Spin-Dependent Resistivity at Transitions between Integer Quantum Hall States

The longitudinal resistivity at transitions between integer quantum Hall states in two-dimensional electrons confined to AlAs quantum wells is found to depend on the spin orientation of the partially filled Landau level in which the Fermi energy resides. The resistivity can be enhanced by an order of magnitude as the spin orientation of this energy level is aligned with the majority spin. We discuss possible causes and suggest a new explanation for the spikelike features observed at the edges of quantum Hall minima near Landau level crossings.

Figure 1

${\rho }_{xx}$ vs $B_{\perp }$ at $T=300\mathrm{mK}$ in a narrow AlAs QW as the sample is tilted through the first ($i=1$) coincidence angle ($\theta \simeq 45°$). (a) A resistance spike is visible near the $\nu =2$ minimum and (b) subsequently merges with the ${\rho }_{xx}$ maximum between $\nu =2$ and 1, leading to a dramatic enhancement of ${\rho }_{xx}$ at that maximum. The two lowest energy levels, labeled by their LL index and spin, and the location of $E_F$ are shown schematically for the indicated ${\rho }_{xx}$ maxima.

Figure 2

(a) Energy level configurations for a 2DES in a narrow AlAs QW as it is tilted in field. Many-body effects near the coincidence angles are not shown. (b),(c) ${\rho }_{xx}$ vs $1/\cos (\theta )$ at $T=20\mathrm{mK}$ for half integer $\nu$ at two densities, with the coincidence angles marked by vertical dotted lines. (d),(e) The same data plotted against $B_{\mathrm{tot}}$ along with parallel-field magnetoresistivity (red or grey traces). The key for the symbols in panels (b)–(e) is in panel (d).

Figure 3

${\rho }_{xx}$ vs $B_{\perp }$ at $T=300\mathrm{mK}$ in a wide AlAs QW for different $\theta$ with the current ($I$) directed (a) along and (b) transverse to the long axis of the occupied valley, as indicated schematically in each panel. The inset of (a) shows a close-up of the $\theta =0°$ trace, and the LL indices and spins for the lowest three energy levels are shown in (b) for the indicated traces.