Type-II quadrupole topological insulators

Abstract

Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery of the so-called quadupole topological insulator. It has been established by a classical electromagnetic theory that in a two-dimensional material the quantized properties for the quadupole topological insulator should satisfy a basic relation. Here we discover a new type of quadrupole topological insulator (dubbed type-II) that violates this relation due to the breakdown of the correspondence that a Wannier band and an edge energy spectrum close their gaps simultaneously. We find that, similar to the previously discovered (referred to as type-I) quadrupole topological insulator, the type-II hosts topologically protected corner states carrying fractional corner charges. However, the edge polarizations only occur at a pair of boundaries in the type-II insulating phase, leading to the violation of the classical constraint. We demonstrate that such new topological phenomena can appear from quench dynamics in non-equilibrium systems, which can be experimentally observed in ultracold atomic gases. We also propose an experimental scheme with electric circuits to realize such a new topological phase of matter. The existence of the new topological insulating phase means that new multipole topological insulators with distinct properties can exist in broader contexts beyond classical constraints.

32 pages, 17 figures

References in corpus (77)

• Quantized Electric Multipole Insulators
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Higher-Order Topological Insulators
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Entanglement spectrum of a topological phase in one dimension
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• Calculation of reduced density matrices from correlation functions
• $(d-2)$-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
• Single-Spin Addressing in an Atomic Mott Insulator
• Topolectrical circuits
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Experimental realization of a symmetry protected topological phase of interacting bosons with Rydberg atoms
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Superfluid-insulator transition in a periodically driven optical lattice
• Experimental reconstruction of the Berry curvature in a topological Bloch band
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Entanglement spectrum of topological insulators and superconductors
• Observation of a dynamical topological phase transition
• Two-dimensional second-order topological insulator in graphdiyne
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Structured Weyl Points in Spin-Orbit Coupled Fermionic Superfluids
• Majorana corner modes in a high-temperature platform
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• High-Temperature Majorana Corner States
• Dynamical Topological Order Parameters far from Equilibrium
• Experimental investigations of the dipolar interactions between single Rydberg atoms
• Topological classification of dynamical phase transitions
• Long range coherent magnetic bound states in superconductors
• Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Higher Order Topological Phases: A General Principle of Construction
• Two-dimensional topological superconductivity in Pb/Co/Si(111)
• Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
• Helical Topological Edge States in a Quadrupole Phase
• Single magnetic adsorbates on s-wave superconductors
• Measuring topology by dynamics: Chern number from linking number
• Dynamical preparation of Floquet Chern insulators
• An anomalous higher-order topological insulator
• Topological Quadrupolar Semimetals
• Uncover Topology by Quantum Quench Dynamics
• Measuring Topological Number of a Chern-Insulator from Quench Dynamics
• Quantum Quenches in Chern Insulators
• Band structure engineering and reconstruction in electric circuit networks
• Probing the Berry Curvature and Fermi Arcs of a Weyl Circuit
• Many-Body Electric Multipole Operators in Extended Systems
• Many-Body Order Parameters for Multipoles in Solids
• Dynamical classification of topological quantum phases
• Topological insulators in magnetic fields: Quantum Hall effect and edge channels with non-quantized θ-term
• Tomography of band insulators from quench dynamics
• Edge modes in band topological insulators
• Reconfigurable topological phases in next-nearest-neighbor coupled resonator lattices
• Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
• Complex classes of periodically driven topological lattice systems
• Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials
• Dynamical topological invariant after a quantum quench
• Dynamical Buildup of a Quantized Hall Response from Non-Topological States
• Topology of one dimensional quantum systems out of equilibrium
• Topological Entanglement-Spectrum Crossing in Quench Dynamics
• Persistent Hall response in a quantum quench
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Topological bands with Chern number C=2 by dipolar exchange interactions
• Classification of topological insulators and superconductors out of equilibrium
• Spin-orbital dynamics in a system of polar molecules
• Pfaffian formalism for higher-order topological insulators
• Topological Gapless Matters in Three-dimensional Ultracold Atomic Gases
• Topologically protected edge states in small Rydberg systems
• Finite-momentum Bose-Einstein condensates in shaken 2D square optical lattices
• Scheme to Equilibrate the Quantized Hall Response of Topological Systems from Coherent Dynamics

Cited by in corpus (32)

• Classical higher-order topological insulators
• Boundary-obstructed topological phases
• Winding Numbers and Generalized Mobility Edges in Non-Hermitian Systems
• Higher-order Topological Anderson Insulators
• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Higher-Order Weyl-Exceptional-Ring Semimetals
• Higher-order Topological Hyperbolic Lattices
• Corner charge and bulk multipole moment in periodic systems
• Higher-order topology in monolayer graphene
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Higher-order topological Anderson insulators in quasicrystals
• The Global Phase Diagram of disordered Higher-order Weyl Semimetals
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Unified characterization for higher-order topological phase transitions
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• Mirror-symmetry-protected dynamical quantum phase transitions in topological crystalline insulators
• Density-driven higher-order topological phase transitions in amorphous solids
• Second-Order Topological Insulator in van der Waals Heterostructures of CoBr${}_2$/Pt${}_2$HgSe${}_3$/CoBr${}_2$
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Spin-Dependent High-Order Topological Insulator and Two Types of Distinct Corner Modes in Monolayer FeSe/GdClO Heterostructure
• Higher-order topology in twisted multilayer systems: a review
• Magnetic flux induced higher-order topological superconductivity
• Finite-temperature topological invariant for higher-order topological insulators
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Proposal for realizing and probing topological crystalline insulators in optical lattices