Weak antilocalization induced by Rashba spin-orbit interaction in layered III-VI compound semiconductor GaSe thin films

Magnetoconductance (MC) at low temperature was measured to investigate spin-related transport affected by spin-orbit interaction (SOI) in III-VI compound $n$-type GaSe thin films. Results reveal that MC shows weak antilocalization (WAL). Its temperature and gate voltage dependences reveal that the dominant spin relaxation is governed by the D’yakonov-Perel’ mechanism associated with the Rashba SOI. The estimated Rashba SOI strength in GaSe is much stronger than that of III-V compound GaAs quantum wells, although the energy gap and spin split-off band in GaSe closely resemble those in GaAs. The angle dependence of WAL amplitude in the in-plane magnetic field direction is almost isotropic. This isotropy indicates that the strength of the Dresselhaus SOI is negligible compared with the Rashba SOI strength. The SOI effect in $n$-GaSe thin films differs greatly from those of III-V compound semiconductors and transition-metal dichalcogenides.

Figure 1

(a) Perspective view of single-layer GaSe unit cell. (b) Top view of GaSe. Orange and green spheres respectively correspond to Se and Ga atoms. (c) Ga and Se atoms form a threefold rotational net in-plane electric dipole moment which is responsible for Dresselhaus SOI. (d) Momentum-dependent effective magnetic field induced by Dresselhaus SOI. Effective magnetic field points perpendicular to the plane, irrespective of momentum direction. (e) Rashba-SOI-induced effective magnetic field. The effective field direction is in-plane and perpendicular to the momentum direction. The strength of the effective field is isotropic.

Figure 2

Temperature dependence of electron mobility $\mu$ and carrier density $N_s$ for device no. 1. $\mu$ and $N_s$ are estimated from ${\rho }_{xx}$ and ${\rho }_{xy}$. The inset presents a photograph of the fabricated multilayered GaSe device structure.

Figure 3

(a) Magnetoconductance (MC) data for device no. 1 observed at low temperature. The MC data are well reproduced by weak antilocalization (WAL) analysis using ILP theory based on the DP spin-relaxation mechanism, as shown by solid curves. Dashed curves are analyzed using HLN theory based on the EY spin-relaxation mechanism. The ILP theory provides better agreement with the experiment. This result demonstrates that the DP mechanism is dominant over the EY mechanism. Theoretical fittings with ILP theory are used to extract spin-relaxation length ${\ell }_{SO}$ and phase coherence length ${\ell }_{\varphi }$. (b) Temperature dependence of phase coherence time ${\tau }_{\varphi }$ and spin-relaxation time ${\tau }_{SO}$. ${\tau }_{\varphi }$ and ${\tau }_{SO}$ are extracted from ${\ell }_{\varphi }$ and ${\ell }_{SO}$ with the assumption of $m^{*}=0.25$. The dotted line shows ${\tau }_{\varphi }\propto T^{-1}$ dependence for comparison. (c) Relation between spin-relaxation rate ${{\tau }_{SO}}^{-1}$ and diffusion constant $D$ for devices no. 1 and no. 2. Diffusion constant $D$ is estimated from the temperature dependence of the electron carrier density and mobility. The dotted line is a guide showing ${{\tau }_{SO}}^{-1}\propto D$.

Figure 4

(a) Back-gate voltage $V_{BG}$ dependence of WAL measured at $T=2\mathrm{K}$ for device no. 2. Arrows indicate magnetoconductance minimum fields, corresponding to the strength of WAL. Solid curves show results of analysis using the ILP theory to extract Rashba SOI parameter α. (b) $V_{BG}$ dependence of phase coherence length ${\ell }_{\varphi }$, spin-relaxation length ${\ell }_{SO}$, and Rashba SOI strength α.

Figure 5

(a) MC for device no. 2 measured at $T=2\mathrm{K}$ and $V_{BG}=0\mathrm{V}$ under constant in-plane magnetic field $B_{//}=1\mathrm{T}$. The amplitude of WAL is defined as $\mathrm{\Delta }{\sigma }_{\mathrm{peak}}$. (b) Color plot for the in-plane field angle dependence of WAL. WAL data were measured by rotating the direction of in-plane magnetic field $B_{//}=1\mathrm{T}$ with the angle step of 5 deg. The current direction is about −50 deg offset from the in-plane magnetic field direction of $\theta =0$ deg. (c) Polar plot of WAL amplitude $\mathrm{\Delta }{\sigma }_{\mathrm{peak}}$ as a function of the in-plane field direction.