Edge instabilities of topological superconductors
Edge instabilities of topological superconductors
复制标题
拓扑超导体的边缘不稳定性
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. Schnyder
中科院分区：
文献类型：
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作者：
Johannes S. Hofmann;F. Assaad;A. Schnyder
节点拓扑超导体显示零能量马约拉纳平坦带在一般的边缘。这些边缘带的平坦性，这是由时间反演和平移对称性保护，引起了广泛的基态简并。因此，即使是任意弱的相互作用也会导致平带边缘态向时间反转和对称性破缺相的不稳定性，从而提升基态简并度。通过对边缘态的Majorana基进行平均场分析，研究了${d}_{xy}$波超导体平带边缘态的不稳定性.主要的不稳定性是马约拉纳质量项，对应于费米语言中粒子-粒子和粒子-空穴通道的相干叠加。我们发现，吸引相互作用诱导三个不同的质量项。一个是相干叠加的虚$s$波配对和电流顺序，另一个结合了电荷密度波和有限动量单重配对。另一方面，排斥相互作用导致铁磁性以及边缘处的自旋三重态配对。我们的量子蒙特卡罗模拟证实了这些发现，并表明，即使在存在强量子涨落的情况下，这些不稳定性也会发生。我们讨论了我们的研究结果对铜氧化物高温超导体的实验的影响。
Nodal topological superconductors display zero-energy Majorana flat bands at generic edges. The flatness of these edge bands, which is protected by time-reversal and translation symmetry, gives rise to an extensive ground-state degeneracy. Therefore, even arbitrarily weak interactions lead to an instability of the flat-band edge states towards time-reversal and translation-symmetry-broken phases, which lift the ground-state degeneracy. We examine the instabilities of the flat-band edge states of ${d}_{xy}$-wave superconductors by performing a mean-field analysis in the Majorana basis of the edge states. The leading instabilities are Majorana mass terms, which correspond to coherent superpositions of particle-particle and particle-hole channels in the fermionic language. We find that attractive interactions induce three different mass terms. One is a coherent superposition of imaginary $s$-wave pairing and current order, and another combines a charge-density-wave and finite-momentum singlet pairing. Repulsive interactions, on the other hand, lead to ferromagnetism together with spin-triplet pairing at the edge. Our quantum Monte Carlo simulations confirm these findings and demonstrate that these instabilities occur even in the presence of strong quantum fluctuations. We discuss the implications of our results for experiments on cuprate high-temperature superconductors.