Realization of an Interacting Two-Valley AlAs Bilayer System

By using different widths for two AlAs quantum wells comprising a bilayer system, we force the $X$-point conduction-band electrons in the two layers to occupy valleys with different Fermi contours, electron effective masses, and $g$ factors. Since the occupied valleys are at different $X$ points of the Brillouin zone, the interlayer tunneling is negligibly small despite the close electron layer spacing. We demonstrate the realization of this system via magnetotransport measurements and the observation of a phase-coherent, bilayer $\nu =1$ quantum Hall state flanked by a reentrant insulating phase.

Figure 1

Fourier transform spectra of the Shubnikov–de Haas oscillations (shown in the insets), measured at 0.3 K, for different values of front and back gate biases. The arrows indicate the expected peak positions, corresponding to the total bilayer density $n_{\mathrm{tot}}$ ($1.7\times {10}^{11}{\mathrm{cm}}^{-2}$ and $2.5\times {10}^{11}{\mathrm{cm}}^{-2}$ in the top and bottom traces, respectively), as determined from the Hall resistance; the bilayer total filling factor $\nu$ is also labeled in the insets. As illustrated by the lower insets, in (a) the electrons are all in the narrow well and occupy the $X_Z$ valley, while in (b) they equally occupy the narrow well ($X_Z$ valley) and the wide well ($X_X$ and $X_Y$ valleys).

Figure 2

Parallel field magnetoresistance for different charge distributions; top trace: $n_N=1.9\times {10}^{11}{\mathrm{cm}}^{-2}$, $n_W=0$; bottom trace: $n_N=n_W=1.5\times {10}^{11}{\mathrm{cm}}^{-2}$. The arrows mark the fields, $B_P$, above which the layer(s) become fully spin polarized. The inset shows $B_P$ versus layer density.

Figure 3

(a) Magnetoresistance, ${\rho }_{xx}$, versus perpendicular magnetic field for the balanced bilayer system, with $n_N=n_W=1.26\times {10}^{11}{\mathrm{cm}}^{-2}$, at three different temperatures, showing a $\nu =1$ QHS flanked by a reentrant insulating phase. (b) The dependence of ${\rho }_{xx}$ at balance on tilt angle. Here, $n_N=n_W=1.30\times {10}^{11}{\mathrm{cm}}^{-2}$.