Luttinger liquid with asymmetric dispersion

V. FERNÁNDEZ; C IUCCI; C NAÓN

Caxambu

Encuentro; XXVI Encontro Nacional de Física da Matéria Condensada; 2003

Sociedade Brasileira de Fisica

In the last years there has been much interest in the study of one-dimensional (1D)co ndensed matter problems. Specific examples of experimentally realized 1D structures are: strongly anisotropic organic conductors, charge transfer salts, quantum wires, edge states in a two-dimensional (2D)electron system in the fractional quantum Hall (FQH)regime and the recently built Carbon Nanotubes. All these systems are no longer described by the usual 3D-like Fermi liquid picture. They are believed to belong to a novel, highly correlated state of matter known as the Luttinger liquid (LL). Very recently, possible LL behavior in 2D high temperature superconductors has also been reported. From the theoretical point of view the most widely studied 1D model is the so-called “g-ology” model, which is known to display the LL behavior characterized by spin-charge separation and by on-universal (interaction dependent) power-law correlation functions. In particular it predicts a momentum distribution function that vanishes at pF as n(p) ∼ (p−pF )2γ, where γ is related to the strength of the electron-electron interaction (in the free case one has γ = 0 and n(p) ∼ θ(pF +p)). One of the simplest and yet very useful version of the “g-ology” model is the exactly solvable Tomonaga-Luttinger (TL) model, which describes left and right-moving electrons subjected to forward-scattering interactions. In this paper we propose a simple modification of the TL model in which left and right-moving electrons have different Fermi velocities vL and vR. Previous studies of LL systems involving more than one Fermi velocity are related to an special class of chiral LL and to multiband and multichain models. Another interesting problem in which one has different values for vF is the interaction between parallel conductors leading to the so called Coulomb drag. We want to stress that the model we shall study is crucially different from all these systems since it is neither a purely chiral LL nor a multiband system with symmetric dispersion. Our theory is formally similar to a recently proposed model for the study of spin-orbit coupling in interacting quasi-1D systems. These authors, however, concentrated their attention on the interplay between velocity asymmetry and spin degrees of freedom, whereas here we derive and analyze physical consequences connected to the asymmetric dispersion only. As we shall see, this point of view allows us to obtain some novel non trivial features of the system. We derive expressions for one-particle Green’s functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference  and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition.