Transport of one-dimensional interacting fermions through a barrier.

We study the transport properties of one-dimensional (1D) interacting Fermions through a barrier by numerically calculating the Kohn charge stiffness constant and the relative Drude weight. We find that the transport properties of the 1D Hubbard model are quite different from those of the 1D spinless Fermion model. For example, the presence of the attractive interaction between electrons in the 1D Hubbard model actually suppresses the DC conductance, while a small repulsive interaction enhances the DC conductance. These results show that the spin degree of freedom plays an important role in the transport properties of the 1D interacting Fermion systems. PACS numbers: 71.30.+h, 75.10.Jm, 73.20.Dx Typeset using REVTEX 1 Recently, there has been increasing interest in one-dimensional (1D) electron systems. [1–8] On the one hand, the progress in ultrafine lithographic technology has made it possible to fabricate and experimentally study quantum wires in which only the lowest subband is occupied, approaching the true 1D limit; on the other hand, there is a renewed interest in the Luttinger liquid because of the suggestion that the high temperature superconductors might be non-Fermi-liquid-like. It is well known that even a weak interaction in a 1D Fermion system will drive the system to become a Luttinger liquid which exhibits quite different behavior from the Fermi liquid system. [9,10] For example, Kane and Fisher have studied the transport properties in a 1D spinless Luttinger liquid with a barrier (or a weak link). They find that an attractive interaction makes the system a perfect conductor while a repulsive interaction makes it an insulator. [7] In this paper we present some results of the transport properties of 1D interacting Fermion systems with a barrier. We study both the interacting spinless Fermion model and the 1D Hubbard model with a barrier by calculating the Kohn charge stiffness constant using the Lanczos algorithm. In particular, we investigate the effect of spin on the transport properties motivated by an interesting statement of Anderson who argued that the theory of the transport in 1D spinless Fermion may be irrelevant for a real electron system which has both charge and spin degrees of freedom. [11] We find that our result for the spinless Fermion model agrees with that of Kane and Fisher qualitatively. But our result of the 1D Hubbard model with a barrier is exact opposite of that of the spinless Fermion model. We find that in the case of the Hubbard model, the presence of the attractive interactions between electrons actually decreases the Kohn charge stiffness constant Dc as well as the relative Drude weight, in contrast to the 1D spinless Fermion case where the presence of attractive interactions increases Dc and the relative Drude weight as long as the attractive interaction is not large enough to cause a phase transition to a phase-separated insulating state. In the case of repulsive interaction, we find that a small repulsive interaction in the 1D Hubbard model with a weak link actually increases Dc and the relative Drude weight, again in contrast to the 1D spinless Fermion model where the repulsive interaction decreases 2 Dc. We first study an interacting spinless Fermion model, so called Heisenberg-Ising model, on a 1D ring with a weak link