Simulating Higher-Order Topological Insulators in Density Wave Insulators
Kuan-Sen Lin, Barry Bradlyn
备注：
v2: approximately published version, fixed typos and references, and added extensions to arbitrary orbital positions. 21+37 pages, 5+10 figures. v1: 20+33 pages, 5+10 figures
Since the discovery of the Harper-Hofstadter model, it has been known that condensed matter systems with periodic modulations can be promoted to non-trivial topological states with emergent gauge fields in higher dimensions. In this work, we develop a general procedure to compute the gauge fields in higher dimensions associated to low-dimensional systems with periodic (charge- and spin-) density wave modulations. We construct two-dimensional (2D) models with modulations that can be promoted to higher-order topological phases with $U(1)$ and $SU(2)$ gauge fields in 3D. Corner modes in our 2D models can be pumped by adiabatic sliding of the phase of the modulation, yielding hinge modes in the promoted models. We also examine a 3D Weyl semimetal (WSM) gapped by charge-density wave (CDW) order, possessing quantum anomalous Hall (QAH) surface states. We show that this 3D system is equivalent to a 4D nodal line system gapped by a $U(1)$ gauge field with a nonzero second Chern number. We explain the recently identified interpolation between inversion-symmetry protected phases of the 3D WSM gapped by CDWs using the corresponding 4D theory. Our results can extend the search for (higher-order) topological states in higher dimensions to density wave systems.
In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a two-fold-rotational symmetry or a mirror symmetry, a gauge-invariant quantity can be defined for arbitrary 1D lines in the Brillouin zone. Such 1D quantities provide a new pathway to compute the $Z_2$ index of topological insulators. In contrast to the generic setup, where the $Z_2$ index generally involves 2D planes in the Brillouin zone with a globally-defined smooth…
In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We then present key experimental results that demonstrate magnetism, Kondo insulation, mirror chirality or topological crystalline order and superconductivity in spin-orbit topological insulator settings and how these new (bulk insulating) phases of matter arise through topological quantum phase transitions from Bloch band insulators via topological or Dirac s…
Conventional topological insulators and superconductors have topologically protected nodal points on their boundaries, and the recent interests in nodal-line semimetals only concerned bulk band structures. Here, we present a novel four-dimensional topological insulator protected by an anti-unitary reflection symmetry, whose boundary band has a single $PT$-symmetric nodal line with double topological charges. Inspired by the recent experimental realization of the four-dimensional quantum Hall effect, we also propose a cold-atom system which realizes the novel topological insulator with tunable …
Persistent Coherence and Spin-Polarization of Topological Surface States on Topological Insulators
拓扑绝缘体上的无带隙表面态可以避免非磁性杂质的弹性散射，这使得它们成为低功率电子应用的有希望的候选者。然而，对于广泛的应用，这些状态应该保持相干，并在环境温度下显着自旋极化。在这里，我们研究的相干性和自旋结构的拓扑状态的表面上的模型拓扑绝缘体，Bi 2 Se 3，在高温下的自旋和角度分辨光电子能谱。我们发现一个非常弱的加宽和基本上没有衰减的自旋极化的拓扑表面状态到室温。我们的研究结果表明，拓扑绝缘体表面的拓扑态可以作为室温电子器件的基础。
Axion electrodynamics, first proposed in the context of particle physics, manifests itself in condensed matter physics in the topological field theory description of 3d topological insulators and gives rise to magnetoelectric effect, where applying magnetic (electric) field $\mathbf{B}(\mathbf{E})$ induces polarization (magnetization) $\mathbf{p}(\mathbf{m})$. We use linear response theory to study the associated topological current using the Fu-Kane-Mele model of 3d topological insulators in the presence of time-dependent uniform weak magnetic field. By computing the dynamical current suscept…
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Lecture-notes: introducing and discussing basics on axion electrodynamics with application in the calculation of the images generated by an electric (or a magnetic) charge located close to an interface ordinary insulator-topological insulator
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