Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice

Abstract

Quantum simulators are an essential tool for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices led the field so far, but electronic quantum simulators are proving to be equally relevant. Simulating topological states of matter is one of the holy grails in the field. Here, we experimentally realize a higher-order electronic topological insulator (HOTI). Specifically, we create a dimerized Kagome lattice by manipulating carbon-monoxide (CO) molecules on a Cu(111) surface using a scanning tunneling microscope (STM). We engineer alternating weak and strong bonds to show that a topological state emerges at the corner of the non-trivial configuration, while it is absent in the trivial one. Contrarily to conventional topological insulators (TIs), the topological state has two dimensions less than the bulk, denoting a HOTI. The corner mode is protected by a generalized chiral symmetry, which leads to a particular robustness against perturbations. Our versatile approach to quantum simulation with artificial lattices holds promises of revealing unexpected quantum phases of matter.

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Cited by in corpus (121)

• Non-Hermitian Physics
• Topological acoustics
• Observation of a higher-order topological bound state in the continuum
• Material design with the van der Waals stacking of bismuth-halide chains realizing a higher-order topological insulator
• Observation of topological flat bands in the kagome semiconductor Nb${}_3$Cl${}_8$
• Boundary-obstructed topological phases
• Hybrid-order topological insulators in a phononic crystal
• Active topolectrical circuits
• Square-root higher-order topological insulator on a decorated honeycomb lattice
• Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
• On the robustness of topological corner modes in photonic crystals
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Sub-symmetry protected topological states
• Screening 2D materials with topological flat bands
• Higher-order topological phases in a spring-mass model on a breathing kagome lattice
• Engineering interfacial quantum states and electronic landscapes by molecular nanoarchitectures
• PAI-graphene: a new topological semimetallic two-dimensional carbon allotrope with highly tunable anisotropic Dirac cones
• Higher-order topological band structures
• Observation of symmetry protected zero modes in topolectrical circuits
• Topological phases of a dimerized Fermi-Hubbard model for semiconductor nano-lattices
• Multi-orbital model reveals second-order topological insulator in 1H-transition metal dichalcogenide
• p Orbital flat band and Dirac cone in the electronic honeycomb lattice
• Exact eigenvectors and eigenvalues of the finite Kitaev chain and its topological properties
• Dislocation as a bulk probe of higher-order topological insulators
• Edge-dependent topology in Kekulé lattices
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• On the topological immunity of corner states in two-dimensional crystalline insulators
• Exact Higher-order Bulk-boundary Correspondence of Corner-localized States
• Higher-order topological pumping and its observation in photonic lattices
• $2^n$-root weak, Chern, and higher-order topological insulators, and $2^n$-root topological semimetals
• Higher-order topology in plasmonic kagome lattices
• Engineered electronic states in atomically precise artificial lattices and graphene nanoribbons
• Simulation of Higher-Order Topological Phases and Related Topological Phase Transitions in a Superconducting Qubit
• Non-Abelian Bloch oscillations in higher-order topological insulators
• Corner modes of the breathing kagome lattice: origin and robustness
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Proximity superconductivity in atom-by-atom crafted quantum dots
• Acoustic corner states in topological insulators with built-in Zeeman-like fields
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• Topological edge and corner states in Bi fractals on InSb
• Construction of topological quantum magnets from atomic spins on surfaces
• Observation of nonlinear fractal higher-order topological insulator
• Discovery of Higher-Order Topological Insulators using the Spin Hall Conductivity as a Topology Signature
• System size dependent topological zero modes in coupled topolectrical chains
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Two-dimensional Kagome Materials: Theoretical Insights, Experimental Realizations, and Electronic Structures
• Second-order topological insulator in breathing square lattice of magnetic vortices
• Observation of higher-order topological states on a quantum computer
• Realization of a one-dimensional topological insulator in ultrathin germanene nanoribbons
• Noncrystalline topological superconductors
• Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices
• Topological excitonic corner states and nodal phase in bilayer quantum spin Hall insulators
• Hidden Breathing Kagome Topology in Hexagonal Transition Metal Dichalcogenides
• Simulation of higher-order topological phases in 2D spin-phononic crystal networks
• Spin-Polarized Fractional Corner Charges and Their Photonic Realization
• Optimization and robustness of topological corner state in second-order topological photonic crystal
• Unified characterization for higher-order topological phase transitions
• Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
• Projected Topological Branes
• Topological States in Dimerized Quantum-Dot Chains Created by Atom Manipulation
• Constructing higher-order topological states in higher dimension
• Impurity bound states as detectors of topological band structures revisited
• Computing observables without eigenstates: applications to Bloch Hamiltonians
• Higher-Order Topological Mott Insulator on the Pyrochlore Lattice
• Second-Order Topological Insulator in van der Waals Heterostructures of CoBr${}_2$/Pt${}_2$HgSe${}_3$/CoBr${}_2$
• Exchange interaction, disorder, and stacking faults in rhombohedral graphene multilayers
• Sublattice-sensitive Majorana Modes
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Colloquium: Synthetic quantum matter in non-standard geometries
• Adatom engineering magnetic order in superconductors: Applications to altermagnetic superconductivity
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Compact localized boundary states in a quasi-1D electronic diamond-necklace chain
• Experimental observation of Dirac cones in artificial graphene lattices
• Dirac cones and higher-order topology in quasi-continuous media
• Inducing a many-body topological state of matter through Coulomb-engineered local interactions
• Wave-function engineering on superconducting substrates: Chiral Yu-Shiba-Rusinov molecules
• Thermodynamic, magnetic and transport properties of the repulsive Hubbard model on the kagome lattice
• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Effective action approach to the filling anomaly in crystalline topological matter
• Observation of topologically distinct corner states in "bearded" photonic Kagome lattices
• Observation of Dual-band Topological Corner Modes in Acoustic Kagome Lattice with Long-range Interactions
• Network model for higher-order topological phases
• Nonlinear Corner States in Topologically Nontrivial Kagome Lattice
• Simulating Floquet topological phases in static systems
• Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice
• Dynamic mass generation on two-dimensional electronic hyperbolic lattices
• Quasiparticle excitations in a one-dimensional interacting topological insulator: Application for dopant-based quantum simulation
• Realization of programmable nanomechanical lattice with both nearest-neighboring and next-nearest-neighboring couplings
• Generalized Lieb's theorem for noninteracting non-Hermitian $n$-partite tight-binding lattices
• High-yield production of quantum corrals in a surface reconstruction pattern
• Floquet higher-order topological phases in momentum space
• Realizing Corner States in Artificial Crystals Based on Topological Spin Textures
• Implementation and characterization of the dice lattice in the electron quantum simulator
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• Higher-order topology protected by latent crystalline symmetries
• Spin-Selective Second-Order Topological Insulators Enabling Cornertronics in 2D Altermagnets
• Thermodynamics of a Higher-Order Topological Insulator
• Emergent metallicity at the grain boundaries of higher-order topological insulators
• Fubini-Study metric and topological properties of flat band electronic states: the case of an atomic chain with $s-p$ orbitals
• Wannier center spectroscopy to identify boundary-obstructed topological insulators
• Topological reflection matrix
• Topological electronic states in holey graphyne
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Wave-particle duality of electrons with spin-momentum locking
• Tuning spinaron and Kondo resonances via quantum confinement
• Model non-Hermitian topological operators without skin effect: A general principle of construction
• Higher-order topology in honeycomb lattice with Y-Kekulé distortions
• Corner states in second-order mechanical topological insulator
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Topological parafermion corner states in clock-symmetric non-Hermitian second-order topological insulator
• Statistical Localization in a Rydberg Simulator of $U(1)$ Lattice Gauge Theory
• Geometric semimetals and their simulation in synthetic matter
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Nonlinear quadrupole topological insulators
• Topological Aspects of Dirac Fermions in a Kagomé Lattice
• Quantized valley Hall response from local bulk density variations
• Nonlinearity-induced corner states in a kagome lattice
• Hidden wallpaper fermion and third-order topological insulator
• Higher-order topological quantum paramagnets
• Nanoimprinted topological laser in the visible
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases