Coulomb blockade and current-voltage characteristics of ultrasmall double tunnel junctions with external circuits

Influence of phase quantum fluctuations on superconducting proximity correction in normal-metal wire conductance

“…In the setup with a gate electrode, there are two degrees of freedom of charge. 30 One is charge Q g induced across the gate capacitance C g , the other is Q c induced across the S/N junction capacitance C. The normal-metal part is the environmental impedance from the viewpoint of the phase motion. The charges are expressed by the island charge q and the continuous charge Q by a canonical transformation;…”

Interplay between the Coulomb blockade and resonant tunneling studied by the Keldysh Green’s-function method

“…, γ is an arbitrary constant [13], and |m is the charge eigenstate of the island with charge em, we obtain…”

“…the external circuit) [9], and the second factor describes quantum fluctuations of the island charge. Using the relation m|e −iγψ(t) e iγψ(0) |m = e −i Ū h [1+2γ(m−nc)]t , wheren c ≡(C L V +C g V g )/e, γ is an arbitrary constant [13], and |m is the charge eigenstate of the island with charge em, we obtain…”

Effect of electromagnetic environment effect on coherent and incoherent Cooper pair tunneling in superconducting C-SET

“…Physics of this system is normally discussed by two parameters E J /E c and α ≡ R q /R qp (E J : Josephson coupling energy, E c ≡ e 2 /2C: charging energy, R qp : resistance for quasi-particle tunneling and R q ≡ 2e 2 / h). However, in order to discuss physics due to Coulomb blockade (CB), consideration of electromagnetic environment effect (EMEE), which can be specified by the parameter ω j /E c ( ω j :energy of electromagnetic environmental mode), is inevitably important even in the double junctions [2]. We first propose the self-consistent microscopic theory of S-SET for arbitrary environmental impedance.…”