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arXiv 1111.0445cond-mat.supr-concond-mat.mes-hall
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拓扑表面态超导邻近效应的数值研究

A Numerical Study of the Superconducting Proximity Effect in Topological Surface States

Roland Grein, Jens Michelsen, Matthias Eschrig

摘要:

研究了在三维拓扑绝缘体Bi $_2$ Se $_3$表面沉积一个s波超导体引起的超导邻近效应.为此,将Bi $_2$ Se $_3$的$\mathbf{k}\cdot\mathbf{p}$ -哈密顿量和BCS-哈密顿量映射到紧束缚链上,我们在界面处通过转移-哈密顿量耦合。然后,我们利用递归格林函数技术得到局域谱函数,并由此推断界面态的色散,与以前的微观研究结果一致,我们发现Fu-Kane模型在能量$ε\ll Δ_{\rm SC}$处是一个合理的近似。然而,对于接近SC体隙的能量,Fu-Kane模型预计将被打破。事实上,我们的数值计算显示出强烈的修改的界面状态分散$ε\gtrsim Δ_{\rm SC} $。我们发现,邻近效应可以是足够强的诱导间隙的表面状态,是可比的超导能隙。的状态的空间分布的分析表明,它们的重量向SC的耦合强度的增加。我们的结论是,一个中间耦合是理想的实现Fu-Kane的情况。

英文摘要:

We study the superconducting proximity effect induced in the surface states of the 3-d topological insulator Bi$_2$Se$_3$ by a singlet, s-wave superconductor deposited on its surface. To this effect, the $\mathbf{k}\cdot\mathbf{p}$-Hamiltonian of Bi$_2$Se$_3$ and the BCS-Hamiltonian are mapped onto tight-binding chains which we couple through a transfer-Hamiltonian at the interface. We then employ the Recursive Green's Function technique to obtain the local spectral function and infer the dispersion of the interface-states from it. In agreement with earlier microscopic studies of this problem, we find that the Fu-Kane model is a reasonable approximation at energies $ε\ll Δ_{\rm SC}$. However, for energies close to the SC bulk gap, the Fu-Kane model is expected to break down. Indeed, our numerical calculations show strong modifications of the interface-state dispersion for $ε\gtrsim Δ_{\rm SC} $. We find that the proximity effect can be strong enough to induce a gap in the surface state that is comparable to the superconducting gap. An analysis of the spatial profile of the states shows that their weight shifts towards the SC as the coupling strength increases. We conclude that an intermediate coupling is ideal for realising the Fu-Kane scenario.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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