Topological insulators from the perspective of non-commutative geometry and index theory
DOI10.1365/s13291-016-0142-5zbMath1361.82037arXiv1607.04013OpenAlexW2490705607MaRDI QIDQ343405
Publication date: 28 November 2016
Published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1607.04013
non-commutative geometry\(K\)-theorybulk-boundary correspondence (BBC)topological solid state systems
Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Many-body theory; quantum Hall effect (81V70) Statistical mechanics of solids (82D20) Noncommutative geometry in quantum theory (81R60) Kasparov theory ((KK)-theory) (19K35) Index theory (19K56) Riemann-Roch theorems, Chern characters (19L10)
Related Items (5)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Bulk and boundary invariants for complex topological insulators. From \(K\)-theory to physics
- Bott periodicity for \(\mathbb Z_2\) symmetric ground states of gapped free-fermion systems
- On the \(K\)-theoretic classification of topological phases of matter
- \(\mathbb Z_{2}\)-indices and factorization properties of odd symmetric Fredholm operators
- \(\mathbb Z_2\) invariants of topological insulators as geometric obstructions
- Index pairings in presence of symmetries with applications to topological insulators
- \(K\)-theory for real \(C^*\)-algebras via unitary elements with symmetries
- Topological invariants of edge states for periodic two-dimensional models
- Persistence of spin edge currents in disordered quantum spin Hall systems
- Twisted equivariant matter
- Bulk-edge correspondence for two-dimensional topological insulators
- Classification of ``real Bloch-bundles: topological quantum systems of type AI
- The bulk-edge correspondence for the quantum Hall effect in Kasparov theory
- Controlled topological phases and bulk-edge correspondence
- The \(K\)-theoretic bulk-edge correspondence for topological insulators
- Topological insulators and \(C^{*}\)-algebras: theory and numerical practice
- \(K\)-theory and pseudospectra for topological insulators
- Absence of diffusion in the Anderson tight binding model for large disorder or low energy
- Non-commutative differential geometry
- Localization at large disorder and at extreme energies: an elementary derivation
- Charge deficiency, charge transport and comparison of dimensions
- Spectral flow for skew-adjoint Fredholm operators
- Orbital polarization and magnetization for independent particles in disordered media
- Classification of ``quaternionic Bloch-bundles: topological quantum systems of type AII
- On the \(C^*\)-algebraic approach to topological phases for insulators
- Index theory for skew-adjoint Fredholm operators
- T-duality simplifies bulk-boundary correspondence
- The ℤ2 index of disordered topological insulators with time reversal symmetry
- A non-commutative framework for topological insulators
- Topological polarization in graphene-like systems
- The non-commutativenth-Chern number (n⩾ 1)
- Index theory for locally compact noncommutative geometries
- Symmetries, dimensions and topological insulators: the mechanism behind the face of the Bott clock
- Periodic table for topological insulators and superconductors
- The noncommutative geometry of the quantum Hall effect
- Self-Adjoint Fredholm Operators And Spectral Flow
- EDGE CURRENT CHANNELS AND CHERN NUMBERS IN THE INTEGER QUANTUM HALL EFFECT
- Chern number and edge states in the integer quantum Hall effect
- Notes on topological insulators
- Spectral flows associated to flux tubes
This page was built for publication: Topological insulators from the perspective of non-commutative geometry and index theory
