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arXiv 2408.07035cond-mat.mes-hallcond-mat.othercond-mat.supr-con
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超导结中倏逝散射模式与有限色散之间的相互作用

Interplay between evanescent scattering modes and finite dispersion in superconducting junctions

Daniel Kruti, Roman-Pascal Riwar

AI总结:

本文推广 Beenakker 方程并结合有效哈密顿量,揭示超导结中有限色散与倏逝模式如何通过超越幺正性的约束维持能隙闭合。

摘要:

超导结是量子硬件的基本构建单元,而其基础行为仍是一个高度活跃的研究领域。一般结的行为可由 Beenakker 行列式公式方便地描述,该公式将亚能隙能谱与表征结的散射矩阵联系起来。特别地,短结中束缚态与连续态之间的能隙闭合源于散射矩阵的幺正性,因而也源于概率守恒。在本工作中,我们批判性地重新评估了两个假设:短结中的散射近似与能量无关,并且由平面通道主导。我们认为,即使导体电子在散射区域内停留的时间很短,其有限色散也会导致强烈依赖于能量的散射;并且我们表明,当跨通道散射很重要时,倏逝模式发挥核心作用。通过推广 Beenakker 方程并映射到一个有效哈密顿量,我们表明能隙闭合与一种手性对称性相关。虽然散射中有限的能量依赖性会破坏手性对称性,但我们展示了两种保持能隙闭合的不同机制,每一种都与超越幺正性、针对能量依赖散射矩阵的新型约束相联系。如果色散模式是平面的,通过对散射过程进行含时概率守恒分析,能隙闭合仍得以保持。如果色散通道是倏逝的,我们推导出一个约束;值得注意的是,该约束不能由概率守恒得出。因此,我们证明 Andreev 物理揭示了远比通常预期更丰富的正常金属散射性质。我们预期,我们的发现将影响受驱结的耗散行为,并为散射矩阵的基础性质提供新的视角。

英文摘要:

Superconducting junctions are essential building blocks for quantum hardware, and their fundamental behaviour remains a highly active research field. The behaviour of generic junctions is conveniently described by Beenakker's determinant formula, linking the subgap energy spectrum to the scattering matrix characterising the junction. In particular, the gap closing between bound and continuum states in short junctions follows from unitarity of the scattering matrix, and thus, from probability conservation. In this work, we critically reassess two assumptions: that scattering in short junctions is approximately energy-independent and dominated by planar channels. We argue that strongly energy-dependant scattering follows from finite dispersion of the conductor electrons even when they spend little time within the scattering region, and show that evanescent modes play a central role when cross-channel scattering is important. By generalising Beenakker's equation and performing a mapping to an effective Hamiltonian, we show that the gap closing is linked to a chiral symmetry. While finite energy dependence in the scattering breaks the chiral symmetry, we show two distinct mechanisms preserving the gap closing, each connected to new types of constraints on energy-dependant scattering matrices beyond unitarity. If the dispersive mode is planar, the gap closing is still preserved through a time-dependant probability conservation analysis of the scattering process. If the dispersive channel is evanescent, we derive a constraint which, notably, cannot follow from probability conservation. We thus demonstrate that Andreev physics reveal a much wider variety of properties of normal-metal scattering than commonly expected. We expect that our findings will have an impact on the dissipative behaviour of driven junctions, and offer a new perspective on fundamental properties of scattering matrices.

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