Photoinduced electronic and spin properties of two-dimensional electron gases with Rashba spin-orbit coupling under perpendicular magnetic fields

We theoretically investigate photoinduced phenomena induced by time-periodic driving fields in two-dimensional electron gases under perpendicular magnetic fields with Rashba spin-orbit coupling. Using perturbation theory, we provide analytical results for the Floquet-Landau energy spectrum appearing due to THz radiation. By employing the resulting photomodulated states, we compute the dynamical evolution of the spin polarization function for an initially prepared coherent state. We find that the interplay of the magnetic field, Rashba spin-orbit interaction, and THz radiation can lead to nontrivial beating patterns in the spin polarization. The dynamics also induces fractional revivals in the autocorrelation function due to interference of the photomodulated quantum states. We calculate the transverse photoassisted conductivity in the linear response regime using Kubo formalism and analyze the impact of the radiation field and Rashba spin-orbit interaction. In the static limit we find that our results reduce to well-known expressions of the conductivity in nonrelativistic and quasirelativistic (topological insulator surfaces) two-dimensional electron gas thoroughly described in the literature. We discuss the possible experimental detection of our theoretical prediction and their relevance for spin-orbit physics at high magnetic fields.

Figure 1

Landau levels (5) given in units of the cyclotron energy $\hslash {\omega }_c$ as a function of the dimensionless parameter ${\lambda }_B/\left(\hslash {\omega }_c\right)$. The solid and dashed lines correspond to each of the SO projections labeled by the quantum number $s$. As detailed in the main text, typical parameters for 2DEG on BiSb monolayers are considered.

Figure 2

Floquet-Landau spectrum (16) given in units of the cyclotron energy $\hslash {\omega }_c$ as function of the dimensionless parameter ${\lambda }_B/\left(\hslash {\omega }_c\right)$. Similarly to Fig. 1, the solid and dotted lines correspond to the two projections labeled by the quantum number $s$. We consider values of the parameters typical for BiSb 2DEGs [31], $\kappa =0.25$ and $\mathrm{\Omega }=3{\omega }_c$.

Figure 3

Time evolution of the spin polarization ${\sigma }_z\left(t\right)$ obtained for different values of the coherent state parameter $\alpha$. We consider the effective radiation strength $\kappa =0.25$ and set ${\lambda }_B/\hslash \mathrm{\Omega }=\delta /\hslash \mathrm{\Omega }=1$ and $B=1$ T.

Figure 4

Expectation value of the spin polarization $\langle {\sigma }_z\rangle$ in $B\text{−}\alpha$ parameter space. We consider an effective radiation strength $\kappa =0.25$ and fix the radiation frequency of the incident light beam by setting $m^{*}{\lambda }^2/\hslash \mathrm{\Omega }=1$.

Figure 5

Magnetic field response of the expectation value of the spin polarization at four representative values of the coherent state parameter $\alpha$. Values of the effective radiation strength $\kappa$ and the radiation frequency $\mathrm{\Omega }$ are set as in Fig. 4.

Figure 6

Time dependence of the autocorrelation function $C\left(t\right)$ as given in Eq. (27) for different values of the coherent state parameter $\alpha$. For larger values of $\alpha$, the autocorrelation function shows partial revivals correlated with the oscillations in the spin polarization seen in Fig. 3. Values of the effective radiation strength $\kappa$, the radiation frequency $\mathrm{\Omega }$, and the magnetic field are set as in Fig. 3.

Figure 7

(a) Static transverse conductivity $Re{\sigma }_{xy}\left(0\right)$ as a function of the normalized chemical potential $\mu /\left(\hslash {\omega }_c\right)$. Each curve corresponds to a different value of the parameter ${\lambda }_B/\left(\hslash {\omega }_c\right)$: 0 (black solid line), 0.1 (orange dotted line), 0.2 (violet dot-dashed line), and 0.3 (green dashed line). The effective level broadening and temperature are $\mathrm{\Gamma }/\left(\hslash {\omega }_c\right)=0.05$ and $k_{B}T/\left(\hslash {\omega }_c\right)=0.01$, respectively. (b) Transverse photoconductivity $Re{\sigma }_{xy}\left(\mathrm{\Omega }\right)$ as a function of $\mu /\left(\hslash {\omega }_c\right)$ for $\mathrm{\Omega }/{\omega }_c=0.5$ (red dotted line). The green solid line corresponds to the static transverse conductivity. We have considered ${\lambda }_B/\left(\hslash {\omega }_c\right)=0.3$ and employed the same temperature and level broadening as in (a).

Figure 8

(a) Transverse conductivity $Re{\sigma }_{xy}\left(\mathrm{\Omega }\right)$ as a function of $\mu /\left(\hslash {\mathrm{\Omega }}_c\right)$ obtained in the limit of strong SO interaction ${\lambda }_B/\left(\hslash {\omega }_c\right)\gg 1$. Here ${\mathrm{\Omega }}_c={\lambda }_B/\hslash$ represents the SO-dependent characteristic frequency. Representative results for the static (black line) and photoinduced cases ($\mathrm{\Omega }/{\mathrm{\Omega }}_c=0.5$, red line) are shown. (b) Transverse conductivity $Re{\sigma }_{xy}\left(\mathrm{\Omega }\right)$ as function of $\mu /\hslash {\omega }_c$ obtained in the limit of vanishing SO interaction ${\lambda }_B/\left(\hslash {\omega }_c\right)\ll 1$. Representative results for the static (black curve) and photoinduced cases ($\omega /{\omega }_c=0.5$, red line) are shown. Solid and dashed lines correspond, respectively, to $\delta /\left(\hslash {\omega }_c\right)=0$ and $\delta /\left(\hslash {\omega }_c\right)\simeq 1.2$. The effective level broadening and the temperature are chosen as in Fig. 7 both for (a) and (b).