Transport of Dirac electrons in a random magnetic field in topological heterostructures

TL;DR

This paper investigates how Dirac electrons on topological insulator surfaces are affected by a random magnetic field from a ferromagnet, revealing temperature-dependent resistivity behaviors near phase transitions.

Contribution

It models the interaction between Dirac surface states and magnetic fluctuations, highlighting the impact of magnetic phase transitions on electron transport properties.

Findings

Resistivity scales linearly with temperature near the BKT transition.

Resistivity exhibits a pronounced maximum as Fermi energy decreases.

Linear resistivity observed at low temperatures within a Fermi liquid framework.

Abstract

We consider the proximity effect between Dirac states at the surface of a topological insulator and a ferromagnet with easy plane anisotropy, which is described by the \emph{XY}-model and undergoes a Berezinskii-Kosterlitz-Thouless (BKT) phase transition. The surface states of the topological insulator interacting with classical magnetic fluctuations of the ferromagnet can be mapped onto the problem of Dirac fermions in a random magnetic field. However, this analogy is only partial in the presence of electron-hole asymmetry or warping of the Dirac dispersion, which results in screening of magnetic fluctuations. Scattering at magnetic fluctuations influences the behavior of the surface resistivity as a function of temperature. Near the BKT phase transition temperature we find that the resistivity of surface states scales linearly with temperature and has a clear maximum which becomes more pronounced as the Fermi energy decreases. Additionally at low temperatures we find linear resistivity, usually associated with non-Fermi liquid behavior, however here it appears entirely within the Fermi liquid picture.