Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator

TL;DR

This work shows that a three-dimensional electronic topological insulator can host a fully gapped, symmetry-preserving surface if it develops intrinsic surface topological order (STO), which is intrinsically non-Abelian. The authors construct the STO by starting from a time-reversal symmetric surface superconductor and proliferating carefully chosen $4\pi$-vortex composites that preserve $U(1)_C$ and TRS, yielding a rich spectrum of anyons with specific charges, spins, and fusion rules. They connect this STO to familiar 2D topological phases (notably Moore-Read–like physics with an extra neutral semion) and show how the STO can be tuned back to conventional surface phases, including TR-symmetric superconductors, half-integer quantum Hall states, and gapless Dirac surfaces, revealing a robust $\mathbb{Z}_2$ structure for the TI surface. The STO thus provides a non-perturbative, symmetry-respecting definition of the electron TI and offers a framework for understanding strongly correlated TI surfaces and potential topological Mott insulating behavior.

Abstract

It is well known that the 3D electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often implicitly assumed that if the TI surface preserves both symmetries then it must be gapless. Here we show that it is possible for the TI surface to be both gapped and symmetry-preserving, at the expense of having surface-topological order. In contrast to analogous bosonic topological insulators, this symmetric surface topological order is intrinsically non-Abelian. We show that the surface-topological order provides a complete non-perturbative definition of the electron TI that transcends a free-particle band-structure picture, and could provide a useful perspective for studying strongly correlated topological Mott insulators.

Figures (2)

• Figure 1: Exchanging two $\frac{hc}{e}$ vortices at the superconducting surface of a TI slab (top panel) leads to a linking of their magnetic field lines, which gives a phase of $-1$, demonstrating that $\frac{hc}{e}$ vortices are semionic.
• Figure 2: The non-fractionalized TR-breaking quantum Hall insulator (QHI) with coating the TI surface with a 2D TR-breaking topologically ordered state with $\sigma_H=\kappa_H=\pm\frac{1}{2}$ (depicted in orange and purple respectively), as explained in the text. The half-integer quantum Hall conductance can be seen by considering a domain between these two coatings as shown in the above figure for a spherical TI,