Intrinsic capacitances and inductances of quantum Hall effect devices

Abstract

Analytic solutions are obtained for the internal capacitances, kinetic inductances, and magnetic inductances of quantum Hall effect devices to investigate whether or not the quantized Hall resistance is the only intrinsic impedance of importance in measurements of the ac quantum Hall effect. The internal capacitances and inductances are obtained by using the results of Cage and Lavine, who determined the current and potential distributions across the widths of quantum Hall effect devices. These intrinsic capacitances and inductances produce small out-of-phase impedance corrections to the in-phase quantized Hall resistance and to the in-phase longitudinal resistance.

Reentrant insulating phases in the integer quantum Hall regime

“…This behavior cannot be explained in the single-particle picture where the kinetic inductance is proportional to the single-particle effective mass and is very small (on the order of 10 μH for the edge currents at integer filling) [25]. Therefore, the enormous inductance measured in these RIP phases confirms a correlated many-body effect.…”

Analyzing the effects of capacitances-to-shield in sample probes on AC quantized Hall resistance measurements

“…While V Pt has been observed to vary with frequency [ 4 – 9 ], it is not clear whether this is due to a frequency dependence of R H ( i ), of ∆ H , or of both R H ( i ) and ∆ H . Calculations of the intrinsic impedance of the 2DEG due to the internal Hall capacitance across the QHE device [ 19 ], however, predict a negligible frequency dependence of R H ( i ) itself, implying a frequency dependence of ∆ H arising from parasitic impedances in the ac QHRS. We therefore simplify the model, and assume that the dc values are appropriate for the R H ( i )/2 resistances in the figure.…”

“…Under these current and magnetic field conditions, the drain contact pad D ′ and the potential probe contact pads 1 ′ , 3 ′ , and 5 ′ at the device periphery are at higher potentials than contact pads S ′ , 2 ′ , 4 ′ , and 6 ′ . These current and flux density directions are chosen to be consistent with those we have used in earlier calculations [ 19 , 22 – 23 ].…”

Large intrinsic inductance in strongly correlated GaAs two-dimensional holes in the integer quantum hall regime

“…21 In this case, a strongly correlated manybody theory is needed to estimate the enhancement of mass and of inductance, instead of single particle models. 20,22 Though this report leaves some questions unanswered due to the complicated interaction effects, the main result of substantial inductance internal to the 2D holes is important both to fundamental science as well as to potential device applications.…”

“…A semi-classical analysis of the QH states in typical Hall bar geometries shows that imaginary contributions to the impedance are very small. 20 Therefore, the enormous reactance must indicate a strong correlation effect. It is unlikely that the out-of-phase signal represents resonant absorption at such low frequencies.…”