Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We compute the dispersion relations of collective modes, one-particle Green’s functions, momentumdistributions and conductivities. Studying these quantities as functions of both the velocities and the strength of the interaction we find a new region in the space of couplings where chiral symmetry is broken and the conductivity becomes negative. A possible experimental realization of this model is proposed. PACS numbers: 71.10.Pm Typeset using REVTEX Corresponding author, e-mail: [email protected] In the last years there has been much interest in the study of one-dimensional (1D) condensed matter problems [1]. Specific examples of experimentally realized 1D structures are: strongly anisotropic organic conductors [2], charge transfer salts [3], quantum wires [4], edge states in a two-dimensional (2D) electron system in the fractional quantum Hall (FQH) regime [5] and the recently built Carbon Nanotubes (CNT) [6]. All these systems are no longer described by the usual 3D-like Fermi liquid (FL) picture. They are believed to belong to a novel, highly correlated state of matter known as the Luttinger liquid (LL) [7]. Very recently, possible LL behavior in 2D high temperature superconductors has also been reported [8]. From the theoretical point of view the most widely studied 1D model is the so-called ”gology” model [9], which is known to display the LL behavior characterized by spin-charge separation and by non-universal (interaction dependent) power-law correlation functions. In particular it predicts a momentum distribution function that vanishes at pF as n(p) ∼ (p − pF ), 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 [10]. In this Letter 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 [11] and to multiband and multichain models [12]. Another interesting problem in which one has different values for vF is the interaction between parallel conductors leading to the so called Coulomb drag [13]. 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. To be specific we start by considering an asymmetric dispersion described by the following Hamiltonian