Zero-energy states bound to a magnetic pi-flux vortex in a two-dimensional topological insulator

TL;DR

This paper demonstrates that topologically non-trivial 2D insulators host zero-energy vortex-bound states, with explicit solutions showing their localization and potential for spin-charge separation, advancing understanding of topological phases.

Contribution

It provides explicit forms of zero-energy vortex-bound states in a 2D topological insulator model, revealing their localization properties and implications for spin-charge separation.

Findings

Zero-energy modes are bound to pi-flux vortices in the topological phase.

Modes are exponentially localized in the vortex core.

Dependence of localization length matches lattice model predictions.

Abstract

We show that the existence of a pair of zero-energy modes bound to a vortex carrying a pi-flux is a generic feature of the topologically non-trivial phase of the M-B model, which was introduced to describe the topological band insulator in HgTe quantum wells. We explicitly find the form of the zero-energy states of the corresponding Dirac equation, which contains a novel momentum-dependent mass term and describes a generic topological transition in a band insulator. The obtained modes are exponentially localized in the vortex-core, with the dependence of characteristic length on the parameters of the model matching the dependence extracted from a lattice version of the model. We consider in full generality the short-distance regularization of the vector potential of the vortex, and show that a particular choice yields the modes localized and simultaneously regular at the origin. Finally, we also discuss a realization of two-dimensional spin-charge separation through the vortex zero-modes.