Exact Conductance through Point Contacts in theν=1/3Fractional Quantum Hall Effect

Abstract

The conductance for tunneling through a point contact between two ν = 1/3 quantum Hall edges is described by a universal scaling function, which has recently been measured experimentally. We compute this universal function exactly, by using the thermodynamic Bethe ansatz and a Boltzmann equation.

The Tomonaga–Luttinger liquid with quantum impurity revisited: Critical line and phase diagram

“…The TLL model has been discussed in various contexts in the literature, such as one dimensional quantum wires [4][5][6][7], Josephson junctions arrays [8][9][10][11], Kondo effects [12][13][14], carbon nanotube [15] and edge states of quantum Hall effects [16][17][18]. The TLL model in the presence of an impurity is formulated as a one dimensional fermion theory with four fermi interactions on a half line and a tunneling interaction through an impurity at the origin.…”

From integrability to conductance, impurity systems

“…There exist various investigations, e.g., [17,13,14,18] for conformal (massless) theories with defect, which exploit the original folding idea of Wong and Affleck [17]. The idea is that a conformal field theory with a purely transmitting or reflecting defect can be mapped into a boundary theory, i.e.…”

“…Generalizing the Landauer transport picture a proposal for the conductance through a quantum wire with a defect (impurity) has been made in [13,14] …”

Non-linear current through a barrier in 1D wires with finite-range interactions

“…as in [1][2][3]7,8,10 . In the limit of weak tunnelling it has been demonstrated 9 that the selfconsistently adjusted chemical potential indeed varies most pronouncedly close to x = 0 .…”

“…Since the discovery of the vanishing transmittivity of a tunnel barrier in a one-dimensional (1D) wire due to the repulsive electron-electron interaction 1 new interest has emerged in the transport properties of 1D electron systems [2][3][4][5][6][7][8][9][10] . Indeed, the influence of the electron correlations shows up strikingly in non-linear current voltage relations which are investigated experimentally in narrow, semiconducting wires 11 .…”