Temperature dependence of the breakdown of the quantum Hall effect studied by induced currents

We have developed a model of the high-current breakdown of the integer quantum Hall effect, as measured in contactless experiments using a highly-sensitive torsion balance magnetometer. The model predicts that, for empirically “low-mobility” samples $\left(\mu <75{\mathrm{m}}^2{\mathrm{V}}^{-1}{\mathrm{s}}^{-1}\right)$, the critical current for breakdown should decrease with, and have a linear dependence on, temperature. This prediction is verified experimentally with the addition of a low-temperature saturation of the critical current at a temperature that depends on both sample number density and filling factor. It is shown that this saturation is consistent with quasielastic inter-Landau-level scattering when the maximum electric field in the sample reaches a large enough value. In addition we show how this model can be extended to give qualitative agreement with experiments on high-mobility samples.

Figure 1

Raw experimental data showing induced currents, as their corresponding magnetic moment, in sample T73 at $50\mathrm{mK}$. There is a slowly varying background arising from the magnetization of the rotor. The induced currents can clearly be seen as they reverse polarity when the field sweep direction is reversed. The inset shows an example of a $M$ vs $\partial B∕\partial t$ curve for $\nu =6$ at $50\mathrm{mK}$, the size of the induced current saturates at fast sweep rates and the value of $M_s$ is indicated.

Figure 2

The temperature dependence of the saturation magnetic moment at $\nu =4$ in sample T73. The linear trend, $M_s\left(T\right)=M_0-\alpha T$, and the values of $T_s$ and $T_0$ are indicated. The two insets demonstrate the similarity in behavior of both a two-dimensional electron system (top) and a two-dimensional hole system (bottom).

Figure 3

The calculated radial electric field profile across the sample when the sweeping magnetic field is applied. The data shown as a dashed line ignore the charge build-up at the sample edge which is accounted for in the data represented by the solid line.

Figure 4

$T_0$ plotted against $1∕\nu$ for sample T73. The odd and even filling factors have different gradients, as indicated. The inset shows data for both T73 and T151 plotted against magnetic field, the even $\nu$ data then have the same gradient (within experimental error). The difference between the odd $\nu$ data reflects the different $g$-factors in these samples.

Figure 5

A sketch of possible inter-Landau level transitions which both conserve spin (solid arrows) and allow spin-flip transitions (dashed arrows).

Figure 6

The temperature dependence of the saturation magnetic moment in the high-mobility sample T393. The experimental data have been fitted to a simple exponential dependence.