Direct prediction of corner state configurations from edge winding numbers in 2D and 3D chiral-symmetric lattice systems

Abstract

Higher-order topological phases feature topologically protected boundary states in lower dimensions. Specifically, the zero-dimensional corner states are protected by the $d$th-order topology of a $d$-dimension system. In this work, we propose to predict different configurations of corner states from winding numbers defined for one-dimensional edges of the system. We first demonstrate the winding number characterization with a generalized two-dimensional square lattice belonging to the BDI symmetry class. In addition to the second-order topological insulating phase, the system may also be a nodal point semimetal or a weak topological insulator with topologically protected one-dimensional edge states coexisting with the corner states at zero energy. A three-dimensional cubic lattice with richer configurations of corner states is also studied. We further discuss several experimental implementations of our models with photonic lattices or electric circuits.

12 pages, 6 figures

References in corpus (28)

• Topological Insulators in Three Dimensions
• Classification of topological insulators and superconductors in three spatial dimensions
• Photonic Floquet Topological Insulators
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantized Electric Multipole Insulators
• Imaging topological edge states in silicon photonics
• Higher-Order Topological Insulators
• Robust optical delay lines via topological protection
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological States and Adiabatic Pumping in Quasicrystals
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topolectrical circuits
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Observation of novel edge states in photonic graphene
• Time Reversal Invariant Topologically Insulating Circuits
• Topological properties of linear circuit lattices
• Topological creation and destruction of edge states in photonic graphene
• Topologically Robust Transport of Photons in a Synthetic Gauge Field
• Lattice models with exactly solvable topological hinge and corner states
• Universal sign-control of coupling in tight-binding lattices
• Entanglement polarization for the topological quadrupole phase

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