Spin splitting in 2D monochalcogenide semiconductors

Abstract

We report ab initio calculations of the spin splitting of the uppermost valence band (UVB) and the lowermost conduction band (LCB) in bulk and atomically thin GaS, GaSe, GaTe, and InSe. These layered monochalcogenides appear in four major polytypes depending on the stacking order, except for the monoclinic GaTe. Bulk and few-layer ε-and γ -type, and odd-number β-type GaS, GaSe, and InSe crystals are noncentrosymmetric. The spin splittings of the UVB and the LCB near the Γ-point in the Brillouin zone are finite, but still smaller than those in a zinc-blende semiconductor such as GaAs. On the other hand, the spin splitting is zero in centrosymmetric bulk and even-number few-layer β-type GaS, GaSe, and InSe, owing to the constraint of spatial inversion symmetry. By contrast, GaTe exhibits zero spin splitting because it is centrosymmetric down to a single layer. In these monochalcogenide semiconductors, the separation of the non-degenerate conduction and valence bands from adjacent bands results in the suppression of Elliot-Yafet spin relaxation mechanism. Therefore, the electron- and hole-spin relaxation times in these systems with zero or minimal spin splittings are expected to exceed those in GaAs when the D’yakonov-Perel’ spin relaxation mechanism is also suppressed.

Large-grain MBE-grown GaSe on GaAs with a Mexican hat-like valence band dispersion

“…This feature cannot be explained by the spin-orbit splitting of the topmost band since the predicted value is in the range of only a few meV. 12,29 It is more likely that the subband is arising from the mixed signals of the Γ 1 + band of exposed monolayer GaSe in the examined region, since the energy difference is in line with theoretical calculations. 6,12 It is worth noting that the second topmost band, (Γ 3 − ) lies below the Γ 1 + bands with an energy difference of~1.1 eV at the Γ point, a value which is also comparable with the reported calculations for both the monolayer and bilayer cases making further distinction difficult.…”

Spin-orbit coupling, optical transitions, and spin pumping in monolayer and few-layer InSe

“…Going on from the monolayer [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] to N -layer films, interlayer hopping between successive layers of InSe splits each band into N subbands, as studied earlier using DFT and tight-binding calculations 31,33,39 . At the Γ-point, v 1 and v 2 split very weakly, whereas c and v, which are dominated by s and p z orbitals on In and Se, exhibit a much stronger splitting.…”

“…The values of the k · p parameters listed in Table II are determined 39 from fitting to DFT dispersions without SOC near Γ. The dispersions of these bands coincide with the DFT-calculated Γ-point dispersion of InSe bands [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] , but with the band gap corrected by a 'scissor correction' adjustment to the bands 39 . The factors eβ 1 (2) cm e , are couplings of the spin-conserving v 1 → c interband transition (B-line), and of the transition between bands v and v 2 49 , respectively, to in-plane polarized light described by vector potential A = (A x , A y ), with β 1(2) = | c(v)| P |v 1 (v 2 ) | the magnitude of the interband matrix element of the momentum operator.…”

“…These experiments have identified two main photoluminescence lines, interpreted 30 as a lower energy transition between bands dominated by s and p z orbitals (A-line) and hot luminescence, involving holes in a deeper valence band based on p x and p y orbitals (B-line). The band structure analysis of mono-and few-layer InSe [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48] has revealed that the conduction and valence band edges near the Γ-point are non-degenerate, being dominated by s and p z orbitals of both metal and chalcogen atoms. Combined with the opposite z → −z (mirror reflection) symmetry of conduction and valence bands, this determines that the transition across the principal band gap has a dominantly electric dipole-like character, coupled to out-of-plane polarized photons.…”

Characteristics of Interlayer Tunneling Field-Effect Transistors Computed by a “DFT-Bardeen” Method

“…22 Additionally we considered other 2D materials such as GaSe. 27 Again, we only consider cases where the energy difference ∆ECV = EC (2) -EV (1) is relatively small, with ∆ECV deduced from the DFT computations (We note that DFT is well known to underestimate experimental band gap values. 28 An approximate correction to the band gaps will cause a right-shift of our results in Fig.…”