Shubnikov–de Haas oscillations in GaAs quantum wells in tilted magnetic fields

We report on quantum magneto-oscillations in an ultrahigh mobility GaAs/AlGaAs quantum well at very high ($⩾{87}^{\circ }$) tilt angles. Unlike previous studies, we find that the spin and cyclotron splittings become equal over a continuous range of angles, but only near certain, angle-dependent filling factors. At high enough tilt angles, Shubnikov–de Haas oscillations reveal a prominent beating pattern, indicative of consecutive level crossings, all occurring at the same angle. We explain these unusual observations by an in-plane field-induced increase of the carrier mass, which leads to accelerated, filling-factor-driven crossings of spin sublevels in tilted magnetic fields.

Figure 1

Oscillatory part of the resistivity $\delta \rho$ (left axis) and amplitude $\delta {\rho }_{\max }$ (right axis) versus the filling factor $\nu$ measured at tilt angles (a) $\theta =87.{00}^{\circ }(\gamma =19.1)$, (b) $\theta =87.{43}^{\circ }(\gamma =22.3)$, (c) $\theta =87.{76}^{\circ }(\gamma =25.6)$, and (d) $\theta =87.{98}^{\circ }(\gamma =28.4)$. Even-$\nu$ (circles) and odd-$\nu$ (squares) amplitudes become equal at $\nu ={\nu }_1$, as marked by $\uparrow$.

Figure 2

Same as Fig. 1 (a) $\theta =88.{04}^{\circ }(\gamma =29.2)$, (b) $\theta =88.{16}^{\circ }(\gamma =31.1)$, (c) $\theta =88.{46}^{\circ }(\gamma =37.2)$.

Figure 3

Same as Figure 1, 2 (a) $\theta =88.{84}^{\circ }(\gamma =49.6)$, (b) $\theta =89.{02}^{\circ }(\gamma =58.1)$, (c) $\theta =89.{09}^{\circ }(\gamma =62.7)$.

Figure 4

Filling factors ${\nu }_1$ (circles), ${\nu }_3$ (squares), and ${\nu }_5$ (triangles) corresponding to crossings of the even-$\nu$ and odd-$\nu$ amplitudes as functions of $\gamma$. Solid lines are fits to the data (see text). Dashed vertical line is the asymptote of the $i=1$ coincidence at large $\nu$.