Journal of the Physical Society of Japan

Effects of Long-Range Coulomb Interaction on Resistivity of a Quantum Wire

Hidetoshi Fukuyama, Hiroshi Kohno, Ryōen Shirasaki

Published Apr 15, 1993• 27 citations

Abstract

Effects of long-range Coulomb interaction on the temperature dependence of the resistivity due to impurity scattering have been investigated for a single-channel quantum wire. The resistivity is seen to diverge as T →0, as in the case of the Luttinger liquid with interaction constants independent of momentum transfer, but in the present case, the effective value of the exponent itself depends on T reflecting the logarithmic momentum dependence of the long-range interaction.

DOI: 10.1143/jpsj.62.1109

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Journal of the Physical Society of Japan

Effects of Long-Range Coulomb Interaction on Resistivity of a Quantum Wire

Hidetoshi Fukuyama, Hiroshi Kohno, Ryōen Shirasaki

Published Apr 15, 1993• 27 citations

Publisher

Abstract

DOI: 10.1143/jpsj.62.1109

Related papers

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

H. Maurey, Thierry Giamarchi

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{\mathit{k}}_{\mathit{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, ${\ensuremath{\xi}}_{\mathrm{cr}}$, 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.

We investigate the behavior of the four-terminal resistance

{R}_{4\text{pt}}

in a quantum wire described by a Luttinger liquid in two relevant situations: (i) in the presence of a single impurity within the wire and (ii) under the effect of asymmetries introduced by disordered voltage probes. In the first case, interactions leave a signature in a power-law behavior of

{R}_{4\text{pt}}

as a function of the voltage

V

and the temperature

T

. In the second case interactions tend to mask the effect of the asymmetries. In both scenarios the occurrence of negative values of

{R}_{4\text{pt}}

is explained in simple terms.

{T}^{*}

the transresistivity follows a power law $\ensuremath{\rho}\ensuremath{\propto}{T}^{x},$ where the interaction-strength dependent exponent x is determined by the Luttinger liquid parameter ${K}_{c\ensuremath{-}}$ of the relative charge mode. At temperature below

{T}^{*}

relative charge displacements are enabled by solitonic excitations, reflected by an exponential temperature dependence. The crossover temperature

{T}^{*}

depends sensitively on the wire width, interwire distance, Fermi wavelength and the effective Bohr radius. For wire distances $\overline{d}\ensuremath{\gg}{k}_{F}^{\ensuremath{-}1}$ it is exponentially suppressed with ${T}^{*}{/E}_{F}\ensuremath{\sim}\mathrm{exp}[\ensuremath{-}\overline{d}{k}_{F}/(1\ensuremath{-}{K}_{c\ensuremath{-}})].$ The behavior changes drastically if each of the two wires develop spin gaps. In this case we find that the transresistivity vanishes at zero temperature. We discuss our results in view of possible experimental realizations in $\mathrm{GaAs}\ensuremath{-}{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ semiconductor structures.