Theory on the Coulomb blockade and current-voltage characteristics in Tomonaga-Luttinger liquid C-SET

摘要

We propose a self-consistent microscopic theory of the Coulomb blockade in the capacitively coupled single-electron transistor structure with Tomonaga-Luttinger liquid island connected with FL electrodes at both ends (TLL C-SET). Candidates for the island of TLL C-SET are carbon nanotubes and quantum wires. In this theory, the charging effect and the Tomonaga-Luttinger nature are treated in a consistent manner by the open boundary bosonization technique with consideration of zero modes based on the theory of C-SET for Fermi liquid electrodes. Analytical expression of the tunneling current in TLL C-SET is obtained up to the lowest order with respect to the tunneling Hamiltonian for arbitrary environmental impedance and it reasonably describes current-voltage characteristics caused by Coulomb blockade in Tomonaga-Luttinger liquid. We show that, in the ultrasmall but finite Tomonaga-Luttinger liquid, interaction-dependent exponent of the power law has system size dependence in addition to contact- (bulk- or edge-) nature dependence. (C) 2003 Elsevier B.V. All rights reserved.