Direction-dependent conductivity in planar Hall set-ups with tilted Weyl/multi-Weyl semimetals
Rahul Ghosh, Ipsita Mandal
Abstract
Abstract We compute the magnetoelectric conductivity tensors in planar Hall set-ups, which are built with tilted Weyl semimetals (WSMs) and multi-Weyl semimetals (mWSMs), considering all possible relative orientations of the electromagnetic fields ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">E</mml:mi> </mml:mrow> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> </mml:mrow> </mml:math> ) and the direction of the tilt. The non-Drude part of the response arises from a nonzero Berry curvature in the vicinity of the WSM/mWSM node under consideration. Only in the presence of a nonzero tilt do we find linear-in- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:math> terms in set-ups where the tilt-axis is not perpendicular to the plane spanned by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">E</mml:mi> </mml:mrow> </mml:mrow> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> </mml:mrow> </mml:math> . The advantage of the emergence of the linear-in- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:math> terms is that, unlike the various <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> <mml:msup> <mml:mo stretchy="false">|</mml:mo> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> -dependent terms that can contribute to experimental observations, they have purely a topological origin, and they dominate the overall response-characteristics in the realistic parameter regimes. The important signatures of these terms are that they (1) change the periodicity of the response from π to 2 π , when we consider their dependence on the angle θ between E and B ; and (2) lead to an overall change in sign of the conductivity depending on θ , when measured with respect to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">B</mml:mi> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> case.