What is a Luttinger liquid? Roughly speaking a Luttinger liquid is a system of interacting electrons in one dimension. In D=1, indeed, the usual Fermi liquid theory dreaks down,
since electronic correlations are so strong that they destroy the single particle picture which holds in D=3.
The Luttinger Liquid theory can describe the effects of electron correlations in several experimental realizations of one-dimensional systems, e.g. single-walled carbon nanotubes, semiconductor-based wires, and edge states of fractional quantum Hall effect bars.
We have analyzed the transport properties of a 1D interacting quantum wire. In particular, the electrical current and the spectrum of current fluctuations (noise) have been computed.
We have taken into account explicitly the finite length of the wire, the contacts with the metallic electrodes, and the
presence of impurities. It has been found out that:
the electric current exhibits oscillations as a function of applied bias, due to the combined effect of finite length and electron interaction in the wire.
while the zero frequency noise only yields the bare electron charge, the analysis of the finite frequency noise gives access to the fractional charge of the elementary excitations of the interacting wire.
Applied techniques
Luttinger Liquid Theory
Bosonization
Keldysh Technique
References
F. Dolcini, B. Trauzettel, I. Safi, H. Grabert, Transport properties of single channel
quantum wires with an impurity: Influence of finite length and temperature on average current
and noise, Phys. Rev. B 71, 165309 (2005).
B. Trauzettel, I. Safi, F. Dolcini, and H. Grabert,
Appearance of fractional charge in the noise of non-chiral
Luttinger liquids ,
Phys. Rev. Lett. 92, 226405 (2004)
F. Dolcini, H. Grabert, I. Safi, and B. Trauzettel, Oscillatory nonlinear conductance of an
interacting quantum wire with an impurity , Phys.
Rev. Lett. 91, 266402 (2003).
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 Oscillations in the electron current as a function of the applied bias U=UL-UR, for different values of electron-electron interaction strength
(black curve = strong interaction; red curve = moderate interaction;
blue curve = weak interaction).
The oscillations are a signature of Luttinger liquid physics, since they would disappear for a non-interacting wire.
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