Dependence of Effective Mass on Spin and Valley Degrees of Freedom

We measure the effective mass ($m^{*}$) of interacting two-dimensional electrons confined to an AlAs quantum well while we change the conduction-band valley occupation and the spin polarization via the application of strain and magnetic field, respectively. Compared to its band value, $m^{*}$ is enhanced unless the electrons are fully valley- and spin-polarized. Incidentally, in the fully spin- and valley-polarized regime, the electron system exhibits an insulating behavior.

Figure 1

The spin ($s$) and valley ($v$) occupations for density $n=3.8\times {10}^{11}{\mathrm{cm}}^{-2}$ are shown as a function of $B_{\parallel }$ and strain; the thick, solid lines mark the boundaries, and the indices 1 and 2 indicate, respectively, whether one or two spin (and/or valley) subbands are occupied. Dashed lines mark the boundary of the upper-right region where the sample exhibits an insulating behavior. Stars mark the ($B_{\parallel }$, $ϵ$) values at which the indicated effective mass was measured.

Figure 2

Sample resistance is shown as a function of (a) $B_{\parallel }$ and (b) $ϵ$ at two temperatures. For each pair of traces in (a), $ϵ$ is kept constant, while for each pair in (b), $B_{\parallel }$ is kept fixed at the indicated values.

Figure 3

Summary of measurements for the ($s=1$, $v=2$) case. (a),(d) Field and strain traces taken at different temperatures ranging from 0.02 to 0.7 K (bottom to top). (b) Energy level diagram. (c) Dingle fits at $\nu =6$. (e) Landau level fan diagram as a function of $ϵ$. (f) Deduced values of $m^{*}$ as a function of $ϵ$.

Figure 4

Magnetoresistance traces, Dingle fits, and energy level diagrams for ($s=1$, $v=1$), ($s=2$, $v=1$), and ($s=2$, $v=2$). The black, red, and green traces were taken at (a) 0.02, 0.39, 1.03; (b) 0.02, 0.60, 0.87; (c) 0.02, 0.24, 0.39 K, respectively.