Periodic table for topological insulators and superconductors
@article{Kitaev2009PeriodicTF, title={Periodic table for topological insulators and superconductors}, author={Alexei Y. Kitaev}, journal={arXiv: Mesoscale and Nanoscale Physics}, year={2009} }
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z_2. The interface between two infinite phases…
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References
SHOWING 1-10 OF 66 REFERENCES
Classification of topological insulators and superconductors in three spatial dimensions
- Physics
- 2008
We systematically study topological phases of insulators and superconductors (or superfluids) in three spatial dimensions. We find that there exist three-dimensional (3D) topologically nontrivial…
Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures
- Physics
- 1997
Normal-conducting mesoscopic systems in contact with a superconductor are classified by the symmetry operations of time reversal and rotation of the electron’s spin. Four symmetry classes are…
Topological Superconductivity and Superfluidity
- Physics
- 2008
We construct time reversal invariant topological superconductors and superfluids in two and three dimensions which are analogous to the recently discovered quantum spin Hall and three-d Z2…
Unpaired Majorana fermions in quantum wires
- Physics
- 2000
Certain one-dimensional Fermi systems have an energy gap in the bulk spectrum while boundary states are described by one Majorana operator per boundary point. A finite system of length L possesses…
Topological phases and the quantum spin Hall effect in three dimensions
- Physics
- 2009
We show the existence of topological phases of Bloch insulators with time-reversal symmetry in three dimensions. These phases are characterized by topological ${Z}_{2}$ invariants whose stability is…
Time-reversal-invariant topological superconductors and superfluids in two and three dimensions.
- PhysicsPhysical review letters
- 2009
It is shown that the time-reversal symmetry naturally emerges as a supersymmetry, which changes the parity of the fermion number associated with each time- reversal invariant vortex and connects each vortex with its superpartner.
Topological insulators with inversion symmetry
- Physics
- 2007
Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by ${Z}_{2}$…
Topological superfluids with time reversal symmetry
- Physics
- 2008
It is shown that superfluids in two and three dimensions which have time reversal invariant ground states have phases which are distinguished by a topological invariant. Further, it is shown that the…
A topological Dirac insulator in a quantum spin Hall phase
- PhysicsNature
- 2008
The direct observation of massive Dirac particles in the bulk of Bi0.9Sb0.1 is reported, which suggests that the observed surface state on the boundary of the bulk insulator is a realization of the ‘topological metal’, which has potential application in developing next-generation quantum computing devices that may incorporate ‘light-like’ bulk carriers and spin-textured surface currents.