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Topological insulators and superconductors
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abstract
Topological insulators are new states of quantum matter which can not be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi$_2$Te$_3$ and Bi$_2$Se$_3$ crystals. We review theoretical models, materials properties and experimental results on two-dimensional and three-dimensional topological insulators, and discuss both the topological band theory and the topological field theory. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. We review the theory of topological superconductors in close analogy to the theory of topological insulators.
Forward citations
Cited by 8 Pith papers
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Structure of Chern-Simons Graviton Scattering Amplitudes from Topological Graviton Equivalence Theorem and Double Copy
Establishes the Topological Graviton Equivalence Theorem to prove large energy cancellations in N-point massive graviton amplitudes and constructs three- and four-point amplitudes via double copy from topologically ma...
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Surface Variables Description of Axion Topological Materials
Axion topological insulators are fully described by surface charge and current densities satisfying integral equations solvable analytically for spheres and numerically for complex shapes.
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Observation of Metal-Insulator and Spectral Phase Transitions in Aubry-Andr\'e-Harper Models
A single-photon quantum-walk experiment realizes the unitary almost-Mathieu operator and observes metal-insulator, parity-time symmetry-breaking, and all-imaginary-quasienergy spectral transitions.
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Quasiparticle tunnelling in two coupled chiral SYK model
Two weakly coupled chiral SYK models in 1+1 dimensions stay gapless and show massless collective tunneling modes, with no temperature-dependent free-energy correction at leading order.
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Dynamical edge modes in Maxwell theory from a BRST perspective, with an application to the Casimir energy
DEM boundary conditions on two parallel plates yield the same Casimir energy as perfectly conducting plates, after restoring BRST invariance with boundary ghost fields.
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Notes from the bulk
A boundary-QFT analysis shows that curved bulk metrics create local edge velocities in topological models and that fracton and linearized-gravity theories carry Kac-Moody boundary algebras.
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Boundary Condition Analysis of First and Second Order Topological Insulators
Derives dispersion relations for edge and hinge states from boundary conditions on Dirac lattice models and shows that nontrivial topology of a gapped edge state ensures a gapless hinge state.
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Coherent and dissipative dynamics at quantum phase transitions
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.
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