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Transport properties of a quantum wire in the presence of impurities and long-range Coulomb forces

H. Maurey·T. Giamarchi
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Abstract

One-dimensional electron systems interacting with long-range Coulomb forces (quantum wires) show a Wigner crystal structure. We investigate in this paper the transport properties of such a Wigner crystal in the presence of impurities. Contrary to what happens when only short-range interactions are included, the system is dominated by $4 k_F$ scattering on the impurities. There are two important length scales in such a problem: one is the pinning length above which the (quasi-)long-range order of the Wigner crystal is destroyed by disorder. The other length $ξ_{cr}$ is the length below which Coulomb interactions are not important and the system is behaving as a standard Luttinger liquid with short-range interactions. We obtain the frequency and temperature dependence of the conductivity. We show that such a system is very similar to a classical charge density wave pinned by impurities, but with important differences due to quantum fluctuations and long-range Coulomb interactions. Finally we discuss our results in comparison with experimental systems.

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H. Maurey, T. Giamarchi. 1994-08-30. Transport properties of a quantum wire in the presence of impurities and long-range Coulomb forces. https://doi.org/10.1103/physrevb.51.10833

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