Josephson current and proximity effect in Luttinger liquids.
Josephson current and proximity effect in Luttinger liquids.
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DOI：
10.1103/physrevb.53.1548
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发表时间：
1995-08
期刊：
影响因子：
--
通讯作者：
Maslov;Stone;Goldbart;Loss
中科院分区：
文献类型：
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作者：
Maslov;Stone;Goldbart;Loss
提出了一种描述一维勒廷格液体与超导体接触的理论。推导了费米子场在接触处描述Andreev反射的边界条件，并用于构造费米子的玻色子表示。约瑟夫森电流通过超导体/卢廷格液体/超导体结被考虑为完美和不良传输界面。在前一种情况下，发现低温下的约瑟夫森电流基本上不受电子-电子相互作用的影响。在后一种情况下，发生显著的约瑟夫森电流重整化。在与超导体接触的半无限Luttinger液体中（诱导）凝析波函数的剖面显示为幂律衰减，指数取决于相互作用的符号和强度。在排斥（吸引）相互作用的情况下，衰变比没有它们时更快（更慢）。利用整个系统的玻色子化（即超导体和Luttinger液体），提出了一种通过Luttinger液体计算Josephson电流的等效方法，并证明其结果与通过描述Andreev反射的边界条件获得的结果等效。
A theory describing a one-dimensional Luttinger liquid in contact with a superconductor is developed. Boundary conditions for the fermion fields describing Andreev reflection at the contacts are derived and used to construct a bosonic representation of the fermions. The Josephson current through a superconductor/Luttinger liquid/superconductor junction is considered for both perfectly and poorly transmitting interfaces. In the former case, the Josephson current at low temperatures is found to be essentially unaffected by electron-electron interactions. In the latter case, significant renormalization of the Josephson current occurs. The profile of the (induced) condensate wave function in a semi-infinite Luttinger liquid in contact with a superconductor is shown to decay as a power law, the exponent depending on the sign and strength of the interactions. In the case of repulsive (attractive) interactions the decay is faster (slower) than in their absence. An equivalent method of calculating the Josephson current through a Luttinger liquid, which employs the bosonization of the system as a whole (i.e., superconductor, as well as Luttinger liquid) is developed and shown to give the results equivalent to those obtained via boundary condition describing Andreev reflection.