Charge Fluctuations in Quantum Point Contacts and Chaotic Cavities in the Presence of Transport

TL;DR

This paper investigates frequency-dependent charge fluctuations in quantum point contacts and chaotic cavities, revealing how these fluctuations are influenced by charge dynamics and exhibit oscillatory and broad distribution behaviors.

Contribution

It introduces an effective scattering approach to analyze charge fluctuations, providing new insights into resistance distributions in quantum conductors.

Findings

Charge fluctuations are linked to charge dynamics via resistances.

Resistances show oscillations with channel openings in point contacts.

Chaotic cavities exhibit broad resistance distributions between 1/4 and 1/2 of a resistance quantum.

Abstract

We analyze the frequency-dependent current fluctuations induced into a gate near a quantum point contact or a quantum chaotic cavity. We use a current and charge conserving, effective scattering approach in which interactions are treated in random phase approximation. The current fluctuations measured at a nearby gate, coupled capacitively to the conductor, are determined by the screened charge fluctuations of the conductor. Both the equilibrium and the non-equilibrium current noise at the gate can be expressed with the help of resistances which are related to the charge dynamics on the conductor. We evaluate these resistances for a point contact and determine their distributions for an ensemble of chaotic cavities. For a quantum point contact these resistances exhibit pronounced oscillations with the opening of new channels. For a chaotic cavity coupled to one channel point contacts the charge relaxation resistance shows a broad distribution between 1/4 and 1/2 of a resistance quantum. The non-equilibrium resistance exhibits a broad distribution between zero and 1/4 of a resistance quantum.