Numerical Renormalization Group Approach to a Quantum Dot Coupled to Normal and Superconducting Leads

Abstract

We study transport through a quantum dot coupled to normal and superconducting leads using the numerical renormalization group method. We show that the low-energy properties of the system are described by the local Fermi liquid theory despite of the superconducting correlations penetrated into the dot due to a proximity effect. We calculate the linear conductance due to the Andreev reflection in the presence of the Coulomb interaction. It is demonstrated that the maximum structure appearing in the conductance clearly characterizes a crossover between two distinct spin-singlet ground states, i.e. the superconducting singlet state and the Kondo singlet state. It is further elucidated that the gate-voltage dependence of the conductance shows different behavior in the superconducting singlet region from that in the Kondo singlet region.

The In-Gap Charge Current through the Correlated Quantum Dot Hybridized with Superconductor

“…Furthermore, for D ∆ s our result (16) reduces to −Γ S as has been independently pointed out by Tanaka et al [5].…”

“…The differential conductance of such current takes either the (75) two-peak (for U = 0) or four-peak (when U = 0) structure because the particle and hole excitations are mixed on the QD. Our study here is complementary to some previous works on this subject [1][2][3][4][5].…”

“…1 we show ρ d (ω) for the energy level located in the center of the superconductor gap ε d = µ β . Distance between the peaks depends on Γ S , the broadenig on Γ N [5] and the weights of the peaks change upon varying ε d as shown in Fig. 4 in Ref.…”

“…3 of our paper [6]. For a simple understanding of the relevant physics we now follow Tanaka et al [5] and focus on the extreme limit of the large energy gap ∆ s . For energies deep inside the superconducting gap ∆ s |ω| we obtain…”

“…where the off-diagonal terms simplify to −Γ s [5] when ∆ s D. Substituting this result to the Dyson equation (5) we can analytically determine the matrix Green function of the noninteracting QD. We obtain the BCS-structure…”