Thermal screening at finite chemical potential on a topological surface and its interplay with proximity-induced ferromagnetism

TL;DR

This paper investigates how temperature, chemical potential, and proximity-induced gaps influence screening and topological properties on the surface of a topological insulator near ferromagnetic materials, revealing conditions for quantized Hall conductivity.

Contribution

It provides an analytical study of the interplay between screening effects, topological mass, and ferromagnetic proximity in topological insulator surfaces at finite temperature and chemical potential.

Findings

Screening energy depends on chemical potential, temperature, and proximity-induced gap.

Topological mass remains nearly quantized inside the gap at finite temperature.

Analytical expressions for the topological mass in the insulating regime.

Abstract

Motivated by recent experiments on EuS/Bi$_2$Se$_3$ heterostructures, we study the temperature dependent screening effects on the surface of a three-dimensional topological insulator proximate to a ferromagnetically ordered system. In general, we find that besides the chemical potential and temperature, the screening energy scale also depends on the proximity-induced electronic gap in an essential way. In particular, at zero temperature the screening energy vanishes if the chemical potential is smaller than the proximity-induced electronic gap. We show that at finite temperature, $T$, and/or chemical potential, $\mu$, the Chern-Simons (topological) mass, which is generated by quantum fluctuations arising from the proximity-effect, can be calculated analytically in the insulating regime. In this case the topological mass yields the Hall conductivity associated to edge states. We show that when the chemical potential is inside the gap the topological mass remains nearly quantized at finite temperature.