Abelian and non-abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect

Details Abelian and non-abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect Abelian and non-abelian anyons in integer quantum anomalous Hall effect and topological phase transitions via superconducting proximity effect

2010-11-17

arxiv.org/abs/1011.3885v4

Phys.Rev.B83:125105,2011

Physics

Condensed Matter

Strongly Correlated Electrons

6 pages, 4 figures, accepted by Phys. Rev. B

Scientific paper

10.1103/PhysRevB.83.125105

We study the quantum anomalous Hall effect described by a class of two-component Haldane models on square lattices. We show that the latter can be transformed into a pseudospin triplet p+ip-wave paired superfluid. In the long wave length limit, the ground state wave function is described by Halperin's (1,1,-1) state of neutral fermions analogous to the double layer quantum Hall effect. The vortex excitations are charge e/2 abelian anyons which carry a neutral Dirac fermion zero mode. The superconducting proximity effect induces `tunneling' between `layers' which leads to topological phase transitions whereby the Dirac fermion zero mode fractionalizes and Majorana fermions emerge in the edge states. The charge e/2 vortex excitation carrying a Majorana zero mode is a non-abelian anyon. The proximity effect can also drive a conventional insulator into a quantum anomalous Hall effect state with a Majorana edge mode and the non-abelian vortex excitations.

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