Polar unidirectional magnetotransport in $p-$type tellurene from quantum geometry

TL;DR

This paper investigates the unidirectional magnetotransport in p-type tellurene, revealing that quantum geometric effects induce both chiral and polar nonlinear responses in its valence band, with implications for topologically trivial materials.

Contribution

It demonstrates that polar eMChA arises in tellurene's valence band via multiband effects and quantum metric dipoles, extending previous work on its conduction band.

Findings

Quantum metric dipoles induce polar eMChA in valence band.

Numerical results match doping-dependent second-harmonic voltage measurements.

Tellurene exhibits combined chiral and polar eMChA, explaining angular dependence shifts.

Abstract

Unidirectional magnetoresistance, or electric magnetochiral anisotropy (eMChA), is a nonlinear magnetotransport phenomenon that arises in noncentrosymmetric conductors , where changes in resistance $R(B)$ are: (i) chiral, $\Delta R(B)/R(0)=2\,\chi\, {\bf I}\cdot{\bf B}$, or (ii) polar, $\Delta R(B)/R(0)=2\,\gamma\, {\bf I}\cdot({\bf P}\times{\bf B})$, with eMChA coefficients $\chi$ and $\gamma$. In [Phys. Rev. Lett. 135, 106602 (2025)], we showed that the eMChA in the conduction band of tellurene is polar ($\chi=0$, $\gamma\neq 0$) and emerges from the quantum metric dipole due to its Weyl node and from the lone pair polarization ${\bf P}$. Here, we extend our work to the valence band of tellurene, where the eMChA is usually said to be chiral ($\chi \neq 0, \gamma = 0$). We show that also a polar coefficient $\gamma \neq 0$ emerges naturally through a downfolding procedure, in which remote Weyl-node containing bands induce momentum-space gradients of the quantum metric in the low-energy levels, activating finite metric dipoles. Combining semiclassical Boltzmann transport with a ${\bf k}\cdot{\bf p}$ description of tellurene, our numerical calculations agree quantitatively with doping ($\mu$) dependent second-harmonic measurements of the longitudinal voltage $V^{2\omega}_\parallel(\mu)$ in perpendicular field. The combined chiral and polar characters ($\chi\neq0, \gamma\neq 0)$ of the eMChA in tellurene also explains the shift in the angular ($\phi$) dependence of $V^{2\omega}_\parallel(\phi)$ for in plane fields. Our results demonstrate that the polar eMChA can arise in topologically trivial bands through multiband effects and establishes tellurene as a platform for quantum-geometric rectification in both electron and hole regimes.