Lifshitz transitions and Weyl semimetals from a topological superconductor with supercurrent flow

TL;DR

This paper explores how supercurrent-induced Lifshitz transitions in a topological superconductor can be understood through a mapping to a Weyl semimetal, revealing phase changes and maximal current limits.

Contribution

It introduces a novel mapping of a supercurrent in a topological superconductor to a Weyl semimetal, uncovering Lifshitz transitions and phase coexistence phenomena.

Findings

Identification of Lifshitz transitions via supercurrent modulation

Mapping of supercurrent states to Weyl semimetal ground states

Determination of maximal sustainable supercurrent in topological phase

Abstract

A current flowing through a superconductor induces a spatial modulation in its superconducting order parameter, characterized by a wavevector $Q$ related to the total momentum of a Cooper pair. Here we investigate this phenomenon in a $p$-wave topological superconductor, described by a one-dimensional Kitaev model. We demonstrate that, by treating $Q$ as an extra synthetic dimension, the current carrying non-equilibrium steady state can be mapped into the ground state of a half-filled two-dimensional Weyl semimetal, whose Fermi surface exhibits Lifshitz transitions when varying the model parameters. Specifically, the transition from Type-I to Type-II Weyl phases corresponds to the emergence of a gapless $p$-wave superconductor, where Cooper pairs coexist with unpaired electrons and holes. Such transition is signaled by the appearance of a sharp cusp in the $Q$-dependence of the supercurrent, at a critical value $Q^*$ that is robust to variations of the chemical potential $\mu$. We determine the maximal current that the system can sustain in the topological phase, and discuss possible implementations.