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Nonunique connection between bulk topological invariants and surface physics

机译：散装拓扑不变性和表面物理之间的非唯一连接

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摘要

At the heart of the study of topological insulators lies a fundamental dichotomy: Topological invariants are defined in infinite systems but surface states as their main footprint only exist in finite systems. In the slab geometry, namely, infinite in two planar directions and finite in the perpendicular direction, the 2D topological invariant was shown to display three different types of behavior. The perpendicular Dirac velocity turns out to be a critical control parameter discerning between different qualitative situations. When it is zero, the three types of behavior extrapolate to the three 3D topologically distinct phases: trivial, weak, and strong topological insulators. We show analytically that the boundaries between types of behavior are topological phase transitions of particular significance since they allow us to predict the 3D topological invariants from finite-thickness transitions. When the perpendicular Dirac velocity is not zero, we identify a new phase with surface states but no band inversion at any finite thickness, disentangling these two concepts which are closely linked in 3D. We also show that at zero perpendicular Dirac velocity, the system is gapless in the 3D bulk and therefore not a topological insulating state, even though the slab geometry extrapolates to the 3D topological phases. Finally, in a parameter regime with strong dispersion perpendicular to the surface of the slab, we encounter the unusual case that the slab physics displays nontrivial phases with surface states but nevertheless extrapolates to a 3D trivial state.
机译：在拓扑绝缘体的研究中，拓扑绝缘体的基本二分术：拓扑不变性在无限系统中定义，但表面状态仅作为它们的主要足迹仅存在有限系统中。在板坯几何形状中，即，在两个平面方向和有限的垂直方向上的无限，显示了2D拓扑不变，显示出三种不同类型的行为。垂直的Dirac速度变成了不同定性情况之间的关键控制参数辨别。当它为零时，三种类型的行为推断到三个3D拓扑上不同的阶段：琐碎，弱和强大的拓扑绝缘体。我们在分析上展示了行为类型之间的边界是特定意义的拓扑相变，因为它们允许我们预测来自有限厚度过渡的3D拓扑不变。当垂直的Dirac速度不为零时，我们识别具有表面状态的新阶段，但在任何有限厚度下没有带频率反转，解开这两个概念，这些概念在3D中紧密连接。我们还表明，在零垂直的Dirac速度下，该系统在3D散装中是高光，因此也不是拓扑绝缘状态，即使板坯几何形状推断到3D拓扑阶段。最后，在具有垂直于板式表面的强色散的参数方案中，我们遇到了平板物理学显示了与表面状态的非动力相位的不寻常情况，但是外推到3D微态。

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  • 来源
    《Physical review》 |2019年第23期|235427.1-235427.11|共11页
  • 作者

    Morice Corentin; Kopp Thilo; Kampf Arno P.;

  • 作者单位

    Univ Augsburg Ctr Elect Correlat & Magnetism Inst Phys Theoret Phys 3 D-86135 Augsburg Germany;

    Univ Augsburg Inst Phys Expt Phys 4 Ctr Elect Correlat & Magnetism D-86135 Augsburg Germany;

    Univ Augsburg Ctr Elect Correlat & Magnetism Inst Phys Theoret Phys 3 D-86135 Augsburg Germany;

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