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arXiv 2007.09348cond-mat.supr-concond-mat.stat-mech
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无自旋超导导线中的输运

Transport in spinless superconducting wires

Junaid Majeed Bhat, Abhishek Dhar

摘要:

我们考虑电子输运在一个模型的无自旋超导体描述的Kitaev型晶格哈密顿电子相互作用建模通过超导配对项。超导体被夹在两种保持不同温度和化学势的正常金属之间,它们本身被模拟为非相互作用的无自旋费米子。对于这种设置,我们计算系统的精确稳态特性的量子朗之万方程的方法。在Landauer型形式下得到了粒子流、能流和其它两点关联的封闭形式的精确表达式,其中包含两个非平衡格林函数。目前的表达式被发现是具有简单物理解释的三项之和。然后,我们讨论了一种数值方法,我们构建的两个点的系统的本征谱描述系统和铅的特征谱的演化。通过从对应于热平衡中的引线的初始状态和系统在任意状态下开始,在递归时间之前,关联的长时间解给出了稳态性质。我们使用这种独立的数值方法来验证精确解的结果。我们还调查分析的存在下,高能量的束缚态,并获得表达式为他们的贡献,两个点的标量。作为我们的一般形式主义的应用程序,我们提出的结果热导和下一个最近的邻居相互作用的Kitaev链的电导,它允许不同的绕组数的拓扑相位。

英文摘要:

We consider electron transport in a model of a spinless superconductor described by a Kitaev type lattice Hamiltonian where the electron interactions are modelled through a superconducting pairing term. The superconductor is sandwiched between two normal metals kept at different temperatures and chemical potentials and are themselves modelled as non-interacting spinless fermions. For this set-up we compute the exact steady state properties of the system using the quantum Langevin equation approach. Closed form exact expressions for particle current, energy current and other two-point correlations are obtained in the Landauer-type forms and involve two nonequilibrium Green's functions. The current expressions are found out to be sum of three terms having simple physical interpretations. We then discuss a numerical approach where we construct the time-evolution of the two point correlators of the system from the eigenspectrum of the complete quadratic Hamiltonian describing the system and leads. By starting from an initial state corresponding to the leads in thermal equilibrium and the system in an arbitrary state, the long time solution for the correlations, before recurrence times, gives us steady state properties. We use this independent numerical method for verifying the results of the exact solution. We also investigate analytically the presence of high energy bound states and obtain expressions for their contributions to two point correlators. As applications of our general formalism we present results on thermal conductance and on the conductance of a Kitaev chain with next nearest neighbour interactions which allows topological phases with different winding numbers.

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