Interacting flat-band Majorana modes at surfaces of noncentrosymmetric superconductors

固体的拓扑性质是凝聚态物理学中最活跃的研究领域之一。这些是它们的电子结构的全局性质，这些性质与在它们的表面局部化的鲁棒电子态的存在有关。一种特殊类型的拓扑固体是由超导体实现的，它们具有强的自旋-轨道耦合和时间反演对称性，但缺乏空间反演对称性。如果超导序参量在动量空间中有节点（零），这样的系统应该支持无色散的零能马约拉纳表面态。马约拉纳性质意味着它们是自己的反粒子。没有色散意味着它们有一个宏观的数量，这使得这些系统特别有趣。本项目解决了无色散零能马约拉纳态的稳定性。一方面，它扩展了我们的前期工作，探索了在什么条件下，通过时间反转或空间对称性的自发破缺，态被转移到非零能量。另一方面，该项目研究马约拉纳州之间（不可避免的）相互作用的影响。相互作用的马约拉纳态形成了一个迷人的新颖的多体系统，因为它的能量只包含相互作用的贡献-由于没有色散，动能为零。我们计划推导出相关的相互作用，研究相应模型的基态和低激发，并对合适的实验探针进行预测。

Topological properties of solids currently form one of the most active areas in condensed matter physics. These are global properties of their electronic structure that are connected with the existence of robust electronic states localized at their surfaces. A specific type of topological solid is realized by superconductors that possess strong spin-orbit coupling and time-reversal symmetry but lack spatial inversion symmetry. If the superconducting order parameter has nodes (zeroes) in momentum space, such systems should support dispersionless zero-energy Majorana surface states. The Majorana property means that they are their own antiparticles. The absence of dispersion implies that there is a macroscopic number of them, which makes these systems particularly intriguing. The present project addresses the stability of the dispersionless zero-energy Majorana states. On the one hand, it extends our preliminary work by exploring under what conditions the states are shifted to nonzero energies by the spontaneous breaking of time-reversal or spatial symmetries. On the other, the project studies the effects of (unavoidable) interactions between the Majorana states. The interacting Majorana states form a fascinating novel many-body system since its energy contains only the contribution from the interactions - the kinetic energy is zero due to the absence of dispersion. We plan to derive the relevant interacitons, study the ground state and low-lying excitations of the corresponding models, and make predictions for suitable experimental probes.