Dissipation-Driven Quantum Phase Transitions in a Tomonaga-Luttinger Liquid Electrostatically Coupled to a Metallic Gate

Abstract

The dissipation induced by a metallic gate on the low-energy properties of interacting 1D electron liquids is studied. As function of the distance to the gate, or the electron density in the wire, the system undergoes a quantum phase transition from the Tomonaga-Luttinger liquid state to two kinds of dissipative phases, one of them with a finite spatial correlation length. We also define a dual model, which describes an attractive one dimensional metal with a Josephson coupling to a dirty metallic lead.PACS numbers: 71.10. Pm,73.63.Nm,73.43.Nq Introduction: In the study of properties of quantum wires (and other mesoscopic systems), proximity to metallic gates is frequently regarded as a source of static screening of the interactions in the wire. Within a classical electrostatic picture, which is valid at long distances from the gate, this arises because electrons in the wire interact, not only amongst themselves, but also with their image charges in the gate. Thus the Coulomb potential becomes a more rapidly decaying dipole-dipole potential. Moreover, metallic environments (e.g. gates) are also a source of de-phasing and dissipation [1, 2, 3, 4] (for experimental research on related topics, see [5]), which arise because the electrons in the wire can exchange energy and momentum with the low-energy electromagnetic modes of the gate. This effect is described by the dissipative part of the screened potential and, as we show below, it can lead to backscattering (i.e. a scattering process where one or several electrons reverse their direction of motion) in a one-dimensional (1D) quantum wire. We find that, for an arbitrarily small coupling to the gate, the backscattering can drive a quantum phase transition provided that the interactions between the electrons in the wire are sufficiently repulsive.The effects of dissipation on quantum phase transitions have attracted much attention [6,7,8,9]. We discuss here transitions induced by dissipation, as in [10,11,12]. Some aspects of this work are also related to previous research on 1D systems coupled to environments [13, 14,

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