Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors

Fully relativistic first-principles calculations based on density functional theory are performed to study the spin-orbit-induced spin splitting in monolayer systems of the transition-metal dichalcogenides MoS${}_2$, MoSe${}_2$, WS${}_2$, and WSe${}_2$. All these systems are identified as direct-band-gap semiconductors. Giant spin splittings of 148–456 meV result from missing inversion symmetry. Full out-of-plane spin polarization is due to the two-dimensional nature of the electron motion and the potential gradient asymmetry. By suppression of the Dyakonov-Perel spin relaxation, spin lifetimes are expected to be very long. Because of the giant spin splittings, the studied materials have great potential in spintronics applications.

Figure 1

(a) Side view of the $2H$-$M{X}_2$ ($M=\text{Mo}$,W and $X=\text{S}$,Se) unit cell, containing two $M{X}_2$ monolayers. (b) Top view. (c) First Brillouin zone of the $M{X}_2$ monolayer. Dashed lines indicate mirror planes.

Figure 2

Electronic band structures calculated for the $M{X}_2$ monolayer systems with (solid line) and without (dotted line) inclusion of the spin-orbit interaction.

Figure 3

Spin splitting within the $k_z=0$ plane as obtained for (a) the uppermost valence band as well as (b) the lowermost conduction band of a WSe${}_2$ monolayer. Dashed lines highlight the first Brillouin zone. Energy isosurfaces are shown for binding energies of (c) 0.2, (d) 0.5, and (e) 0.8 eV. Spin orientations are indicated by different colors.

Figure 4

Spin splitting as a function of $k_{\parallel }$ along the line $\Gamma$-K: (a) uppermost valence band as well as (b) lowermost conduction band. The sign reflects the spin orientation. Orbitally resolved contributions of Se and W are presented in the bottom panels (in arbitrary units).