An anomalous higher-order topological insulator

Abstract

Topological multipole insulators are a class of higher order topological insulators (HOTI) in which robust fractional corner charges appear due to a quantized electric multipole moment of the bulk. This bulk-corner correspondence has been expressed in terms of a topological invariant computed using the eigenstates of the Wilson loop operator, a so called "nested Wilson loop" procedure. We show that, similar to the unitary Floquet operator describing periodically driven systems, the unitary Wilson loop operator can realize "anomalous" phases, that are topologically non-trivial despite having a trivial topological invariant. We introduce a concrete example of an anomalous HOTI, which has a quantized bulk quadrupole moment and fractional corner charges, but a vanishing nested Wilson loop index. A new invariant able to capture the topology of this phase is then constructed. Our work shows that anomalous topological phases, previously thought to be unique to periodically driven systems, can occur and be used to understand purely time-independent HOTIs. arXiv:1807.09050v2 [cond-mat.mes-hall]

Topological Phases without Crystalline Counterparts

“…In contrast, in higher-order topological insulators (HOTI) both the bulk and the boundaries are gapped. Instead, the protected gapless modes form at the intersections of two or more boundaries-the corners and hinges of a crystal [20][21][22][23][24][25][26]. Unlike in topological crystalline insulators, the corners/hinges may break the lattice symmetry responsible for protecting the HOTI.…”

Majorana corner and hinge modes in second-order topological insulator/superconductor heterostructures

“…In a later influential paper[30], Qi et al pointed out that quantum anomalous Hall insulator (QAHI)/SC heterostructures provide a simple realization of 2d chiral TSCs which harbor not only vortex-core MZMs, but also chiral Majorana edge modes. These two theoretical works have triggered a lot of experimental works on TI(QAHI)/SC heterostructures [28,29,[31][32][33][34][35][36][37][38][39][40][41], and remarkable progress in detecting vortex-core MZMs has been witnessed in recent years [28,29,40,41].Very recently, TIs and TSCs have been generalized to include their higher-order counterparts [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Importantly, higher-order TIs (HOTIs) and TSCs (HOTSCs) have extended the conventional bulk-boundary correspondence.…”

“…Very recently, TIs and TSCs have been generalized to include their higher-order counterparts [42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Importantly, higher-order TIs (HOTIs) and TSCs (HOTSCs) have extended the conventional bulk-boundary correspondence.…”

Higher-order Floquet topological phases with corner and bulk bound states

“…However, since the interpretation of Wilson loops and their Berry phases in terms of bulk and edge polarization leaves us with only a Z 2 invariant, this approach may not yield the general classification. A more recent study found parallels between the topological structure of Wilson loops and those of Floquet operators, including the presence of anomalous bound states in the Wannier bands [48]. However, this relationship is not in general well understood.…”