Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors

Abstract

Bound states at sharp corners have been widely viewed as the hallmark of two-dimensional second-order topological insulators and superconductors. In this work, we show that the existence of sublattice degrees of freedom can enrich the tunability of bound states on the boundary and hence lift the constraint on their locations. We take the Kane-Mele model with honeycomb-lattice structure to illustrate the underlying physics. With the introduction of an in-plane exchange field to the model, we find that the boundary Dirac mass induced by the exchange field has a sensitive dependence on the boundary sublattice termination. We find that the sensitive sublattice dependence can lead bound states to emerge at a specific type of boundary defects named as sublattice domain walls if the exchange field is of ferromagnetic nature, even in the absence of any sharp corner on the boundary. Remarkably, this sensitive dependence of the boundary Dirac mass on the boundary sublattice termination allows the positions of bound states to be manipulated to any place on the boundary for an appropriately-designed sample. With a further introduction of conventional s-wave superconductivity to the model, we find that, no matter whether the exchange field is ferromagnetic, antiferromagnetic, or ferrimagnetic, highly controllable Majorana zero modes can be achieved at the sublattice domain walls. Our work reshapes the understanding of boundary physics in second-order topological phases, and meanwhile opens potential avenues to realize highly controllable bound states for potential applications.

arXiv comment15 pages, 9 figures

References in corpus (99)

• The electronic properties of graphene
• Topological Insulators
• Topological insulators and superconductors
• 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
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Quantum Spin Hall Effect in Silicene
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Quantum Spin Hall Effect
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Low-energy effective Hamiltonian involving spin-orbit coupling in Silicene and Two-Dimensional Germanium and Tin
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Valley-Polarized Metals and Quantum Anomalous Hall Effect in Silicene
• Topolectrical circuit realization of topological corner modes
• Josephson Current and Noise at a Superconductor-Quantum Spin Hall Insulator-Superconductor Junction
• 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 insulators in twisted transition metal dichalcogenide homobilayers
• Direct observation of corner states in second-order topological photonic crystal slabs
• Classical higher-order topological insulators
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Second-Order Topological Phases in Non-Hermitian Systems
• Novel Topological Phase with Zero Berry Curvature
• Observation of second-order topological insulators in sonic crystals
• Corner states of light in photonic waveguides
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Elastic higher-order topological insulator with topologically protected corner states
• Majorana corner modes in a high-temperature platform
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• High-Temperature Majorana Corner States
• Higher-Order Topological Insulators in Quasicrystals
• Higher Order Topological Phases: A General Principle of Construction
• Experimental Observation of Higher-Order Topological Anderson Insulators
• Weak-Pairing Higher Order Topological Superconductors
• Engineering Corner States from Two-Dimensional Topological Insulators
• Material design with the van der Waals stacking of bismuth-halide chains realizing a higher-order topological insulator
• Observation of a Majorana zero mode in a topologically protected edge channel
• Universal Approach to Magnetic Second-Order Topological Insulator
• Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields
• Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Higher Order Topology and Nodal Topological Superconductivity in Fe(Se,Te) Heterostructures
• Helical Hinge Majoranas in Iron-Based Superconductors
• Higher-order topological odd-parity superconductors
• Dynamical Singularities of Floquet Higher-Order Topological Insulators
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Evidence of Higher Order Topology in Multilayer WTe${}_2$ from Josephson Coupling through Anisotropic Hinge States
• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Room-temperature quantum spin Hall edge state in a higher-order topological insulator Bi${}_4$Br${}_4$
• Second-order Topological Superconductors with Mixed Pairing
• Inversion-protected higher order topological superconductivity in monolayer WTe${}_2$
• In-plane Zeeman field induced Majorana corner and hinge modes in an $s$-wave superconductor heterostructure
• Lattice symmetry assisted second order topological superconductors and Majorana patterns
• Topological and holonomic quantum computation based on second-order topological superconductors
• Higher-order Topological Mott Insulators
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Non-Abelian Majorana Doublets in Time-Reversal Invariant Topological Superconductor
• Evidence for Higher order topology in Bi and Bi${}_{0.92}$Sb${}_{0.08}$
• Higher-order topological superconductors in $\mathcal{P}$-, $\mathcal{T}$-odd quadrupolar Dirac materials
• Braiding Majorana corner modes in a second-order topological superconductor
• First- and Second-Order Topological Superconductivity and Temperature-Driven Topological Phase Transitions in the Extended Hubbard Model with Spin-Orbit Coupling
• Higher-Order Topological Superconductivity of Spin-Polarized Fermions
• Boundary-obstructed topological high-T${}_c$ superconductivity in iron pnictides
• Phase tunable second-order topological superconductor
• All-electrically tunable networks of Majorana bound states
• Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor
• Higher-order topological superconductivity: possible realization in Fermi gases and Sr${}_2$RuO${}_4$
• Majorana corner modes with solitons in an attractive Hubbard-Hofstadter model of cold atom optical lattices
• Kramers pairs of Majorana corner states in a topological insulator bilayer
• Acoustic corner states in topological insulators with built-in Zeeman-like fields
• Vortex-line topology in iron-based superconductors with and without second-order topology
• Fragile topologically flat band in the checkerboard antiferromagnetic monolayer FeSe
• Majorana corner flat bands in two-dimensional second-order topological superconductors
• Symmetry-protected non-Abelian braiding of Majorana Kramers' pairs
• Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors
• Intrinsic first and higher-order topological superconductivity in a doped topological insulator
• Two-particle Berry phase mechanism for Dirac and Majorana Kramers pairs of corner modes
• Tunable Majorana corner modes in noncentrosymmetric superconductors: Tunneling spectroscopy and edge imperfections
• Quantum Computing with Majorana Kramers Pairs
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Boundary Topological Superconductors
• Surface Bogoliubov-Dirac cones and helical Majorana hinge modes in superconducting Dirac semimetals
• Sublattice-sensitive Majorana Modes
• Spin liquid in twisted homobilayers group-VI gichalcogenides
• Rotational symmetry breaking and partial Majorana corner states in a high-Tc superconductor based heterostructure
• Multiorder topological superfluid phase transitions in a two-dimensional optical superlattice
• Effective Hamiltonian with tunable mixed pairing in driven optical lattices
• Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites

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• Topological Superconductivity in Two-Dimensional Altermagnetic Metals
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• The General Principle behind Magnetization-induced Second-Order Topological Corner States in the Kane-Mele Model
• Topological Domain Walls in Graphene Nanoribbons with Carrier Doping
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field
• Higher-order topology in twisted multilayer systems: a review
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Antiferromagnetic topological insulators in heavy-fermion systems