Bosonic topological insulator in three dimensions and the statistical Witten effect

TL;DR

This paper introduces a bosonic topological insulator in three dimensions that exhibits a 'statistical Witten effect,' where monopoles inside the insulator change their statistics from bosonic to fermionic, leading to unique surface topological order.

Contribution

It proposes a bosonic analog of the Witten effect, demonstrating monopole statistics transmutation and the necessity of surface topological order in 3D bosonic topological insulators.

Findings

Monopoles inside the bosonic topological insulator become fermionic.

Surface must support intrinsic 2D topological order.

Surface properties cannot be realized in purely 2D systems.

Abstract

It is well-known that one signature of the three-dimensional electron topological insulator is the Witten effect: if the system is coupled to a compact electromagnetic gauge field, a monopole in the bulk acquires a half-odd-integer polarization charge. In the present work, we propose a corresponding phenomenon for the topological insulator of bosons in 3d protected by particle number conservation and time-reversal symmetry. We claim that although a monopole inside a topological insulator of bosons can remain electrically neutral, its statistics are transmuted from bosonic to fermionic. We demonstrate that this ``statistical Witten effect" directly implies that if the surface of the topological insulator is neither gapless, nor spontaneously breaks the symmetry, it necessarily supports an intrinsic two-dimensional topological order. Moreover, the surface properties cannot be fully realized in a purely 2d system. We also confirm that the surface phases of the bosonic topological insulator proposed by Vishwanath and Senthil (arXiv:1209.3058) provide a consistent termination of a bulk exhibiting the statistical Witten effect. In a companion paper, we will provide an explicit field-theoretic, lattice-regularized, construction of the 3d topological insulator of bosons, employing a parton decomposition and subsequent condensation of parton-monopole composites.