Magnetotransport across Weyl semimetal grain boundaries

A clean interface between two Weyl semimetals features a universal, field-linear tunnel magnetoconductance of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mrow> <a:mo>(</a:mo> <a:msup> <a:mi>e</a:mi> <a:mn>2</a:mn> </a:msup> <a:mo>/</a:mo> <a:mi>h</a:mi> <a:mo>)</a:mo> </a:mrow> <a:msub> <a:mi>N</a:mi> <a:mi>ho</a:mi> </a:msub> </a:mrow> </a:math> per magnetic flux quantum, where <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>N</b:mi> <b:mi>ho</b:mi> </b:msub> </b:math> is the number of chirality-preserving topological interface Fermi arcs. In this work we show that the linearity of the magnetoconductance is robust with respect to interface disorder. The slope of the magnetoconductance changes at a characteristic field strength <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:msub> <c:mi>B</c:mi> <c:mi>arc</c:mi> </c:msub> </c:math> —the field strength for which the time taken to traverse the Fermi arc due to the Lorentz force is equal to the mean inter-arc scattering time. For fields much larger than <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:msub> <d:mi>B</d:mi> <d:mi>arc</d:mi> </d:msub> </d:math> , the magnetoconductance is unaffected by disorder. For fields much smaller than <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"> <e:msub> <e:mi>B</e:mi> <e:mi>arc</e:mi> </e:msub> </e:math> , the slope is no longer determined by <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:msub> <f:mi>N</f:mi> <f:mi>ho</f:mi> </f:msub> </f:math> but by the simple fraction <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:msub> <g:mi>N</g:mi> <g:mi mathvariant="normal">L</g:mi> </g:msub> <g:msub> <g:mi>N</g:mi> <g:mi mathvariant="normal">R</g:mi> </g:msub> <g:mo>/</g:mo> <g:mrow> <g:mo>(</g:mo> <g:msub> <g:mi>N</g:mi> <g:mi mathvariant="normal">L</g:mi> </g:msub> <g:mo>+</g:mo> <g:msub> <g:mi>N</g:mi> <g:mi mathvariant="normal">R</g:mi> </g:msub> <g:mo>)</g:mo> </g:mrow> </g:mrow> </g:math> , where <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:msub> <l:mi>N</l:mi> <l:mi mathvariant="normal">L</l:mi> </l:msub> </l:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML"> <n:msub> <n:mi>N</n:mi> <n:mi mathvariant="normal">R</n:mi> </n:msub> </n:math> are the numbers of Weyl-node pairs in the left and right Weyl semimetal, respectively. We also consider the effect of spatially correlated disorder potentials, where we find that <p:math xmlns:p="http://www.w3.org/1998/Math/MathML"> <p:msub> <p:mi>B</p:mi> <p:mi>arc</p:mi> </p:msub> </p:math> decreases exponentially with increasing correlation length. Our results provide a possible explanation for the recently observed robustness of the negative linear magnetoresistance in grained Weyl semimetals.