Relaxation Time of a Chiral QuantumR−LCircuit

Abstract

We report on the GHz complex admittance of a chiral one-dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor $L$) in series with a tunable resistor ($R$) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission independent. This shows that the relaxation time of a chiral $R\mathrm{\text{−}}L$ circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the circuit.