Electronic structure of the surface superconducting Weyl semimetal PtBi$_2$

TL;DR

This paper investigates the electronic structure and surface superconductivity of PtBi$_2$, a Weyl semimetal, using first-principles calculations and effective models, revealing the nature of Weyl points, spin textures, and Josephson junction phenomena.

Contribution

It provides a detailed theoretical analysis of PtBi$_2$'s bulk and surface electronic structures, including a symmetry-adapted model for surface superconductivity and Josephson effects.

Findings

Identification of Weyl points and Fermi arcs in PtBi$_2$

Construction of an effective four-band model for surface states

Prediction of zero-energy Andreev bound states in Josephson junctions

Abstract

Trigonal PtBi$_2$ is a layered semimetal without inversion symmetry, featuring 12 Weyl points in the vicinity of the Fermi energy. Its topological Fermi arcs were recently shown to superconduct at low temperatures where bulk superconductivity is absent. Here, we perform first-principles calculations to investigate in detail the bulk and surface electronic structure of PtBi$_2$, and obtain the spin texture as well as the momentum-dependent localization of the arcs. Motivated by the experimentally observed recovery of inversion symmetry under pressure or upon doping, we interpolate between the two structures and determine the energy and momentum dependence of the Weyl nodes. For deeper insights into the surface superconductivity of PtBi$_2$, we construct a symmetry-adapted effective four-band model that accurately reproduces the Weyl points of PtBi$_2$. We supplement this model with an analysis of the symmetry-allowed pairings between the Fermi arcs, which naturally mix spin-singlet and spin-triplet channels. Moreover, the presence of surface-only superconductivity facilitates an intrinsic superconductor-semimetal-superconductor Josephson junction, with the semimetallic phase sandwiched between the two superconducting surfaces. For a phase difference of $\pi$, zero-energy Andreev bound states develop between the two terminations.