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首页> 外文期刊>Physical review >Near-zero modes in condensate phases of the Dirac theory on the honeycomb lattice
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Near-zero modes in condensate phases of the Dirac theory on the honeycomb lattice

机译：蜂窝格上狄拉克理论在凝聚相中的接近零模

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摘要

We investigate a number of fermionic condensate phases on the honeycomb lattice to determine whether topological defects (vortices and edges) in these phases can support bound states with zero energy. We argue that topological zero modes bound to vortices and at edges are not only connected, but should in fact be identified. Recently, it has been shown that the simplest s-wave superconducting state for the Dirac fermion approximation of the honeycomb lattice at precisely half filling, supports zero modes inside the cores of vortices [P. Ghaemi and F. Wilczek, arXiv:0709.2626 (unpublished)]. We find that within the continuum Dirac theory the zero modes are not unique, either to this phase or to half filling. In addition, we find the exact wave functions for vortex bound zero modes, as well as the complete edge state spectrum of the phases we discuss. The zero modes in all the phases we examine have even-numbered degeneracy, and as such pairs of any Majorana modes are simply equivalent to one ordinary fermion. As a result, contrary to bound-state zero modes in p_x+ip_y superconductors, vortices here do not exhibit non-Abelian exchange statistics. The zero modes in the pure Dirac theory are seemingly topologically protected by the effective low-energy symmetry of the theory, yet on the original honeycomb lattice model these zero modes are split, by explicit breaking of the effective low-energy symmetry.
机译：我们研究了蜂窝状晶格上的许多铁离子冷凝相，以确定这些相中的拓扑缺陷（旋涡和边缘）是否可以以零能量支持束缚态。我们认为，结合到涡旋和边缘的拓扑零模不仅是相连的，而且实际上应该被识别。最近，研究表明，在精确的半填充状态下，用于蜂窝晶格的狄拉克费米子逼近的最简单的s波超导状态在涡流核内部支持零模态[P. P.]。 Ghaemi和F. Wilczek，arXiv：0709.2626（未出版）。我们发现在连续狄拉克理论中，零模对于该阶段或半填充不是唯一的。此外，我们找到了涡旋零界模的确切波函数，以及我们讨论的相位的完整边缘状态谱。我们研究的所有阶段中的零模均具有偶数简并数，因此，任何Majorana模对都等效于一个普通费米子。结果，与p_x + ip_y超导体中的束缚态零模相反，此处的涡旋不表现出非阿贝尔交换统计量。纯狄拉克理论中的零模态在理论上似乎受到该理论的有效低能对称性的保护，但是在原始的蜂窝晶格模型中，这些零模因显式破坏了有效的低能对称性而被分裂。

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