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

Abstract

The influence of the charging effect on the proximity correction in the conductance of a mesoscopic superconductor(S)/normal-metal(N) coupled system is theoretically investigated. The most important contribution of the proximity correction in the conductance of a diffusive normal metal comes from the correction in the local conductivity ␦(r). The correction in the conductance is given by ␦Gϭ(1/L N 2 )͐ vol. ␦(r)dr. Because of the retro property of Andreev reflection and the long rangeness of the Cooperon ͑particle-particle ladder͒, Andreev reflection at the S/N interface affects the local conductivity at a point in the normal region far from the interface ͑within the phase coherence length L ). If the S/N interface is very small and has a low transparency, single Andreev reflection is strongly suppressed by the Coulomb blockade at a low temperature (k B TϽE C , E C ϭe 2 /2C) in an exponential manner exp͕Ϫ4E C /(k B T)͖, where C is the capacitance of the S/N junction. Nevertheless, the proximity correction in the conductance is only suppressed with power law k B T/(4E C ) because the charged state is an intermediate state in the process of the proximity correction in the conductivity. This is quite different from the charging effect on the proximity correction of the current flowing through the S/N interface, which is strongly suppressed by the charging effect.

Superconducting proximity effect and reentrant behaviors in random network carbon nanotubes

“…The conductance becomes higher and reaches a maximum at about 8 K related to E th , and then becomes lower at low temperature. This reentrant behavior of conductance have been studied in both theory [7][8][9] and experiments on metal and 2DEG semiconductor [18,19]. The higher E th was observed in our experiment because of high D. We estimated the diffusion constant D of network-like CNTs by…”

“…The AB oscillation amplitude in DG N is the order of G 2 T0 =G N0 , and it should change as a function of T, V in the same way it does in a single quasi 1D wire. The explicit form of DG N (V, T, B) as the function of V, T, B has been given in many literatures [7][8][9]. Here, we drop the expression for an A-B ring in Nakano and Takayanagi's Eq.…”

“…3. Theoretically, a model has been constructed by the proximity correction to quasi 1D normal conductor with the loop of AB-type oscillation and the reentrant behavior of DG A (T) has been predicted [7,9]. When T > T m , DG A (T) is proportional to 1/T.…”

“…Here, we drop the expression for an A-B ring in Nakano and Takayanagi's Eq. (51) [9] because it is convenient for our present purpose. Thus, we have …”

“…Here, we consider a CNTs are diffusive quasi 1D dimensional quantum wires as normal conductors and showed that the proximity correction to the conductance by updated proximity effect theory [7][8][9]. In this type of SN junction, there are two effects in the conductance caused by the attached superconductor.…”