Hopping conduction and magnetoresistance of a GaAs/Al${}_x$Ga${}_{1-x}$As quantum well with embedded InAs dots

Magnetoresistance and temperature-dependent conductance are measured in the sample made of a GaAs/Al${}_x$Ga${}_{1-x}$As quantum well with self-assembled InAs dots. Conductance is analyzed by Mott’s hopping theory; the localization lengths have been extracted at various gate voltages. The sample is in the transition from near to metal-insulator to the deeply hopping regime with the combined effect of the long- and short-range scattering potentials. The magnitude of the negative magnetoresistance increases with increasing negative gate voltage. The magnetic-field dependence of the resistance can be explained by the theory of the interference model of hopping electrons.

Figure 1

TEM image of the InAs dots in the sample. The scale bar on the right bottom represents 200 nm.

Figure 2

Temperature-dependent conductance. From top to bottom, the gate voltage is set at $-0.04$, $-0.08$, $-0.12$, and $-0.15$ V. Symbols are measured results, and the curve is the linear fit of the data. For the four fixed-gate voltages from top to bottom, the localization lengths are 35, 31, 23, and 12 nm; typical hopping lengths are 57, 54, 49, and 39 nm.

Figure 3

Magnetoresistance as a function of magnetic field, $B$. The measurements are performed at 2.0 K. From top to bottom, the gate voltage is fixed at 0, $-0.04$, $-0.08$, and $-0.12$ V. For the gate voltage at 0 V, the sample does not show hopping behavior.

Figure 4

Magnetoresistance for four gate voltages $V_g=0$, $-0.04$, $-0.08$, and $-0.12$ V from bottom to top. Dashed lines are linear fits of the resistance in logarithmic scale to $B^{1/2}$. Note in this plot at field $B>0.01$ T, if we ignore the feature of the Shubnikov–de Haas oscillations of the resistance, the field dependence of the curves is linear and the slopes of the four sets of data are approximately the same.