Topological defect-mediated corner states and higher-order bulk topology in a two-dimensional crystalline insulator

Abstract

We report appearance of non-trivial zero energy corner modes in the form of topological defects (trimers) in a carefully designed 2D crystalline topological insulator. The proposed scenario is developed via an unconventional stacking of 1D topological atomic chains with crystalline mirror symmetry along the diagonal (y=x) line. Our analysis shows that by systematically varying the hopping parameters t (intra-chain), v (within the unit cell) and w (between the unit cells) the system exhibits more than one distinct non-trivial second order topological phases. These phases are distinguished by the zero energy corner modes. In one of these phases the system supports four zero modes. Two of them reside on the trimers and the rest on isolated sites situated at the corner along the diagonal line. However, in the second case, the zero modes on the isolated sites persist at the corners while the zero modes on the trimers vanish. A critical look at the phase evolution of the Bloch states helps in investigating the topology of these phases via using winding numbers. Our work also shows the bulk-corner correspondence that exist between the invariants and the zero modes at the corners. With four zero modes at the corners and a winding number as 2, we conclude that the system has transformed into a second order topological insulator via tuning of the hopping amplitudes.

References in corpus (64)

• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Non-Abelian Anyons and Topological Quantum Computation
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Unpaired Majorana fermions in quantum wires
• Topological Insulators in Three Dimensions
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological invariants of time-reversal-invariant band structures
• Quantized Electric Multipole Insulators
• Topological Insulator Materials
• Higher-Order Topological Insulators
• Topological superconductors: a review
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• 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
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Topological Semimetals
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• A beginner's guide to the modern theory of polarization
• Direct observation of corner states in second-order topological photonic crystal slabs
• Photonic quadrupole topological phases
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Second-order photonic topological insulator with corner states
• Novel Topological Phase with Zero Berry Curvature
• Edge states and topological phases in one-dimensional optical superlattices
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• The strong side of weak topological insulators
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• Topological Mirror Superconductivity
• Majorana Kramers pairs in higher-order topological insulators
• Measuring topology by dynamics: Chern number from linking number
• Dimensional Crossover of Topological Edge States in Su-Schrieffer-Heeger Model
• Higher-order topological odd-parity superconductors
• Geometrical engineering of a two-bands Chern insulator in two dimensions with arbitrary topological index
• Higher-order topological insulators in synthetic dimensions
• Topolectric circuits: Theory and construction
• Weak Topological Insulators and Composite Weyl Semimetals: $\beta$-Bi${}_4$X${}_4$ (X=Br, I)
• Topological and holonomic quantum computation based on second-order topological superconductors
• Generating a second-order topological insulator with multiple corner states by periodic driving
• Quantum Order: a Quantum Entanglement of Many Particles
• Braiding Majorana corner modes in a second-order topological superconductor
• Mirror winding number and helical edge modes in honeycomb lattice with hopping-energy texture
• Zak phase of photons in optical waveguide lattices
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Probing one-dimensional topological phases in waveguide lattices with broken chiral symmetry
• Topological Mirror Insulators in One Dimension
• Hierarchy of higher-order topological superconductors in three dimensions
• Dirac States in an Inclined Two-Dimensional Su-Schrieffer-Heeger Model
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Engineering topological phases of any winding and Chern numbers in extended Su-Schrieffer-Heeger models
• Braiding higher-order Majorana corner states through their spin degree of freedom
• Floquet states and optical conductivity of an irradiated two dimensional topological insulator
• Topological quantum phase transitions and criticality in a longer-range Kitaev chain
• Topological insulation in a ladder model with particle-hole and reflection symmetries
• Cataloging topological phases of $N$-stacked Su-Schrieffer-Heeger chains by a systematic breaking of symmetries
• Calculating the polarization in bi-partite lattice models: application to an extended Su-Schrieffer-Heeger model
• Weyl Nodal-Ring Semimetallic Behavior and Topological Superconductivity in Crystalline Forms of Su-Schrieffer-Heeger Chains
• A numerically exact study of Weyl superconductivity
• Quench dynamics of edge states in a finite extended Su-Schrieffer-Heeger system