Enhanced and stable spin Hall conductivity in a disordered time-reversal and inversion symmetry broken topological insulator thin film

TL;DR

This paper investigates how disorder, magnetic exchange, and electric fields influence the spin Hall conductivity in a topological insulator thin film, revealing conditions for large and stable spin currents.

Contribution

It provides a detailed analysis of spin Hall conductivity in disordered topological insulator films with broken symmetries, including effects of vertex corrections and disorder stability.

Findings

Large spin conductivity occurs at small electric potential difference with high magnetic exchange.

Large electric potential difference enhances spin conductivity even at low magnetic exchange.

Spin conductivity remains stable against disorder effects under certain conditions.

Abstract

We consider a disordered topological insulator thin film placed on the top of a ferromagnetic insulator with a perpendicular exchange field $M$ and subjected to a perpendicular electric field. The presence of ferromagnetic insulator causes that bottom surface states of the topological insulator thin film become spin polarized and the electric field provides a potential difference $V$ between the two surface states, resulting in breaking of time-reversal and inversion symmetry in the system. Using Kubo formalism and employing the first Born approximation as well as the self-consistent Born approximation, we calculate the spin Hall conductivity. We find that for small values of $V$, a large spin conductivity can be generated through large values of $M$ away from the charge neutrality point. But for large values of $V$, the spin conductivity can be promoted even with small values of $M$ around the charge neutrality point. The effect of vertex corrections and the stability of the obtained large spin conductivity against disorders are also examined.