Transport through asymmetric two-lead junctions of Luttinger liquid wires

We calculate the conductance of a system of two spinless Luttinger liquid wires with different interaction strengths g_1, g_2, connected through a short junction, within the scattering state formalism. Following earlier work we formulate the problem in current algebra language, and calculate the scale dependent contribution to the conductance in perturbation theory keeping the leading universal contributions to all orders in the interaction strength. From that we derive a renormalization group (RG) equation for the conductance. The analytical solution of the RG-equation is discussed in dependence on g_1, g_2. The regions of stability of the two fixed points corresponding to conductance G=0 and G=1, respectively, are determined.Comment: 6 pages, 3 figures, REVTE

Transport of interacting electrons through a potential barrier: nonperturbative RG approach

We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g_2, and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the basis of scattering states into an effective low energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) \beta-function are identified. A universal part of the \beta-function is given by a ladder series and summed to all orders in g_2. First non-universal corrections beyond the ladder series are discussed. The RG-equation for the temperature dependent conductance is solved analytically. Our result agrees with known limiting cases.Comment: 6 pages, 5 figure

Shot noise in Weyl semimetals

We study the effect of inelastic processes on the magneto-transport of a quasi-one dimensional Weyl semi-metal, using a modified Boltzmann-Langevin approach. The magnetic field drives a crossover to a ballistic regime in which the propagation along the wire is dominated by the chiral anomaly, and the role of fluctuations inside the sample is exponentially suppressed. We show that inelastic collisions modify the parametric dependence of the current fluctuations on the magnetic field. By measuring shot noise as a function of a magnetic field, for different applied voltage, one can estimate the electron-electron inelastic length $l_{\rm ee}$.Comment: 7 pages, 1 figur