Berry phase theory of planar Hall effect in topological insulators

S. Nandy,A. Taraphder,Sumanta Tewari

doi:10.1038/s41598-018-33258-5

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.

Highlights

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
Another intriguing phenomenon, negative longitudinal magnetoresistance (LMR) (and positive longitudinal magnetoconductivity (LMC)) in the presence of parallel electric and magnetic fields, has been discovered from the bulk conduction contribution in 3D topological insulators[8,9,10,11,12]. The observation of this effect in TIs is quite puzzling because the negative LMR in topological semimetals such as Weyl semimetals is widely believed to be due to non-conservation of separate electron numbers of opposite chirality for relativistic massless fermions, an effect known as the chiral or Adler-Bell-Jackiw anomaly[13,14,15,16,17,18,19,20,21,22,23]
The main objective of our work is to suggest the existence of planar Hall effect, from the bulk states of 3D topological insulators, in systems exhibiting negative longitudinal magnetoresistance[8,9,10,11,12]

Summary

Introduction

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. Several transport studies on TIs have revealed various anomalous quantum phenomena associated with the topological surface states, such as the Aharonov-Bohm oscillations in Bi2Se3 nanoribbons[3], the weak anti-localization in Bi2Se3 and Bi2Te3 thin films[4,5,6], and the two-dimensional SdH oscillations in Bi2Te37 Very recently, another intriguing phenomenon, negative longitudinal magnetoresistance (LMR) (and positive longitudinal magnetoconductivity (LMC)) in the presence of parallel electric and magnetic fields, has been discovered from the bulk conduction contribution in 3D topological insulators[8,9,10,11,12]. We predict specific magnitudes and direction dependence of PHC and LMC on the applied fields that can be tested in experiments

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Results

Conclusion