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

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.