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

Abstract

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) β-function are identified. A universal part of the β-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.

6 pages, 5 figures

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Cited by in corpus (14)

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• Observation of Majorana Quantum Critical Behavior in a Resonant Level Coupled to a Dissipative Environment
• Conductance through a potential barrier embedded in a Luttinger liquid: nonuniversal scaling at strong coupling
• Numerical Renormalization Group at marginal spectral density: application to quantum tunneling in Luttinger liquids
• Transport Signatures of Majorana Quantum Criticality Realized by Dissipative Resonant Tunneling
• Transport properties of a two-lead Luttinger liquid junction out of equilibrium: fermionic representation
• A fermionic approach to tunneling through junctions of multiple quantum wires
• Hierarchical equations of motion approach to transport through an Anderson impurity coupled to interacting Luttinger liquid leads
• Y-junction of Luttinger-liquid wires out of equilibrium
• Friedel oscillations and dynamical density of states of an inhomogeneous Luttinger liquid
• Electron-electron interaction effects on transport through mesoscopic superconducting hybrid junctions
• Conductance of inhomogeneous Luttinger liquids with a finite bandwidth
• Impurity entropy of junctions of multiple quantum wires
• Breaking a "poor man" RG approach in the Luttinger liquid with one impurity