Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction
Quantum phase transition in a minimal model for the Kondo effect in a Josephson junction
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DOI：
10.1143/jpsj.73.2494
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发表时间：
2004-09-01
影响因子：
1.7
通讯作者：
Hewson, AC
中科院分区：
文献类型：
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作者：
Oguri, A;Tanaka, Y;Hewson, AC
我们提出了一个在Kondo区域中通过量子点的约瑟夫森电流的最小模型。我们从一个由Anderson杂质连接到两个超导(SC)引线的模型开始，其中α=L，R表示左右两边的引线。结果表明，当其中一个SC能隙比另一个\DeltaL远大于\Delta(R)时，起始模型可以精确地映射到单通道模型上，该模型由Delta(R)的右引线和Anderson杂质组成，其中Delta(D)的额外Sc能隙相当于Gamma(L)e(ItetaL)。这里，关于起始模型定义了θ(L)和伽马(L)，伽马(L)是由于与左侧引线的耦合而产生的电平宽度。基于这一简化模型，我们用数值重整化群(NRG)方法研究了非对称带隙的基态性质，得到了远大于D(R)的非对称能隙(L)。结果表明，产生约瑟夫森电流的SC能隙的相位差Phi相当于theta(R)-theta(L)，干扰了局域矩的屏蔽，从而破坏了Kondo系统典型的单重态基态的稳定性。它还可以驱动量子相变到磁偶基态，并且在临界点上约瑟夫森电流呈现不连续的变化。两个Sc带隙的不对称性导致了重入磁相，其中带隙内束缚态接近费米能级。
We propose a minimal model for the Josephson current through a quantum dot in a Kondo regime. We start with the model that consists of an Anderson impurity connected to two superconducting (SC) leads with the gaps Delta(alpha) = \Delta(alpha)\(ithetaalpha), where alpha = L, R for the lead at left and right. We show that, when one of the SC gaps is much larger than the others \DeltaL\ much greater than \Delta(R)\, the starting model can be mapped exactly onto the single-channel model, which consists of the right lead of Delta(R) and the Anderson impurity with an extra onsite SC gap of Delta(d) equivalent to Gamma(L)e(ithetaL). Here theta(L) and Gamma(L) are defined with respect to the starting model, and Gamma(L) is the level width due to the coupling with the left lead. Based on this simplified model,we study the ground-state properties for the asymmetric gap, \Delta(L)\ much greater than \Delta(R)\, using the numerical renormalization group (NRG) method. The results show that the phase difference of the SC gaps phi equivalent to theta(R) - theta(L), which induces the Josephson current, disturbs the screening of the local moment to destabilize the singlet ground state typical of the Kondo system. It can also drive the quantum phase transition to a magnetic doublet ground state, and at the critical point the Josephson current shows a discontinuous change. The asymmetry of the two SC gaps causes a re-entrant magnetic phase, in which the in-gap bound state lies close to the Fermi level.