnetic moment induces linear magnetic-field contributions, while chiral anomaly yields quadratic response accompanied by expected angular profiles. Tilt direction and orientation strongly affect LMOC such as, transverse tilt gives symmetric non-monotonic behavior, whereas parallel tilt leads to asymmetric, nearly monotonic response. Notably, negative LMOC arises intrinsically for parallel tilt, but requires orbital magnetic moment for transverse tilt. These results highlight frequency-dependent conductivity as a sensitive probe of chiral relaxation in MHz-THz magneto-optical experiments.

Comments
15 pages, 11 figures

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We develop a semiclassical Boltzmann theory for frequency-dependent magneto-optical transport in Weyl semimetals (WSMs), incorporating momentum-dependent relaxation via a scattering matrix approach. The interplay of orbital magnetic moment, Weyl cone tilt, intervalley scattering, and electromagnetic driving is analyzed to obtain the full conductivity tensor in the presence of a static magnetic field. For untilted WSMs with orbital magnetic moment, strong intervalley scattering in the weak ac regime induces a sign reversal of the longitudinal magneto-optical conductivity (LMOC), thereby suppressing the chiral anomaly. In contrast, in the strong ac regime, intervalley scattering fails to neutralize the chiral imbalance within a driving cycle, and no sign reversal is observed. Orbital magnetic moment induces linear magnetic-field contributions, while chiral anomaly yields quadratic response accompanied by expected angular profiles. Tilt direction and orientation strongly affect LMOC such as, transverse tilt gives symmetric non-monotonic behavior, whereas parallel tilt leads to asymmetric, nearly monotonic response. Notably, negative LMOC arises intrinsically for parallel tilt, but requires orbital magnetic moment for transverse tilt. These results highlight frequency-dependent conductivity as a sensitive probe of chiral relaxation in MHz-THz magneto-optical experiments.
Abstract In this work, we describe a toolbox to realize and probe synthetic axial gauge fields in engineered Weyl semimetals. These synthetic electromagnetic fields, which are sensitive to the chirality associated with Weyl nodes, emerge due to spatially and temporally dependent shifts of the corresponding Weyl momenta. First, we introduce two realistic models, inspired by recent cold-atom developments, which are particularly suitable for the exploration of these synthetic axial gauge fields. Second, we describe how to realize and measure the effects of such axial fields through center-of-mass observables, based on semiclassical equations of motion and exact numerical simulations. In particular, we suggest realistic protocols to reveal an axial Hall response due to the axial electric field E 5 , as well as axial cyclotron orbits and chiral pseudo-magnetic effect due to the axial magnetic field B 5 .
Although Weyl semimetals have been extensively studied for exploring rich topological physics, the direct observation of the celebrated chiral magnetic effect (CME) associated with the so-called dipolar chiral anomaly has long intrigued and challenged physicists, still remaining elusive in nature.Here we propose a feasible scheme for experimental implementation of ultracold atoms that may enable us to probe the CME with a pure topological current in an artificial Weyl semimetal.The paired Weyl points with the dipolar chiral anomaly emerge in the presence of the well-designed spin-orbital coupling and laser-assisted tunneling.Both of the two artificial fields are readily realizable and highly tunable via current optical techniques using ultracold atoms trapped in threedimensional optical lattices, providing a reliable way for manipulating Weyl points in the momentum-energy space.By applying a weak artificial magnetic field, the system processes an auxiliary current originated from the topology of a paired Weyl points, namely, the pure CME current.This topological current can be extracted from measuring the center-of-mass motion of ultracold atoms, which may pave the way to directly and unambiguously observe the CME in experiments.
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Using two approaches to strongly correlated systems, the extremely correlated Fermi liquid theory and the dynamical mean field theory, we compute the transverse transport coefficients, namely, the Hall constants RH{R}_{H}RH​ and Hall angles ${\ensuremath{\theta}}_{H}$, and the longitudinal and transverse optical response of the $U=\ensuremath{\infty}$ Hubbard model in the limit of infinite dimensions. We focus on two successive low-temperature regimes, the Gutzwiller-correlated Fermi liquid (GCFL) and the Gutzwiller-correlated strange metal (GCSM). We find that the Hall angle $cot{\ensuremath{\theta}}_{H}$ is proportional to T2{T}^{2}T2 in the GCFL regime, while upon warming into the GCSM regime it first passes through a downward bend and then continues as T2{T}^{2}T2. Equivalently, RH{R}_{H}RH​ is weakly temperature dependent in the GCFL regime, but becomes strongly temperature dependent in the GCSM regime. Drude peaks are found for both the longitudinal optical conductivity ${\ensuremath{\sigma}}_{xx}(\ensuremath{\omega})$ and the optical Hall angles $tan{\ensuremath{\theta}}_{H}(\ensuremath{\omega})$ below certain characteristic energy scales. By comparing the relaxation rates extracted from fitting to the Drude formula, we find that in the GCFL regime there is a single relaxation rate controlling both longitudinal and transverse transport, while in the GCSM regime two different relaxation rates emerge. We trace the origin of this behavior to the dynamical particle-hole asymmetry of the Dyson self-energy, arguably a generic feature of doped Mott insulators.
Studies of the 3D quantum Hall effect (QHE) have primarily emphasized transport features that mimic the well-established 2D QHE. In this work, we show that qualitatively new features arise when an in-plane magnetic field is applied to a 3D Weyl semimetal in the quantum Hall regime. An unexpected Hall quantum oscillation, distinct from the Weyl-orbit oscillation, coexists with the QHE, along with an unquantized two-terminal magnetoresistance. Moreover, unconventional antichiral transmission enables a peculiar disorder-robust negative longitudinal resistance. Quantization tunable by the lead configuration is further found in this transport geometry. A unique type of nonlocal quantum backscattering channels underlies these phenomena. Our work demonstrates a breakdown of the topological characterization of transport even with 3D Chern numbers and reveals hidden 3D QHE transport properties. It opens a new class of transport measurements and phenomena.
The quasi-particle excitations in Weyl semimetals, known as Weyl fermions, are usually forced to emerge in charge-conjugate pairs by the Nielsen--Ninomiya theorem. When the Brillouin zone is non-orientable, this constraint is replaced by a Z2\mathbb{Z}_2Z2​ charge cancellation, as a result of the chirality becoming ill-defined on such manifolds; this results in configurations with seemingly non-zero total chirality. Here, we set out to explain this behaviour from a purely topological perspective, and provide a classification of non-orientable Weyl semimetal topology in terms of exact sequences of twisted (co)homology groups. This leads to several discoveries of direct physical importance: in particular, we recover the Z2\mathbb{Z}_2Z2​ charge cancellation in a coordinate-independent way, allowing meaningful limits to be set on its physical interpretation. A detailed discussion is provided on a specific Klein bottle-like topology induced by a momentum-space glide symmetry, including a full review of the insulating and semimetallic invariants of the system and a classification of the surface states on the non-orientable boundary. Beyond this, we provide a complete survey of all possible non-orientable Brillouin zones and their associated invariants, and extend our formalism into the realm of non-Hermitian topological physics and inversion-symmetric Weyl semimetals. Our work exemplifies the vast potential of fundamental mathematical descriptions to not only aid the corresponding physical intuition, but also predict novel and hitherto overlooked phenomena of great relevance throughout the physics research forefront.