标题： 石墨烯晶格中狄拉克费米子的拓扑特性 显示英文标题

标题： Topological Aspects of Dirac Fermions in a Kagomé Lattice

摘要： 在kagomé晶格中具有线性色散的狄拉克费米子决定了六边形布里渊区两个不等价角上的不同谷的低能物理性质。基于亚晶格的循环排列对称性构建的有效哈密顿量表明，这两个谷中的狄拉克费米子的拓扑特性由相反的绕数表征。对于无自旋费米子，多体相互作用产生谷间散射，并驱动具有自发平移对称性破缺的谷间相干态。狄拉克费米子从同时的电荷和键序中获得质量项。在此相中，kagomé晶格三倍的维格纳-赛茨原胞中出现的键纹理呈现出空心大卫之星图案。进一步证明，狄拉克质量与涡旋度的扭曲导致涡旋核心处出现零狄拉克模，这些模与分数化密切相关。显示空心大卫之星相具有与狄拉克质量符号相反的相位的 distinct $\mathbb{Z}_6$ Berry 相，即六边形相，这为涡旋核心周围零狄拉克模的拓扑起源提供了见解。 显示英文摘要

摘要： The Dirac fermion with linear dispersion in the kagom\'e lattice governs the low-energy physics of different valleys at two inequivalent corners of hexagonal Brillouin zone. The effective Hamiltonian based on the cyclic permutation symmetry of sublattices is constructed to show that the topology of Dirac fermions at these two valleys is characterized by opposite winding numbers. For spinless fermions, the many-particle interactions produce intervalley scattering and drive an intervalley coherent state with spontaneous translation symmetry breaking. The Dirac fermions acquire a mass term from the simultaneous charge and bond orderings. In this phase, the developed bond texture underlies a hollow-star-of-David pattern in a tripled Wigner-Seitz cell of kagom\'e lattice. It is further demonstrated that the twisting of Dirac mass with vorticity leads to zero Dirac modes at the vortex core, which are intimately related to fractionalization. The hollow-star-of-David phase is shown to have a distinct $\mathbb{Z}_6$ Berry phase with its sign-change counterpart of Dirac mass, i.e. the hexagonal phase, shedding light on the topological origin of zero Dirac modes around the vortex core.