Quantum Electric Circuits Analogous to Ballistic Conductors

TL;DR

This paper introduces quantum electric circuits that mimic mesoscopic electron transport, revealing a new charge-conductance uncertainty relation and providing insights into the minimum conductivity in graphene.

Contribution

It presents novel quantum circuit models that replicate mesoscopic conductance phenomena, offering a new perspective on the origin of minimum conductivity in graphene.

Findings

Derived a new charge-conductance uncertainty relation.

Introduced quantum circuits analogous to 2D electron gases and graphene.

Provided insights into the minimum conductivity in graphene.

Abstract

The conductance steps in a constricted two-dimensional electron gas and the minimum conductivity in graphene are related to a new uncertainty relation between electric charge and conductance in a quantized electric circuit that mimics the electric transport in mesoscopic systems. This uncertainty relation makes specific use of the discreteness of electric charge. Quantum electric circuits analogous to both constricted two-dimensional electron gas and graphene are introduced. In the latter case a new insight into the origin of minimum conductivity is obtained.