谁是指环王：马约拉纳，狄拉克还是利夫希茨？超冷费米子中的自旋-轨道-塞曼传奇
Who is the Lord of the Rings: Majorana, Dirac or Lifshitz? The Spin-Orbit-Zeeman Saga in Ultra-cold Fermions
摘要：
讨论了自旋轨道、塞曼场和相互作用变化时，超冷费米子超流相动量空间零能激发环的出现。我们表明，包含环的节点具有非平凡的拓扑不变量的阶段，不同的拓扑相位之间的相变属于Lifshitz类。当穿越相界时，处于无隙相的无质量狄拉克费米子消失，在相界处产生零模马约拉纳费米子，然后在有隙相中变成有质量狄拉克费米子。我们通过激发光谱、光谱函数和动量分布等光谱性质对这些可调拓扑相变进行了表征。由于环的出现或消失导致动量空间的拓扑转变，我们得出结论，Lifshitz是环的主。
英文摘要：
We discuss the emergence of rings of zero-energy excitations in momentum space for superfluid phases of ultra-cold fermions when spin-orbit, Zeeman fields and interactions are varied. We show that phases containing rings of nodes possess non-trivial topological invariants, and that phase transitions between distinct topological phases belong to the Lifshitz class. Upon crossing phase boundaries, existing massless Dirac fermions in the gapless phase anihilate to produce bulk zero-mode Majorana fermions at phase boundaries and then become massive Dirac fermions in the gapped phase. We characterize these tunable topological phase transitions via several spectroscopic properties, including excitation spectrum, spectral function and momentum distribution. Since the emergence or disappearance of rings leads to topological transitions in momentum space, we conclude that Lifshitz is the lord of the rings.
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