# Non-Abelian statistics of half-quantum vortices in p-wave superconductors.

@article{Ivanov2001NonAbelianSO, title={Non-Abelian statistics of half-quantum vortices in p-wave superconductors.}, author={Dmitri A. Ivanov}, journal={Physical review letters}, year={2001}, volume={86 2}, pages={ 268-71 } }

Excitation spectrum of a half-quantum vortex in a p-wave superconductor contains a zero-energy Majorana fermion. This results in a degeneracy of the ground state of the system of several vortices. From the properties of the solutions to Bogoliubov-de Gennes equations in the vortex core we derive the non-Abelian statistics of vortices identical to that for the Moore-Read (Pfaffian) quantum Hall state.

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## References

SHOWING 1-10 OF 24 REFERENCES

The energy-level statistics in the core of a vortex in a p-wave superconductor

- Physics
- 1999

In the presence of strong disorder, the statistics of quasiparticle levels in the core of a vortex in a two-dimensional p-wave superconductor belongs to the universality class B corresponding to the…

2n-quasihole states realize 2n−1-dimensional spinor braiding statistics in paired quantum Hall states

- Physics
- 1996

Quasiholes and fermionic zero modes of paired fractional quantum Hall states: The mechanism for non-Abelian statistics.

- PhysicsPhysical review. B, Condensed matter
- 1996

The quasihole states of several paired states, the Pfaffian, Haldane-Rezayi, and 331 states, are studied, analytically and numerically, in the spherical geometry for the Hamiltonians for which the ground states are known exactly.

Monopole, half-quantum vortex, and nexus in chiral superfluids and superconductors

- Physics
- 1999

Two exotic objects are still not identified experimentally in chiral superfluids and superconductors. These are the half-quantum vortex, which plays the part of the Alice string in relativistic…

Mutual friction in superfluid 3He: Effects of bound states in the vortex core.

- PhysicsPhysical review. B, Condensed matter
- 1991

Mutual friction is calculated within a microscopic quantum-mechanical Green's-function formalism, valid for dynamical processes, and it is predicted that strong dissipation should be observed at a resonant frequency of about 10 kHz, owing to transitions between the bound-state energy levels.

Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect

- Physics
- 2000

We analyze pairing of fermions in two dimensions for fully gapped cases with broken parity (P) and time reversal (T), especially cases in which the gap function is an orbital angular momentum (l)…

Fermionic quantum computation

- Physics
- 2000

We define a model of quantum computation with local fermionic modes (LFMs) — sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m…