Valley spin polarization in two-dimensional h-MN (M = Nb, Ta) monolayers: Merger of valleytronics with spintronics

The search for new two-dimensional (2D) semiconductors with strong spin-orbit coupling, merging Rashba effect with valley physics, is essential for advancing the emerging fields of spintronics and valleytronics. h-MN (M = Nb, Ta) monolayers are found to host valley physics together with Rashba effect. h-NbN (TaN) monolayers show Zeeman-type valley spin splitting of 32 (112) meV and 130 (406) meV at valence-band and conduction-band edges, respectively, based on density-functional theory calculations. One of the three degenerate valleys around the K/K' point in the first Brillouin zone (BZ) lies fully enclosed within the first BZ. Berry curvature similar to 50(73) angstrom(2) shown by h-NbN (TaN) monolayers is much higher than that in MoS2 monolayer (similar to 11 angstrom(2)), owing to the lower band gap and wave vector magnitude in h-NbN (TaN) monolayers. The Rashba energy splitting and Rashba constant induced by strong spin-orbit coupling (SOC) in h-NbN (TaN) monolayer is found to be 52 (74) meV and 2.9 (4.23) eV angstrom respectively, which are amongst the giant Rashba spin-splitting parameters observed so far in 2D materials. The degree of Zeeman-type valley spin splitting and Rashba-type spin splitting is substantially tunable via in-plane biaxial strain and out of-plane electric field. Higher SOC in h-TaN monolayer relative to h-NbN monolayer caused by the heavier Ta atoms gives rise to a higher Berry curvature, valley-, and Rashba spin splitting in the former as compared to the latter. Valleytronic and spintronic properties in the studied monolayers are found to be superior to that in h-MoS2 and Janus MoSSe monolayers and are therefore proposed for an effective coupling of spin and valley physics.