Weyl nodes as topological defects of the Wannier-Stark ladder: From surface to bulk Fermi arcs

TL;DR

This paper reveals how the topological structure of Weyl semimetals, characterized by Zak phase winding, leads to the emergence of bulk Fermi arcs as topological defects in the Wannier-Stark ladder, connecting surface and bulk phenomena.

Contribution

It introduces the concept of bulk Fermi arcs as topological defects of the Wannier-Stark ladder, linking surface Fermi arcs to bulk properties via Zak phase analysis.

Findings

Zak phase determines surface Fermi arc locations

Winding of Zak phase manifests as topological defects

Bulk Fermi arcs coexist with surface Fermi arcs

Abstract

A hallmark of Weyl semimetal is the existence of surface Fermi arcs connecting two surface-projected Weyl nodes with opposite chiralities. An intriguing question is what determines the connectivity of surface Fermi arcs, when multiple pairs of Weyl nodes are present. To answer this question, we first show that the locations of surface Fermi arcs are predominantly determined by the condition that the Zak phase integrated along the normal direction to the surface is $\pi$. More importantly, the Zak phase can reveal the peculiar topological structure of Weyl semimetal directly in the bulk. Here, we show that the non-trivial winding of the Zak phase around each projected Weyl node manifests itself as a topological defect of the Wannier-Stark ladder, the energy eigenstates emerging under an electric field. Remarkably, this structure leads to "bulk Fermi arcs," i.e., open line segments in the bulk momentum spectra. It is argued that bulk Fermi arcs should exist in conjunction with the surface counterparts to conserve the Weyl fermion number under an electric field, which is supported by explicit numerical evidence.