The Hodge structure of Berry-phase transport: topology, geometry, and noise

Zhi-Wei Wang; Samuel L. Braunstein

Home/Archive/arXiv

arXiv · 2608.15789

The Hodge structure of Berry-phase transport: topology, geometry, and noise

Zhi-Wei Wang·Samuel L. Braunstein

View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that the Hodge-de Rham decomposition of the Berry curvature organises the transport of a Bloch band and its fluctuations within a single geometric structure. Splitting the curvature into $L^2$-orthogonal harmonic, exact, and co-exact sectors yields a dictionary for both moments of the current. In the mean response the harmonic sector carries the topological anomalous-Hall conductivity, the exact sector the Fermi-surface geometry and the antisymmetric Berry-curvature dipole of polar metals, and, in three dimensions, the co-exact sector the chiral anomaly, quantised by the Weyl-node charges. In the fluctuations, described by a particle-conserving stochastic Boltzmann equation constrained by the fluctuation-dissipation theorem (FDT), the harmonic sector is silent, so topological transport is noiseless, while the field-driven noise is sourced by the geometric sectors (solely the exact sector in two dimensions); current-noise spectroscopy therefore separates global band topology from local band geometry. We prove that the harmonic null-space protection is dimension-independent, and we settle the remaining sector: the co-exact (monopole) sector carries no conservation law and, under the thermal sampling measure, mixes with the exact sector at $\mathcal{O}(1)$, so it furnishes no clean noise observable. The separation the noise provides is therefore two-way, topology versus geometry, in both two and three dimensions.

Explore related subjects

cond-mat.mes-hall cond-mat.stat-mech cond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Zhi-Wei Wang, Samuel L. Braunstein. 2026-08-16. The Hodge structure of Berry-phase transport: topology, geometry, and noise. https://arxiv.org/abs/2608.15789

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Emergence of spin-orbit coupling among spin, atomic orbital, and Bloch dynamics in Janus double-transition-metal MXenes

We found a spin-orbit coupling to cause a simultaneous correlation among three degrees of freedom, the electronic spin, orbital, and Bloch dynamics in an investigation into the electronic structure of Janus double-transition-metal MXenes, Mo$_2$HfC$_2$OS and W$_2$HfC$_2$OS. In this paper, it is also revealed that the spin-orbit coupling causes a staggered spin configuration with a trigonal pattern around the $\Gamma$ point near the insulating gap. We developed a reduced Hamiltonian describing the electronic states and show that the spin-orbit coupling cannot be equated with conventional forms for a single electron in solids, LS, Rashba, and Dresselhaus couplings, even in the approximation under the low-energy and small wave number condition. Because of the intrinsic shape of the conduction band, a trigonally alternating spin-momentum locking emerges with the spin axis perpendicular to the layer plane. The theoretical analysis shows that these Janus materials can provide a platform for exploring the spin-related phenomena due to the trigonal spin-momentum locking other than Rashba and Dresselhaus types.

cond-mat.mes-hall↗

arXiv2026

A substrate booster for P-type 2D ferromagnetic semiconductor

Spin transistors with its both charge and spin properties tuned via electrostatic gating are believed capable for widespread use, which however have proven challenging due to the extreme rareness of their physical base -- magnetic semiconductors. The latter are limited within very few systems including diluted magnetic semiconductors (DMS) and two-dimensional ferromagnetic semiconductors (2D-FMS), and known to suffer from inadequate gate-tunability of their electric and/or magnetic properties. Here, we show a substrate engineering paradigm by interfacing few-layered Cr$_{2}$Ge$_{2}$Te$_{6}$ (FL-CGT) with an antiferromagnetic insulator CrOCl. Owing to the subtle interfacial charge transfer couplings, CGT can be drastically turned from an ambipolar semiconductor into a high performance P-type semiconductor. When cooled below the Curie temperature, the ON-OFF ratio in such substrate-boosted FMS field-effect transistor (FET) reaches 10$^{5}$ with its coercive field $H_{c}$ of magnetic hysteresis loop tunable by a factor of more than 200$\%$, enabling {gate-assisted magnetic switching in the prototype semiconducting spin transistor architecture}. A crossover from critical power-law scaling to a dual power-law behaviour under heavy hole doping was further observed. Our findings {signify} an efficient interfacial charge transfer and electrically modulated magnetic anisotropy energy supported by calculations. This high performance P-type FMS-FET system suggests that active substrate-boosting paradigm might be a powerful path for the investigation of future gate-tunable spintronic devices.

cond-mat.mes-hall↗

arXiv2026

In-plane magnetic field control of anomalous Hall response enabled by magnetic anisotropy engineering

Engineering magnetic anisotropy provides a powerful route to control magnetization orientation and unlock emerging functionalities in opto-spintronic and current-driven devices. Beyond its role in magnetization reversal, the effective anisotropy can strongly influence the magnetotransport response, offering an additional degree of freedom to tune new device functionalities. In this work, we report a magnetotransport study of a ferrimagnetic [Tb/Co]$_{\times 5}$ multilayer grown with a Tb thickness gradient, whose wedge-shaped tilts the uniaxial anisotropy axis slightly away from the film normal. Anomalous Hall resistivity measurements from 80 K to 300 K reveal a spin reorientation transition, while the angular dependence of the magnetotransport responses exposes the crucial role of the tilted anisotropy. A simplified macrospin model reproduces the full angular response across the transition and shows that the observed anomalous Hall effect when the in-plane magnetic field is applied originates from the tilt of the uniaxial anisotropy axis, which supplies a built-in symmetry-breaking mechanism, enabling in-plane field control over the out-of-plane anomalous Hall response, sign included. These findings establish tilted magnetic anisotropy as a promising route toward Hall effect-based sensor applications and highlight Tb/Co multilayers as a versatile platform for anisotropy-engineered spintronic devices.

cond-mat.mes-hall↗