Nonlinear response in overlapping and separated Landau levels of GaAs quantum wells

We have studied magnetotransport properties of a high-mobility two-dimensional electron system subject to weak electric fields. At low magnetic field $B$, the differential resistivity acquires a correction $\delta r\propto -{\lambda }^2{j}^2/B^2$, where $\lambda$ is the Dingle factor and $j$ is the current density, in agreement with theoretical predictions. At higher magnetic fields, however, $\delta r$ becomes $B$ independent, $\delta r\propto -j^2$. While the observed change in behavior can be attributed to a crossover from overlapping to separated Landau levels, full understanding of this behavior remains a subject of future theories.

Figure 1

Normalized differential resistivity $r/\rho$ versus direct current of density $j$ at different magnetic fields from 0.3 kG (top curve) to 1.0 kG (bottom curve) in steps of 0.1 kG. The maxima of HIRO at $B=0.3$ kG are marked by integers (cf. $1,2$).

Figure 2

Normalized differential resistivity $r/\rho$ versus ${\epsilon }_j$ at different magnetic fields from 0.3 to 1.0 kG in steps of 0.1 kG (solid lines). Dotted lines are fits to the data with $r/\rho =1-\alpha {\epsilon }_j^2$ over the range $-0.1⩽{\epsilon }_j⩽0.1$.

Figure 3

Obtained from the fits (cf. Fig. 2) of parameter $\alpha /12{\pi }^2$ (circles) versus inverse magnetic field $1/B$ plotted on a log-linear scale. The fit (solid line) to the lower $B$ part of the data, $B⩽0.5$ kG, with $\alpha ={\alpha }_0\exp (-2\pi /{\omega }_{\text{c}}{\tau }_{\text{q}})$—see Eq. (4)—generates ${\tau }_{\text{q}}=15.2$ ps and ${\alpha }_0/12{\pi }^2=2.25$.

Figure 4

Obtained from the fits (cf. Fig. 2) parameter $\alpha /12{\pi }^2$ (circles) versus $B^2$. The fit (solid line) to the higher $B$ part of the data, $B⩾1.3$ kG, with $\alpha /12{\pi }^2=B^2/B_0^2$ generates $B_0\approx 0.93$ kG.

Figure 5

Normalized differential resistivity $r/\rho$ versus ${\epsilon }_j$ measured at $B=0.5$ kG at $T$ from 1.5 K to 4.0 K, in a step of 0.5 K (solid lines). Dashed lines are fits to the data with $r/\rho =1-\alpha {\epsilon }_j^2$ over the range $-0.1⩽{\epsilon }_j⩽0.1$.