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arXiv:cond-mat/0112199

Unstable particles versus resonances in impurity systems, conductance in quantum wires

Olalla A. Castro-Alvaredo, Andreas Fring

Published Dec 11, 2001• 0 citations
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Abstract

We compute the DC conductance for a homogeneous sine-Gordon model and an impurity system of Luttinger liquid type by means of the thermodynamic Bethe ansatz and standard potential scattering theory. We demonstrate that unstable particles and resonances in impurity systems lead to a sharp increase of the conductance as a function of the temperature, which is characterized by the Breit-Wigner formula.

DOI
10.48550/arxiv.cond-mat/0112199

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We compute the DC conductance for a homogeneous sine-Gordon model and an impurity system of Luttinger liquid type by means of the thermodynamic Bethe ansatz and standard potential scattering theory. We demonstrate that unstable particles and resonances in impurity systems lead to a sharp increase of the conductance as a function of the temperature, which is characterized by the Breit-Wigner formula.
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The quantum physics of one dimensional systems exhibits many remarkable and exotic physical phenomena. These are the result of the strong correlations which exist in such systems due to the reduced dimensionality and in many cases can be described by Luttinger Liquid theory. Likewise quantum impurity systems, where a bath of particles couples to the same impurity, exhibit well known non perturbative phenomena like the Kondo effect. In this thesis we study the physics of quantum impurities in interacting environments - the intersection of these two areas. Such Luttinger-impurity systems can be realized experimentally in a range of different settings from quantum wires and carbon nano tubes to edges of fractional quantum hall systems and cold atom gases. We show that many of the models used to describe these experiments are integrable and can be studied by means of the Bethe Ansatz. This powerful and exact method provides us with the exact eigenstates and energy levels of the model Hamiltonian. The models considered include two which describe a Lutttinger liquid coupled to a back scattering impurity, the Kane-Fisher and weak tunnelling model as well as Luttinger liquids coupled a quantum dot in various geometries: at the boundary, sidecoupled and embedded. To incorporate both the backscattering nature of the impurities and the interacting bulk particles a new formulation of the Bethe Ansatz is developed and implemented. The eigenstates and spectra of the models are found and used to investigate their ground state and thermodynamic properties.
Thermal transport through one-dimensional systems of strongly interacting electrons is studied in two cases: (i) a finite Luttinger liquid (LL) wire containing a strong impurity, and (ii) a LL ring connected by quantum wires to noninteracting electron reservoirs. It is shown that, for (i), a temperature-induced resonant transport takes place under certain conditions. In case (ii) the heat conductance under resonance conditions does not depend on the electron-electron interaction and the system thermal conductance coincides with the maximal Fermi-liquid thermal value.
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 4kF{\mathit{k}}_{\mathit{F}}kF​ 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.