Refined Density Functional Theory Recipe and Renormalization of Band-Edge Parameters for Electrons in Monolayer MoS₂ Informed by the Measured Spin-Orbit Splitting.

Abstract

Conduction band-edge spin-orbit splitting (SOS) in monolayer transition metal dichalcogenides determines a competition between bright and dark excitons and sets conditions for spintronics applications of these semiconductors. Here, we report the SOS measurement for electrons in monolayer MoS₂, found from the threshold density, <i>n</i>_*, for the upper spin-orbit split band population, which exceeds by an order of magnitude the values expected from the conventional density functional theory (DFT). Theoretically, half of the observed SOS value can be attributed to the exchange enhancement of SOS in a finite-density electron gas, but explaining the rest requires refining the DFT approach. As the conduction band SOS in MoS₂ is set by a delicate balance between the contribution of sulfur p_<i>x</i> and p_<i>y</i> orbitals and d_<i>z</i>²-d_<i>xz</i> and d_<i>z</i>²-d_<i>yz</i> mixing in molybdenum, we use a DFT + <i>U</i> + <i>V</i> framework, which includes both on-site (<i>U</i>) and intersite (<i>V</i>) Hubbard interactions for fine-tuning the orbital composition of the relevant band-edge states, which enables us to achieve a close agreement with the experiment.