Hydrostatic pressure control of the spin-orbit proximity effect, spin relaxation, and thermoelectricity in a phosphorene-WSe$_2$ heterostructure

Abstract: Effective control of interlayer interactions is a key element in modifying the properties of van der Waals heterostructures and the next step toward their practical applications. Focusing on the phosphorene-WSe$_2$ heterostructure, we demonstrate, using first-principles calculations, proximity-induced amplification of the spin-orbit coupling in phosphorene by applying vertical pressure. We simulate external pressure by changing the interlayer distance between bilayer constituents and show that it is possible to tune the spin-orbit field of phosphorene holes in a controllable way. By fitting effective electronic states of the proposed Hamiltonian to the first principles data, we reveal that the spin-orbit coupling in phosphorene hole bands is enhanced more than two times for experimentally accessible pressures up to 17 kbar. Correspondingly, we find that the pressure-enhanced spin-orbit coupling boosts the Dyakonov-Perel spin relaxation mechanism, reducing the spin lifetime of phosphorene holes by factor 4. We further explore the role of the lateral shift on the spin-orbit field and reveal that the spin-orbit strength of phosphorene holes can be sizably modulated when strong pressure is applied. We also found that the thermopower is governed mainly by the phosphorene and pressure reduces the overall thermoelectric efficiency of the heterostructure.