Magnetic Field Symmetry of Dynamic Capacitances

TL;DR

This paper investigates the symmetry properties of dynamic capacitances in multi-terminal systems under magnetic fields, revealing asymmetries and predicting quantized resistances in Hall systems, aligning with recent experiments.

Contribution

It demonstrates that dynamic capacitance matrices generally obey Onsager-Casimir relations rather than full symmetry, and predicts quantized four-terminal resistances in insulating Hall samples.

Findings

Dynamic capacitance matrices are generally asymmetric under magnetic fields.

Experimental observations of asymmetry in quantum Hall systems are explained.

Quantization of four-terminal resistances in insulating Hall samples is predicted.

Abstract

While the static capacitance matrix is always symmetric and thus an even function of the magnetic field, the dynamic capacitance matrix of multi-terminal samples obeys in general only the weaker Onsager-Casimir symmetry relations. Our results are in accordance with recent experimental observations of asymmetric dynamic capacitances in quantized Hall systems. We predict quantization of the four-terminal resistances of an insulating Hall sample.