Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry

Abstract

Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground state only contains short-range entanglement and does not break symmetries spontaneously, they generically realize crystalline fermionic symmetry-protected topological phases (cFSPTs), supporting gapless modes at the boundaries or at the lattice defects. Here, we provide an exhaustive classification of cFSPTs in two dimensions with $\mathrm{U}(1)$ charge-conservation and spinful time-reversal symmetries, namely, those generically present in spin-orbit coupled insulators, for any of the 17 wallpaper groups. It has been shown that the classification of cFSPTs can be understood from appropriate real-space decorations of lower-dimensional subspaces, and we expose how these relate to the Wyckoff positions of the lattice. We find that all nontrivial one-dimensional decorations require electronic interactions. Furthermore, we provide model Hamiltonians for various decorations, and discuss the signatures of cFSPTs. This classification paves the way to further explore topological interacting insulators, providing the backbone information in generic model systems and ultimately in experiments.

References in corpus (114)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Symmetry protected topological orders and the group cohomology of their symmetry group
• The (High Quality) Topological Materials In The World
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Observation of a phononic quadrupole topological insulator
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Nonlocal edge state transport in the quantum spin Hall state
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Higher-Order Topology in Bismuth
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Lieb-Schultz-Mattis in Higher Dimensions
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• The effects of interactions on the topological classification of free fermion systems
• Topology of crystalline insulators and superconductors
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Fragile Topology and Wannier Obstructions
• Single particle Green's functions and interacting topological insulators
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Detection of Symmetry Protected Topological Phases in 1D
• Classification of Topological Insulators and Superconductors
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Interacting fermionic topological insulators/superconductors in three dimensions
• Magnetic Topological Quantum Chemistry
• Topological classification with additional symmetries from Clifford algebras
• String order and symmetries in quantum spin lattices
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Symmetry protected topological phases from decorated domain walls
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
• Interacting topological phases and modular invariance
• Topological Mirror Superconductivity
• Reflection positivity and invertible topological phases
• Topological phases protected by point group symmetry
• Building crystalline topological phases from lower-dimensional states
• Gauging spatial symmetries and the classification of topological crystalline phases
• Topological non-symmorphic crystalline insulators
• Rotation Anomaly and Topological Crystalline Insulators
• Interaction effect on topological classification of superconductors in two dimensions
• Topological Classification of Crystalline Insulators with Point Group Symmetry
• Realising the Symmetry-Protected Haldane Phase in Fermi-Hubbard Ladders
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Floquet symmetry-protected topological phases in cold atomic systems
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Quantum phase transition between cluster and antiferromagnetic states
• Band Representations and Topological Quantum Chemistry
• A new class of $(2+1)$-d topological superconductor with ${\mathbb{Z}}_8$ topological classification
• Room-temperature quantum spin Hall edge state in a higher-order topological insulator Bi${}_4$Br${}_4$
• Fractional corner charges in spin-orbit coupled crystals
• Symmetry Protected Topological States of Interacting Fermions and Bosons
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Many-body topological invariants for fermionic symmetry-protected topological phases
• Many-body topological invariants for fermionic short-range entangled topological phases protected by antiunitary symmetries
• Topological Hamiltonian as an Exact Tool for Topological Invariants
• Lieb-Schultz-Mattis Theorem and its generalizations from the Perspective of the Symmetry Protected Topological phase
• Topological invariants for interacting topological insulators with inversion symmetry
• Evidence for Higher order topology in Bi and Bi${}_{0.92}$Sb${}_{0.08}$
• Crystalline topological phases as defect networks
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Sufficient Conditions for Topological Order in Insulators
• Topological zero modes and Dirac points protected by spatial symmetry and chiral symmetry
• Construction and classification of symmetry protected topological phases in interacting fermion systems
• Classification and construction of higher-order symmetry protected topological phases of interacting bosons
• Classification of (2+1)D invertible fermionic topological phases with symmetry
• Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
• Interacting fermionic symmetry-protected topological phases in two dimensions
• Twisted boundary condition and Lieb-Schultz-Mattis ingappability for discrete symmetries
• General Lieb-Schultz-Mattis type theorems for quantum spin chains
• Two-dimensional Shiba lattices as possible platform for crystalline topological superconductivity
• Purely rotational symmetry-protected topological crystalline insulator $\alpha$-Bi4Br4
• Fragile Mott Insulators
• Loop Braiding Statistics and Interacting Fermionic Symmetry-Protected Topological Phases in Three Dimensions
• Fragile topological phases in interacting systems
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Electronic Mechanism of Superconductivity in the Cuprates, C${}_{60}$, and Polyacenes
• Local Antiferromagnetic Correlations and $d_{x^2-y^2}$ Pairing
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Construction and classification of point group symmetry protected topological phases in 2D interacting fermionic systems
• Rotation Symmetry-Protected Topological Phases of Fermions
• Lieb-Schultz-Mattis type theorems for Majorana models with discrete symmetries
• Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Correlation effects on topological crystalline insulators
• The classification of symmetry protected topological phases of one-dimensional fermion systems
• Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries
• Interacting topological quantum chemistry of Mott atomic limits
• Elementary band representations for the single-particle Green's function of interacting topological insulators
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Complete crystalline topological invariants from partial rotations in (2+1)D invertible fermionic states and Hofstadter's butterfly
• Lieb-Schultz-Mattis theorem with a local twist for general one-dimensional quantum systems
• Characterization and classification of interacting (2+1)D topological crystalline insulators with orientation-preserving wallpaper groups
• Elementary derivation of the stacking rules of invertible fermionic topological phases in one dimension
• Interacting Edge States of Fermionic Symmetry-Protected Topological Phases in Two Dimensions
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries

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