Quantum phase transition in quantum wires controlled by an external gate

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 $n{x}_0$.

18 pages, 8 figures, minor changes, published version

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Cited by in corpus (14)

• Zigzag Phase Transition in Quantum Wires
• Density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multi-layer configurations: exact treatment of exchange interactions
• Spin-Peierls Quantum Phase Transitions in Coulomb Crystals
• Helical nuclear spin order in two-subband quantum wires
• Renormalization of anticrossings in interacting quantum wires with Rashba and Dresselhaus spin-orbit couplings
• Ginzburg-Landau theory of the zig-zag transition in quasi-one-dimensional classical Wigner crystals
• Helical gaps in interacting Rashba wires at low electron densities
• Generic ordering of structural transitions in quasi-one-dimensional Wigner crystals
• Nonlinear conductance of long quantum wires at a conductance plateau transition: Where does the voltage drop?
• Topological quasi-one-dimensional state of interacting spinless electrons
• Quantum criticality with multiple dynamics
• Statistics-tuned phases of pseudofermions in one dimension
• Lifshitz transition in the phase diagram of two-leg $t$-$J$ ladder systems at low filling
• A strongly coupled zig-zag transition