Tunable Berry curvature, valley and spin Hall effect in Bilayer MoS$_2$

TL;DR

This paper investigates how inter-layer and intra-layer couplings in bilayer MoS₂ influence Berry curvature, enabling tunable valley and spin Hall effects through stacking and electric fields, with potential for sign reversal of conductivities.

Contribution

It reveals the significant role of inter-layer coupling in Berry curvature and demonstrates tunability of valley and spin Hall effects in bilayer MoS₂ based on stacking and electric fields.

Findings

Berry curvature depends on stacking type and electric field.

Valley and spin Hall conductivities can change sign with external fields.

Inter-layer coupling significantly affects electronic properties.

Abstract

The chirality of electronic Bloch bands is responsible for many intriguing properties of layered two-dimensional materials. We show that in bilayers of transition metal dichalcogenides (TMDCs), unlike in few-layer graphene and monolayer TMDCs, both intra-layer and inter-layer couplings give important contributions to the Berry-curvature in the $K$ and $-K$ valleys of the Brillouin zone. The inter-layer contribution leads to the stacking dependence of the Berry curvature and we point out the differences between the commonly available 3R type and 2H type bilayers. Due to the inter-layer contribution the Berry curvature becomes highly tunable in double gated devices. We study the dependence of the valley Hall and spin Hall effects on the stacking type and external electric field. Although the valley and spin Hall conductivities are not quantized, in MoS$_2$ 2H bilayers they may change sign as a function of the external electric field which is reminiscent of the behaviour of lattice Chern insulators.