Interplay between direct and crossed Andreev reflections in hybrid nanostructures

Abstract

The interplay between various many body effects in a quantum dot attached to two normal and one superconducting lead is considered in the limit of large superconducting gap. By the proximity effect the superconducting lead induces pairing correlations on the quantum dot. In the subgap region one observes the anomalous tunneling via direct and crossed Andreev scattering, whereas the usual single particle electronic transfer is suppressed. The interactions of electrons on the dot leading to such phenomena as the Coulomb blockade and the Kondo effect severely modify the currents flowing in the system. In particular: (i) they prevent the existence of the negative differential conductance observed for non-interacting quantum dot over the whole range of voltages, (ii) affect the distribution of the currents as function of the applied voltage and (iii) lead to the appearance of additional low bias feature due to the formation of the Abrikosov-Suhl resonance. The non-local correlations in the Coulomb blockade regime are most pronounced for the particle-hole symmetric dot and thus can be easily tuned by means of gate voltage. They are observed even in the Kondo regime and dominate the behavior close to the Abrikosov-Suhl resonance showing convincingly that Kondo correlations do not destroy subtle entanglement between electrons.

Cooper Pair Splitting Efficiency in the Hybrid Three-Terminal Quantum Dot

“…Figure 2 presents the CPS efficiency (6) obtained for the correlated quantum dot, where the Coulomb interactions are treated in the Hubbard I approximation (e.g. [12,21]). For finite U , in contrast to the noninteracting case, four Andreev bound states [12] appear in the density of states of the QD.…”

“…In what follows, we investigate the CPS efficiency (6) (b) (a) for producing the entangled electrons as a consequence of competition between the CAR and other transport channels. the Andreev bound states (at energies ± 2 0 + Γ S /4) which are formed in the QD due to the proximity effect [12]. The increase of η with Γ R is caused by the CAR processes, dominant over the DAR currents (for Γ R > 2Γ L ).…”

“…Here,α denotes normal electrode different from α while In order to establish the optimal CPS efficiency, we guide ourselves by the previous studies [12,13], looking for the model parameters where the CAR processes are dominant. We use the following definition of CPS efficiency…”

“…Regions in the parameter space, where CAR processes are dominant under realistic experimental conditions [12,13,15], are expected to be also useful for the efficient CPS. It is the aim of this work to quantify such conjecture by calculating CPS efficiency as defined in (6) below.…”

“…We have previously analysed the Y-shape junction with only a single quantum dot [12], where interplay between the local and non-local processes is controlled by suitable choice of the quantum dot level, the couplings and applied voltages [13]. The analysis of the thermoelectric properties [14,15] of this three terminal hybrid system has shown that Seebeck coefficient can be large, but the symmetry of the model prevents a direct contribution of the CAR to both the local and non-local thermopower [15].…”