Barrier and finite size effects on the extension of topological surface-states into magnetic insulators

TL;DR

This paper theoretically investigates how barrier potential and finite size effects influence the extension and gap of topological surface states into magnetic insulators, revealing non-monotonic behaviors and counterintuitive size-dependent phenomena.

Contribution

It provides new insights into how interface barriers and finite thickness affect topological surface states in magnetic insulator structures, guiding future experimental designs.

Findings

Surface state gap depends non-monotonically on barrier strength.

A finite barrier can enhance surface state penetration into the magnetic insulator.

Increasing spin-splitting in thin samples can reduce the surface state gap.

Abstract

The interplay between magnetic and topological order can give rise to phenomena such as the quantum anomalous Hall effect. The extension of topological surface states into magnetic insulators (MIs) has been proposed as an alternative to using intrinsically magnetic topological insulators (TIs). Here, we theoretically study how this extension of surface states into a magnetic insulator are influenced both by the interface barrier potential separating a topological insulator and a magnetic insulator and by finite size effects in such structures. We find that the the gap in the surface states depends non-monotonically on the barrier strength. A small, but finite, barrier potential turns out to be advantageous as it permits the surface states to penetrate even further into the MI. Moreover, we find that due to finite size effects in thin samples, increasing the spin-splitting in the MI can actually decrease the gap of the surface states, in contrast to the usual expectation that the gap opens as the spin-splitting increases.