Magnetic warping in topological insulators

TL;DR

This paper investigates how magnetic ordering affects the electronic structure of topological insulators, revealing changes in surface state symmetry and proposing a new method to detect magnetic order through surface electronic measurements.

Contribution

It demonstrates the change from hexagonal to trigonal warping of Dirac cones at magnetic transition temperatures and links surface state energy splittings to magnetic ordering detection.

Findings

Dirac cone warping changes symmetry at magnetic transition.

Energy splitting between surface states indicates magnetic order.

Trigonal warping is sensitive to surface magnetic flux direction.

Abstract

We analyze the electronic structure of topological surface states in the family of magnetic topological insulators MnBi$_{2n}$Te$_{3n+1}$. We show that, at natural-cleavage surfaces, the Dirac cone warping changes its symmetry from hexagonal to trigonal at the magnetic ordering temperature. In particular, an energy splitting develops between the surface states of same band index but opposite surface momenta upon formation of the long-range magnetic order. As a consequence, measurements of such energy splittings constitute a simple protocol to detect the magnetic ordering via the surface electronic structure, alternative to the detection of the surface magnetic gap. Interestingly, while the latter signals a nonzero surface magnetic flux, the trigonal warping predicted here is, in addition, sensitive to the direction of the surface magnetic flux.