超流体中的Andreev-Majorana束缚态
Andreev-Majorana bound states in superfluids
摘要：
本文研究了$p$波超流体的表面、界面和涡旋上的零能量Andreev-Majorana（AM）束缚态。我们讨论了手征超流$^3$ He-A，和时间反演不变相：超流$^3$ He-B，平面相和极性相。AM零模是由体拓扑决定的，它们在超流体从拓扑态到非拓扑态的量子相变时消失。拓扑展示了维度的相互作用。特别地，手征超流体中的零维Weyl点（动量空间中的Berry相单极）在表面上产生AM束缚态的一维费米弧，在涡核中产生AM模的一维平坦带。极性相的一维节线在表面产生二维的AM模平带。维度的相互作用也将不同维度的超流体中的AM态联系起来。例如，三维$^3$ He-B中的束缚态谱的拓扑性质与二维平面相（薄膜）中的谱的性质相关联。
英文摘要：
We consider Andreev-Majorana (AM) bound states with zero energy on surfaces, interfaces and vortices in different phases of the $p$-wave superfluids. We discuss the chiral superfluid $^3$He-A, and time reversal invariant phases: superfluid $^3$He-B, planar and polar phases. The AM zero modes are determined by topology in bulk, and they disappear at the quantum phase transition from the topological to non-topological state of the superfluid. The topology demonstrates the interplay of dimensions. In particular, the zero-dimensional Weyl points in chiral superfluids (the Berry phase monopoles in momentum space) give rise to the one-dimensional Fermi arc of AM bound states on the surface and to the one-dimensional flat band of AM modes in the vortex core. The one-dimensional nodal line in the polar phase produces the two-dimensional flat band of AM modes on the surface. The interplay of dimensions also connects the AM states in superfluids with different dimensions. For example, the topological properties of the spectrum of bound states in the three-dimensional $^3$He-B is connected to the properties of the spectrum in the two-dimensional planar phase (thin film).
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