Tomonaga-Luttinger physics in electronic quantum circuits

TL;DR

This paper demonstrates experimentally that the conductance behavior in mesoscopic quantum circuits with a resistance can be mapped onto the Tomonaga-Luttinger liquid model, linking quantum circuit phenomena with correlated electron physics.

Contribution

It establishes an experimental connection between dynamical Coulomb blockade effects in quantum circuits and Tomonaga-Luttinger liquid physics, confirming a theoretical mapping.

Findings

Experimental conductance data matches TLL predictions.

Reformulated phenomenological conductance expression validated.

Universal TLL conductance curve observed in circuit data.

Abstract

In one-dimensional conductors, interactions result in correlated electronic systems. At low energy, a hallmark signature of the so-called Tomonaga-Luttinger liquids (TLL) is the universal conductance curve predicted in presence of an impurity. A seemingly different topic is the quantum laws of electricity, when distinct quantum conductors are assembled in a circuit. In particular, the conductances are suppressed at low energy, a phenomenon called dynamical Coulomb blockade (DCB). Here we investigate the conductance of mesoscopic circuits constituted by a short single-channel quantum conductor in series with a resistance, and demonstrate a proposed link to TLL physics. We reformulate and establish experimentally a recently derived phenomenological expression for the conductance using a wide range of circuits, including carbon nanotube data obtained elsewhere. By confronting both conductance data and phenomenological expression with the universal TLL curve, we demonstrate experimentally the predicted mapping between DCB and the transport across a TLL with an impurity.