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

Abstract

The transport properties of a tunnel barrier in a one-dimensional wire are investigated at finite voltages and temperatures. We generalize the Luttinger model to account for finite ranges of the interaction. This leads to deviations from the power law behaviour first derived by Kane and Fisher 1 . At high energies the influence of the interaction disappears and the Coulomb blockade is suppressed. The crossover in the voltage or in the temperature dependence can provide a direct measure for the range of the interaction.Keywords : electron-electron interactions, electronic transport, tunnelling.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 2-10 . 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 . Local interactions, v(x−x ′ ) = v 0 δ(x−x ′ ) are described within the Luttinger model for which the power-law 1-5has been predicted for the current-voltage relation through a tunnel barrier with tunnel resistance R T , at zero temperature T = 0 . A similar behaviour has been found for the linear conductance ∼ T 2/g−2 as a function of temperature 1,2,5 . The exponent depends on

Renormalization of the Coulomb blockade gap due to extended tunneling in nanoscopic junctions

“…At larger bias, however, the Ohmic regime is recovered, with the I-V curve having an offset of order 1/2C. As pointed out by some authors, [19][20][21][22][23] the peculiar power-law behavior of the tunneling current reveals an interesting relationship between the dynamical CB and the zero-bias anomaly predicted within the Luttinger liquid (LL) theory. [24][25][26] In Ref.…”