Berry phase theory of planar Hall effect in topological insulators

Abstract

The appearance of negative longitudinal magnetoresistance (LMR) in topological semimetals such as Weyl and Dirac semimetals is understood as an effect of chiral anomaly, whereas such an anomaly is not well-defined in topological insulators. Nevertheless, it has been shown recently in both theory and experiments that nontrivial Berry phase effects can give rise to negative LMR in topological insulators even in the absence of chiral anomaly. In this paper, we present a quasi-classical theory of another intriguing phenomenon in topological insulators – also ascribed to chiral anomaly in Weyl and Dirac semimetals– the so-called planar Hall effect (PHE). PHE implies the appearance of a transverse voltage in the plane of applied non-parallel electric and magnetic fields, in a configuration in which the conventional Hall effect vanishes. Starting from Boltzmann transport equations we derive the expressions for PHE and LMR in topological insulators in the bulk conduction limit, and show the important role played by orbital magnetic moment. Our theoretical results for magnetoconductance with non-parallel electric and magnetic fields predict detailed experimental signatures in topological insulators – specifically of planar Hall effect – that can be observed in experiments.

Magnetotransport signatures of Weyl physics and discrete scale invariance in the elemental semiconductor tellurium

“…The above-discussed experimental observations of the NLMR and PHE in Te crystals adhere well to the chiral-anomaly mechanism in materials possessing Weyl fermions. On the other hand, it has been theoretically proposed that both the NLMR and PHE can be observed in a system with nonzero Berry curvature at the Fermi level (36,37). One notices that the nonzero Berry curvature is also induced by either inversion or time-reversal symmetry breaking, which is the same to the realization of Weyl fermions (3,38).…”

Correlated Magnetic Weyl Semimetal State in Strained Pr2Ir2O7

“…Since the current jetting effect could also cause negative LMR, [ 48 ] then negative LMR alone cannot confirm the chiral anomaly. With this concern, we also performed PHE measurements ( Figure a) on the PIO film to exclude the current jetting and confirm the existence of the chiral anomaly [ 21,49–53 ] and AIAO ordering. The planar Hall conductivity, , for the PIO film in the magnetic WSM state can be written as where and are the contributions from the chiral anomaly and AIAO ordering, respectively.…”

“…Since the current jetting effect could also cause negative LMR, [48] then negative LMR alone cannot confirm the chiral anomaly. With this concern, we also performed PHE measurements (Figure 5a) on the PIO film to exclude the current jetting and confirm the existence of the chiral anomaly [21,[49][50][51][52][53]…”

The Flow of the Berry Curvature Vector Field

“…It ignited the search for topological properties of electrons in solids and resulted in several novel discoveries in various fields. It found success especially in lower dimensional systems and became the main focus in research areas such as topological insulators [2,3,4,5], photonic crystals [6,7,8,9,10,11], and Weyl semimetals [12,13,14,15,16].…”