Floquet higher-order topological insulators and superconductors with space-time symmetries
arXiv:1909.08634 · doi:10.1103/PhysRevResearch.2.013124
Abstract
Floquet higher-order topological insulators and superconductors (HOTI/SCs) with an order-two space-time symmetry or antisymmetry are classified. This is achieved by considering unitary loops, whose nontrivial topology leads to the anomalous Floquet topological phases, subject to a space-time symmetry/antisymmetry. By mapping these unitary loops to static Hamiltonians with an order-two crystalline symmetry/antisymmetry, one is able to obtain the groups for the unitary loops and thus complete the classification of Floquet HOTI/SCs. Interestingly, we found that for every order-two nontrivial space-time symmetry/antisymmetry involving a half-period time translation, there exists a unique order-two static crystalline symmetry/antisymmetry, such that the two symmetries/antisymmetries give rise to the same topological classification. Moreover, by exploiting the frequency-domain formulation of the Floquet problem, a general recipe that constructs model Hamiltonians for Floquet HOTI/SCs is provided, which can be used to understand the classification of Floquet HOTI/SCs from an intuitive and complimentary perspective.
arXiv comment34 pages, 4 figures
References in corpus (37)
- Topological Insulators
- Topological insulators and superconductors
- Classification of topological insulators and superconductors in three spatial dimensions
- Classification of topological quantum matter with symmetries
- Topological insulators and superconductors: ten-fold way and dimensional hierarchy
- Topological Crystalline Insulators
- Quantized Electric Multipole Insulators
- Floquet Topological Insulator in Semiconductor Quantum Wells
- Higher-Order Topological Insulators
- Photovoltaic Hall effect in graphene
- Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
- Transport properties of non-equilibrium systems under the application of light: Photo-induced quantum Hall insulators without Landau levels
- -dimensional edge states of rotation symmetry protected topological states
- Reflection symmetric second-order topological insulators and superconductors
- Topological Defects and Gapless Modes in Insulators and Superconductors
- Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
- Topological classification of crystalline insulators through band structure combinatorics
- Inversion Symmetric Topological Insulators
- Higher-order topological insulators and superconductors protected by inversion symmetry
- Topology of crystalline insulators and superconductors
- Second-order topological insulators and superconductors with an order-two crystalline symmetry
- Classification of topological insulators and superconductors in the presence of reflection symmetry
- Periodic Table for Floquet Topological Insulators
- Photoinduced transition between conventional and topological insulators in two-dimensional electronic systems
- Higher-order bulk-boundary correspondence for topological crystalline phases
- Symmetry indicators and anomalous surface states of topological crystalline insulators
- Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
- Topological invariants of Floquet systems: General formulation, special properties, and Floquet topological defects
- Scattering theory of topological insulators and superconductors
- Topological Floquet Spectrum in Three Dimensions via a Two-Photon Resonance
- Boundary Green functions of topological insulators and superconductors
- Floquet second-order topological insulators from nonsymmorphic space-time symmetries
- Higher-order Floquet topological phases with corner and bulk bound states
- Coupled-wire construction of static and Floquet second-order topological insulators
- Floquet topological phases protected by time glide symmetry
- Generating a second-order topological insulator with multiple corner states by periodic driving
- Out of equilibrium higher-order topological insulator: Floquet engineering and quench dynamics
Cited by in corpus (50)
- Classical higher-order topological insulators
- Universal Approach to Magnetic Second-Order Topological Insulator
- Floquet generation of Second Order Topological Superconductor
- Floquet higher order topological insulator in a periodically driven bipartite lattice
- All-electrically tunable networks of Majorana bound states
- Hierarchy of higher-order topological superconductors in three dimensions
- Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
- Phonon-induced Floquet second-order topological phases protected by space-time symmetries
- Time-induced second-order topological superconductors
- Weyl nodes with higher-order topology in an optically driven nodal-line semimetal
- Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
- Topological space-time crystal
- Higher-order topological phases in crystalline and non-crystalline systems: a review
- Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
- Floquet Second Order Topological Superconductor based on Unconventional Pairing
- Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
- Floquet higher-order Weyl and nexus semimetals
- Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
- Dynamical construction of Quadrupolar and Octupolar topological superconductors
- Superconductors with anomalous Floquet higher-order topology
- Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
- Hybrid-order topological odd-parity superconductors via Floquet engineering
- Hinge mode dynamics of periodically driven higher-order Weyl semimetals
- Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
- Floquet second-order topological Anderson insulator hosting corner localized modes
- Dynamic bulk-boundary correspondence for anomalous Floquet topology
- Tailoring Quadrupole Topological Insulators with Periodic Driving and Disorder
- Time evolution of Majorana corner modes in Floquet second-order topological superconductor
- Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
- Dynamical Fragile Topology in Floquet Crystals
- Photoinduced spin-Hall resonance in a k^3-Rashba spin-orbit coupled two dimensional hole system
- Floquet higher-order topological phases in momentum space
- Gapless higher-order topology and corner states in Floquet systems
- Light driven magnetic transitions in transition metal dichalcogenide heterobilayers
- Hierarchical Topological States in Thermal Diffusive Networks
- Distinct Floquet topological classifications from color-decorated frequency lattices with space-time symmetries
- Topological excitations at time vortices in periodically driven systems
- Majorana modes in trapped-ion system and their Floquet engineering
- Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites
- Dynamical Chiral Symmetry and Symmetry-Class Conversion in Floquet Topological Insulators
- Direct driving of electronic and phononic degrees of freedom in a honeycomb bilayer with infrared light
- Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
- Automated detection of symmetry-protected subspaces in quantum simulations
- Floquet Möbius topological insulators
- Multiple tunable real-space degeneracies in graphene irradiated by twisted light
- Symmetry-protected topological corner modes in a periodically driven interacting spin lattice
- Engineering micromotion in Floquet prethermalization via space-time symmetries
- Dynamical Symmetry Indicators for Floquet Crystals
- Breakdown of the symmetry constraint in a Floquet topological insulator
- Floquet second-order topological insulator in strained graphene