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Stable topological superconductivity in a family of two-dimensional fermion models

Stable topological superconductivity in a family of two-dimensional fermion models We show that a large class of two-dimensional spinless fermion models exhibit topological superconducting phases characterized by a nonzero Chern number. More specifically, we consider a generic one-band Hamiltonian of spinless fermions that is invariant under both time reversal, T , and a group of rotations and reflections, G , which is either the dihedral point-symmetry group of an underlying lattice, G = D n , or the orthogonal group of rotations in continuum, G = O ( 2 ) . Pairing symmetries are classified according to the irreducible representations of T ⊗ G . We prove a theorem that for any two-dimensional representation of this group, a time-reversal symmetry-breaking paired state is energetically favorable. This implies that the ground state of any spinless fermion Hamiltonian in continuum or on a square lattice with a singly connected Fermi surface is always a topological superconductor in the presence of attraction in at least one channel. Motivated by this discovery, we examine phase diagrams of two specific lattice models with nearest-neighbor hopping and attraction on a square lattice and a triangular lattice. In accordance with the general theorem, the former model exhibits only a topological ( p + i p ) -wave state while the latter shows a doping-tuned quantum phase transition from such state to a nontopological but still exotic f -wave superconductor. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

Stable topological superconductivity in a family of two-dimensional fermion models

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Publisher
American Physical Society (APS)
Copyright
Copyright © 2010 The American Physical Society
ISSN
1550-235X
DOI
10.1103/PhysRevB.81.024504
Publisher site
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Abstract

We show that a large class of two-dimensional spinless fermion models exhibit topological superconducting phases characterized by a nonzero Chern number. More specifically, we consider a generic one-band Hamiltonian of spinless fermions that is invariant under both time reversal, T , and a group of rotations and reflections, G , which is either the dihedral point-symmetry group of an underlying lattice, G = D n , or the orthogonal group of rotations in continuum, G = O ( 2 ) . Pairing symmetries are classified according to the irreducible representations of T ⊗ G . We prove a theorem that for any two-dimensional representation of this group, a time-reversal symmetry-breaking paired state is energetically favorable. This implies that the ground state of any spinless fermion Hamiltonian in continuum or on a square lattice with a singly connected Fermi surface is always a topological superconductor in the presence of attraction in at least one channel. Motivated by this discovery, we examine phase diagrams of two specific lattice models with nearest-neighbor hopping and attraction on a square lattice and a triangular lattice. In accordance with the general theorem, the former model exhibits only a topological ( p + i p ) -wave state while the latter shows a doping-tuned quantum phase transition from such state to a nontopological but still exotic f -wave superconductor.

Journal

Physical Review B – American Physical Society (APS)

Published: Jan 1, 2010

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