论文标题
磁场中巨大的狄拉克·费米恩的边界刺激性拓扑阶段
Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
论文作者
论文摘要
众所周知，在某些高阶拓扑绝缘子（HOTIS）中，拓扑阶段不是由散装状态的间隙封闭而是边缘状态的差距区分，而边缘状态被称为边界凸起的拓扑阶段（BOTPS）。在本文中，我们构建了均匀磁场中二维（2D）Su-Schrieffer-Heeger（SSH）模型的BOTP转变的有效理论。该模型在每个plaquette的$π$通量时，对应于Benalcazar，Bernevig和Hughes（BBH）提出的Hotis典型模型。 BBH模型可以通过具有两种质量术语的Dirac Fermions近似，这将称为BBH Dirac绝缘子。为了阐明围绕$π$通量的2D SSH模型的BOTP过渡，我们在存在磁场的情况下研究了此类BBH Dirac绝缘子。另一方面，通常在连续的狄拉克模型中，众所周知，与哈密顿人的墓穴相关的边界条件在确定边缘状态方面起着至关重要的作用。我们首先证明，对于具有单个质量项的常规dirac fermion，即使在存在磁场的情况下，这种边界条件也确实决定了边缘状态。接下来，施加了与BBH汉密尔顿的晶格终止和对称性一致的边界条件以及BBH Dirac绝缘子的墓穴，我们在磁场中获得了BBH Dirac绝缘子的边缘状态，并重现其BOTP转换。特别是，我们表明导致光谱不对称的未配对的Landau水平产生了负责BOTP过渡的边缘状态。
It is known that in some higher-order topological insulators (HOTIs), topological phases are distinguished not by gap closings of bulk states but by those of edge states, which are called boundary-obstructed topological phases (BOTPs). In this paper, we construct an effective theory of the BOTP transition of two-dimensional (2D) Su-Schrieffer-Heeger (SSH) model in a uniform magnetic field. At $π$ flux per plaquette, this model corresponds to the typical model of HOTIs proposed by Benalcazar, Bernevig, and Hughes (BBH). The BBH model can be approximated by Dirac fermions with two kinds of mass terms, which will be referred to as BBH Dirac insulator. To clarify the BOTP transition of the 2D SSH model around $π$ flux, we study such BBH Dirac insulator in the presence of a magnetic field. On the other hand, generically in continuum Dirac models, boundary conditions associated with the Hermiticity of Hamiltonians are known to play a crucial role in determining the edge states. We first demonstrate that for the conventional Dirac fermion with a single mass term, such boundary conditions indeed determine the edge states even in the presence of a magnetic field. Next, imposing boundary conditions consistent to the lattice terminations and symmetries of the BBH Hamiltonian as well as to the Hermiticity of the BBH Dirac insulator, we obtain the edge states of the BBH Dirac insulator in a magnetic field and reproduce its BOTP transition. In particular, we show that the unpaired Landau levels, which cause the spectral asymmetry, yield the edge states responsible for the BOTP transition.
