Quantum phase transition in quantum wires controlled by an external gate

Tobias Meng, Mehul Dixit, Markus Garst, and Julia S. Meyer
Phys. Rev. B 83, 125323 – Published 31 March 2011

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 nx0, where n is the electron density and x0 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 nx0.

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  • Received 30 December 2010

DOI:https://doi.org/10.1103/PhysRevB.83.125323

©2011 American Physical Society

Authors & Affiliations

Tobias Meng1, Mehul Dixit2, Markus Garst1, and Julia S. Meyer3

  • 1Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, D-50937 Köln, Germany
  • 2Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
  • 3SPSMS, UMR-E CEA/UJF-Grenoble 1, INAC, Grenoble, F-38054, France

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Vol. 83, Iss. 12 — 15 March 2011

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