Control of electron-spin coherence using Landau level quantization in a two-dimensional electron gas

Time-resolved optical measurements of electron-spin dynamics in modulation-doped InGaAs quantum wells are used to explore electron spin coherence times and spin precession frequencies in a regime where an out-of-plane magnetic field quantizes the states of a two-dimensional electron gas into Landau levels. Oscillatory features in the transverse spin coherence time and effective $g$ factor as a function of the applied magnetic field exhibit a correspondence with Shubnikov–de Haas oscillations, illustrating a coupling between spin and orbital eigenstates. We present a theoretical model in which inhomogeneous dephasing due to the population of different Landau levels limits the spin coherence time and captures the essential experimental results.

Figure 1

(a) Transmission and (b) 45° reflection measurement geometries. (c) Effective $g$ factor $g*$ (∎) and spin coherence time $T_2^{*}$ (◻) as a function of angle $\alpha$ at $B=6\mathrm{T}$ and $T=2\mathrm{K}$ on sample E. The solid curve is a fit to Eq. (2). The dotted line is calculated using Eq. (5). (d) Faraday rotation as a function of the time delay $\Delta t$ on sample E at $\alpha =5°$, 15°, and 30° for $B=6\mathrm{T}$ and $T=2\mathrm{K}$.

Figure 2

$g*$ measured as a function of magnetic field $B$ at 45° (×) and 30° (엯) with respect to the growth direction $z$ for sample E and calculated values of $g_z$ (▴) and $g_x$ (▾). The hollow symbols show $g_z$ (▵) and $g_x$ (▿) as calculated from the angle-dependent fit shown in Fig. 1c.

Figure 3

$g_{45}$ measured in the 45° reflection geometry for samples A (barrier doping density $5\times {10}^{16}{\mathrm{cm}}^{-3}$), sample B $(1\times {10}^{17}{\mathrm{cm}}^{-3})$, sample C $(3\times {10}^{17}{\mathrm{cm}}^{-3})$, sample D $(5\times {10}^{17}{\mathrm{cm}}^{-3})$, and sample E $(8\times {10}^{17}{\mathrm{cm}}^{-3})$.

Figure 4

(Color) (a) $g*$ measured in the 45° reflection geometry for sample E as a function of $B$ at $T=2\mathrm{K}$, $5\mathrm{K}$, and $20\mathrm{K}$ (symbols). Also plotted (dashed lines) is $g(B,n)=g_0-c(n+\frac{1}{2})B$, with $g_0=0.405$ and $c=0.00314$ for $n=4$ to 12. (b) $T_2^{*}$ measured (symbols) as a function of B at $T=2\mathrm{K}$, $5\mathrm{K}$, and $20\mathrm{K}$ and calculated (lines) from a spin relaxation model at $T=2\mathrm{K}$, $4\mathrm{K}$, and $12\mathrm{K}$. (c) $R_{xx}$ as a function of $B$ at $T=2\mathrm{K}$, $5\mathrm{K}$, and $20\mathrm{K}$. Also shown are dotted lines indicating the position of $B_n$ for $n=6$ to 16.