Flux Response of Rotation-Invariant Topological Insulators

TL;DR

This paper explores how flux threading in 3D topological insulators with rotation symmetry reveals a refined classification of topological phases, leading to potential realization of Majorana modes in nanowires.

Contribution

It introduces a new $ ext{Z}_2 imes ext{Z}_2$ classification for flux response in rotation-symmetric topological insulators and proposes nanowire platforms for topological superconductivity.

Findings

Flux threading reveals a refined topological classification.

Two types of flux-bound helical modes distinguished by angular momentum.

Proposal for nanowires hosting multiple Majorana modes.

Abstract

Threading magnetic flux into topological phases can induce bound states that reveal intrinsic properties of the ground state. In a 3D $\mathbb{Z}_2$ topological insulator, a quantized $\pi$ flux traps a pair of 1D helical modes, whereas a trivial insulator hosts none. In this work, we show that in the presence of even-fold rotation symmetry $C_n$, a 3D band insulator features a refined $\mathbb{Z}_2 \times \mathbb{Z}_2$ classification of the flux response. Specifically, it can host two distinct types of helical flux-bound modes that are distinguished by their angular momentum. When both types of flux modes coexist, the system is not a strong topological insulator, but a $C_n$-protected topological crystalline insulator. Building on this result, we propose that flux-threaded nanowires of such topological phase provide a natural platform for realizing 1D crystalline topological superconductors with multiple $C_n$-protected Majorana modes.