Spin-Flip Effects on Current in a Quantum Dot with a Josephson Junction System

Abstract

In this study, we consider the current in a system composed of a superconductor/quantum dot/superconductor junction and a Josephson junction in a parallel configuration. In the model, the spin-flip and the Coulomb interaction in the quantum dot are taken into consideration. The effects of direct tunneling, the spin-flip, and the Coulomb interaction on current and the relation between the current jump and the formation of the -junction are examined. The dependence of the current on the quantum dot energy level shows the Fano characteristics. The spin-flip causes the splitting of the Andreev bound state, thereby resulting in a current jump. The region of the -junction is spread along the current jump positions. We conclude that the spin-flip causes the formation of the -junction but direct tunneling suppresses it. For large values of spin-flip, the Coulomb interaction shifts the central position of the formed region of the -junction.

Josephson Current through a Quantum Dot Connected with Superconducting Leads

“…In our Lacroix approximation, 〈〈d σ ; d † σ 〉〉 was expressed by the variables P σ , Q σ , R σ , and T σ . When the connected term F c dσ was not considered, P σ , Q σ , and T σ vanished, giving 〈〈d σ ; d † σ 〉〉 � 1/R σ , which recovered the expression obtained by the HF approximation [27]. e denominator of 〈〈d σ ; d † σ 〉〉 was defined as D(ω).…”

“…On the contrary, in the Lacroix approximation, [G r dσ (ω)] 11 is given by equation (12), which is described by the variables P σ , Q σ , R σ , and T σ . If P σ , Q σ , and T σ are neglected, [G r dσ (ω)] 11 � 1/R σ (ω), which agrees with the result obtained from the HF approximation [27]. When the connected term F c dσ is considered, P σ , Q σ , and T σ appear in the expression of [G r dσ (ω)] 11 .…”

“…where ρ 0 (ω) � ρ(ω)/ω. In our previous study [27], we considered the spin-flip effects on the current in an S/QD/S junction with a Josephson junction in the range |ω| < Δ. For the system, the HF approximation was applied by neglecting the pairing correlation functions 〈d † σ d † σ 〉 and 〈d σ d σ 〉.…”

“…Beyond the Hartree approximation, the Hartree-Fock (HF) approximation is proposed, where up to the first order of the tunneling amplitude is considered. is method was applied to the level-crossing quantum phase transition between the BCS-singlet and the magnetic doublet states [24][25][26][27]. e above two approximations can be applied to describe singleparticle physics.…”