Exactly soluble model for a fractionalized Weyl semimetal

Fabian Hotz,Tobias Meng,Oguz Turker,Apoorv Tiwari,Titus Neupert,Maciej Koch-Janusz,Ady Stern

doi:10.1103/physrevresearch.1.033029

Abstract

We construct an exactly solvable lattice model of a fractional Weyl semimetal (FWS). The low energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect (CPGE) and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function they provide strong experimental signatures for this exotic gapless state of matter.

Highlights

Electronic systems jointly described as topological fall into two conceptually distinct classes: short-range entangled, which can be transformed into a product state by means of local unitaries, and those characterized by long-range entanglement, which cannot
While many symmetryprotected topological states (SPTs) originate in the properties of the noninteracting band structure and topological order crucially requires interactions, these subsets are not mutually exclusive: Symmetry-enriched topological phases such as a fractional topological insulator (FTI) [3,4,5] can arise due to the interplay of the two ingredients
We show that the circular photogalvanic effect (CPGE), a second-order response, is universally quantized to fractional values, in clear contrast to standard Weyl semimetal

Summary

INTRODUCTION

Electronic systems jointly described as topological fall into two conceptually distinct classes: short-range entangled, which can be transformed into a product state by means of local unitaries, and those characterized by long-range entanglement, which cannot. The former include symmetryprotected topological states (SPTs), including topological insulators or the Haldane phase [1], and Weyl and Dirac semimetals. We show a violation of the Wiedemann-Franz law and a gap in the single-particle electronic spectral function, which provide experimental signatures

SOLVABLE MODEL

FRACTIONAL CURRENTS

FRACTIONAL CPGE

ELECTRONIC GREEN’S FUNCTION

WIEDEMANN-FRANZ LAW VIOLATION

CONCLUSION