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, $\mathbb{T}$, and a group of rotations and reflections, $\mathbb{G}$, which is either the dihedral point-symmetry group of an underlying lattice, $\mathbb{G}=D_n$, or the orthogonal group of rotations in continuum, $\mathbb{G}=\text{O}\left(2\right)$. Pairing symmetries are classified according to the irreducible representations of $\mathbb{T}\otimes \mathbb{G}$. 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 $\left(p+ip\right)$-wave state while the latter shows a doping-tuned quantum phase transition from such state to a nontopological but still exotic $f$-wave superconductor.

• Received 24 August 2009

DOI:https://doi.org/10.1103/PhysRevB.81.024504