From an array of quantum wires to three-dimensional fractional topological insulators

TL;DR

This paper extends the coupled-wires approach to three dimensions to construct a fractional strong topological insulator with exotic surface states, revealing new topological phases and fractional Majorana modes.

Contribution

It introduces a 3D fractional topological insulator model using coupled wires, demonstrating novel surface states and topological phases not described by free fermion theories.

Findings

Discovery of a fractional Dirac liquid surface state.

Gapped phases exhibit fractional Hall conductance of  rac{e^2}{mh}.

Identification of fractional Majorana modes at domain boundaries.

Abstract

The coupled-wires approach has been shown to be useful in describing two-dimensional strongly interacting topological phases. In this manuscript we extend this approach to three-dimensions, and construct a model for a fractional strong topological insulator. This topologically ordered phase has an exotic gapless state on the surface, called a fractional Dirac liquid, which cannot be described by the Dirac theory of free fermions. Like in non-interacting strong topological insulators, the surface is protected by the presence of time-reversal symmetry and charge conservation. We show that upon breaking these symmetries, the gapped fractional Dirac liquid presents unique features. In particular, the gapped phase that results from breaking time-reversal symmetry has a halved fractional Hall conductance of the form $\sigma_{xy}=\frac{1}{2}\frac{e^{2}}{mh}$ if the filling is $\nu=1/m$. On the other hand, if the surface is gapped by proximity coupling to an $s$-wave superconductor, we end up with an exotic topological superconductor. To reveal the topological nature of this superconducting phase, we partition the surface into two regions: one with broken time-reversal symmetry and another coupled to a superconductor. We find a fractional Majorana mode, which cannot be described by a free Majorana theory, on the boundary between the two regions. The density of states associated with tunneling into this one-dimensional channel is proportional to $\omega^{m-1}$, in analogy to the edge of the corresponding Laughlin state.