费米面的单猴鞍奇点及其不稳定性
Single monkey-saddle singularity of a Fermi surface and its instabilities
AI总结：
本文研究费米面高阶猴鞍奇点在不破坏时间反演和反演对称性时成对出现，并探讨孤立奇点在不同相互作用下的稳定性，发现自旋电子中排斥作用破坏奇点，而无自旋电子在平均场下可稳定。
摘要：
费米面在参数平滑变化下可以经历急剧的转变。这类转变可以具有拓扑特征，例如当在转变处出现一个需要三次或更高次项来描述奇点附近电子色散的高阶奇点时。当存在时间反演和反演对称性时，奇点只能在布里渊区内成对出现。在这种情况下，伴随这些奇点的态密度增强与奇点对之间的嵌套相结合，导致了相互作用驱动的不稳定性。我们给出了在时间反演和反演对称性被破坏时单个$n=3$（猴鞍）奇点的例子。然后我们转向奇点孤立时可能出现哪些不稳定的问题。对于自旋电子，我们发现包含排斥相互作用会通过发展Stoner或Lifshitz不稳定性来破坏非相互作用谱中存在的任何孤立猴鞍奇点。相比之下，对于无自旋电子且在平均场水平上，我们表明在短程排斥相互作用存在下，孤立的猴鞍奇点可以被稳定。
英文摘要：
Fermi surfaces can undergo sharp transitions under smooth changes of parameters. Such transitions can have a topological character, as is the case when a higher-order singularity, one that requires cubic or higher-order terms to describe the electronic dispersion near the singularity, develops at the transition. When time-reversal and inversion symmetries are present, odd singularities can only appear in pairs within the Brillouin zone. In this case, the combination of the enhanced density of states that accompany these singularities and the nesting between the pairs of singularities leads to interaction driven instabilities. We present examples of single $n=3$ (monkey saddle) singularities when time-reversal and inversion symmetries are broken. We then turn to the question of what instabilities are possible when the singularities are isolated. For spinful electrons, we find that the inclusion of repulsive interactions destroys any isolated monkey-saddle singularity present in the noninteracting spectrum by developing Stoner or Lifshitz instabilities. In contrast, for spinless electrons and at the mean-field level, we show that an isolated monkey-saddle singularity can be stabilized in the presence of short-range repulsive interactions.
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