Irreducible momentum-space spin structure of Weyl semimetals and its signatures in Friedel oscillations

TL;DR

This paper explores how the momentum-space spin structure of Weyl semimetals influences Friedel oscillations, revealing distinct signatures depending on the relative spin configurations of Weyl point pairs.

Contribution

It demonstrates that the relative spin structure of Weyl point pairs causes observable differences in Friedel oscillation decay rates in centrosymmetric Weyl semimetals.

Findings

Friedel oscillation amplitude decays as 1/r^4 when Weyl points have the same spin structure.

Friedel oscillation amplitude decays as 1/r^3 when Weyl points have inverted spin structures.

Signatures of Weyl spin structure can be detected through electromagnetic response measurements.

Abstract

Materials that break time-reversal or inversion symmetry possess nondegenerate electronic bands, which can touch at so-called Weyl points. The spinor eigenstates in the vicinity of a Weyl point exhibit a well-defined chirality $\pm 1$. Numerous works have studied the consequences of this chirality, for example in unconventional magnetoelectric transport. However, even a Weyl point with isotropic dispersion is not only characterized by its chirality but also by the momentum dependence of the spinor eigenstates. For a single Weyl point, this momentum-space spin structure can be brought into standard "hedgehog" form by a unitary transformation, but for two or more Weyl points, this is not possible. In this work, we show that the relative spin structure of a pair of Weyl points has strong qualitative signatures in the electromagnetic response. Specifically, we investigate the Friedel oscillations in the induced charge density due to a test charge for a centrosymmetric system consisting of two Weyl points with isotropic dispersion. The most pronounced signature is that the amplitude of the Friedel oscillations falls off as $1/r^4$ in directions in which both Weyl points exhibit the same spin structure, while for directions with inverted spin structures, the amplitude of the Friedel oscillations decreases as $1/r^3$.