Second-order topological insulator and fragile topology in topological circuitry simulation
arXiv:2009.09167
Abstract
Second-order topological insulators (SOTIs) are the topological phases of matter in d dimensions that manifest (d-2)-dimensional localized modes at the intersection of the edges. We show that SOTIs can be designed via stacked Chern insulators with opposite chiralities connected by interlayer coupling. To characterize the bulk-corner correspondence, we establish a Jacobian-transformed nested Wilson loop method and an edge theory that are applicable to a wider class of higher-order topological systems. The corresponding topological invariant admits a filling anomaly of the corner modes with fractional charges. The system manifests a fragile topological phase characterized by the absence of a Wannier gap in the Wilson loop spectrum. Furthermore, we argue that the proposed approach can be generalized to multilayers. Our work offers perspectives for exploring and understanding higher-order topological phenomena.
arXiv comment5 pages, 4 figures
References in corpus (28)
- Topological Insulators
- Topological insulators and superconductors
- Quantum Spin Hall Effect in Graphene
- Topological Order and the Quantum Spin Hall Effect
- Berry Phase Effects on Electronic Properties
- Colloquium: Topological Band Theory
- -dimensional edge states of rotation symmetry protected topological states
- An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
- Acoustic higher-order topological insulator on a Kagome lattice
- Higher-Order Topology in Bismuth
- Quantization of fractional corner charge in -symmetric higher-order topological crystalline insulators
- Topolectrical circuits
- Finite size effects of helical edge states in HgTe/CdTe quantum wells
- Fragile Topology and Wannier Obstructions
- Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
- Two-dimensional second-order topological insulator in graphdiyne
- Acoustic realization of quadrupole topological insulators
- Higher-Order Topological Insulator in Twisted Bilayer Graphene
- Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
- Realization of an acoustic third-order topological insulator
- Higher-Order Topological Insulators in Quasicrystals
- Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
- Engineering Corner States from Two-Dimensional Topological Insulators
- Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
- Edge modes in band topological insulators
- Magnetic second-order topological insulators and semimetals
- Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
- Electric circuits for non-Hermitian Chern insulators