Theory of a 3+1D fractional chiral metal: interacting variant of the Weyl semimetal

TL;DR

This paper develops a theoretical framework for a fractionalized, strongly correlated analogue of the Weyl semimetal, called the fractional chiral metal, using a 4+1D quantum Hall insulator construction and bosonization techniques.

Contribution

It introduces a novel fractional chiral metal phase derived from stacking Weyl semimetals and applying electron-electron interactions, extending topological phase classifications.

Findings

Derived a 4+1D quantum Hall insulator model for fractional Weyl semimetals.

Established the boundary theory as a 3+1D fractional chiral state with anomalous electromagnetic response.

Predicted a fractionalized chiral anomaly as a hallmark of the phase.

Abstract

Formulating consistent theories describing strongly correlated metallic topological phases is an outstanding problem in condensed matter physics. In this work we derive a theory defining a fractionalized analogue of the Weyl semimetal state: the fractional chiral metal. Our approach is to construct a 4+1D quantum Hall insulator by stacking 3+1D Weyl semimetals in a magnetic field. In a strong enough field the low-energy physics is determined by the lowest Landau level of each Weyl semimetal, which is highly degenerate and chiral, motivating us to use a coupled-wire approach. The one-dimensional dispersion of the lowest Landau level allows us to model the system as a set of degenerate 1+1D quantum wires that can be bosonized in the presence of electron-electron interactions and coupled such that a gapped phase is obtained, whose response to an electromagnetic field is given in terms of a Chern-Simons field theory. At the boundary of this phase we obtain the field theory of a 3+1D gapless fractional chiral state, which we show is consistent with a previous theory for the surface of a 4+1D Chern-Simons theory. The boundary's response to an external electromagnetic field is determined by a chiral anomaly with a fractionalized coefficient. We suggest that such anomalous response can be taken as a working definition of a fractionalized strongly correlated analogue of the Weyl semimetal state.