Quantum phase transition in quantum wires controlled by an external gate

TL;DR

This paper investigates the quantum phase transition in electrons confined in quantum wires, highlighting two mechanisms: a Wigner crystal deformation at low densities and a subband filling transition at high densities, with implications for electron liquid stability.

Contribution

It introduces a comprehensive analysis of the quantum phase transition in quantum wires, combining Wigner crystal deformation and subband filling perspectives, with detailed critical behavior and phase diagram insights.

Findings

Transition at low density resembles a Wigner crystal to zigzag structure.

At high density, the transition is a Lifshitz transition of impenetrable polarons.

The spin sector remains decoupled during the transition.

Abstract

We consider electrons in a quantum wire interacting via a long-range Coulomb potential screened by a nearby gate. We focus on the quantum phase transition from a strictly one-dimensional to a quasi-one-dimensional electron liquid, that is controlled by the dimensionless parameter $n x_0$, where $n$ is the electron density and $x_0$ is the characteristic length of the transverse confining potential. If this transition occurs in the low-density limit, it can be understood as the deformation of the one-dimensional Wigner crystal to a zigzag arrangement of the electrons described by an Ising order parameter. The critical properties are governed by the charge degrees of freedom and the spin sector remains essentially decoupled. At large densities, on the other hand, the transition is triggered by the filling of a second one-dimensional subband of transverse quantization. Electrons at the bottom of the second subband interact strongly due to the diverging density of states and become impenetrable. We argue that this stabilizes the electron liquid as it suppresses pair-tunneling processes between the subbands that would otherwise lead to an instability. However, the impenetrable electrons in the second band are screened by the excitations of the first subband, so that the transition is identified as a Lifshitz transition of impenetrable polarons. We discuss the resulting phase diagram as a function of $n x_0$.