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Abstract: We show that a large class of two-dimensional spinless fermion models exhibittopological superconducting phases characterized by a non-zero Chern number.More specifically, we consider a generic one-band Hamiltonian of spinlessfermions that is invariant under both time-reversal, $\mathbb{T}$, and a groupof rotations and reflections, $\mathbb{G}$, which is either the dihedralpoint-symmetry group of an underlying lattice, $\mathbb{G}=D n$, or theorthogonal group of rotations in continuum, $\mathbb{G}={ m O}2$. Pairingsymmetries are classified according to the irreducible representations of $\mathbb{T} \otimes \mathbb{G}$. We prove a theorem that for any two-dimensionalrepresentation of this group, a time-reversal symmetry breaking paired state isenergetically favorable. This implies that the ground state of any spinlessfermion Hamiltonian in continuum or on a square lattice with a singly-connectedFermi surface is always a topological superconductor in the presence ofattraction in at least one channel. Motivated by this discovery, we examinephase diagrams of two specific lattice models with nearest-neighbor hopping andattraction on a square lattice and a triangular lattice. In accordance with thegeneral theorem, the former model exhibits only a topological $p + ip$-wavestate, while the latter shows a doping-tuned quantum phase transition from suchstate to a non-topological, but still exotic $f$-wave superconductor.



Autor: Meng Cheng, Kai Sun, Victor Galitski, S. Das Sarma

Fuente: https://arxiv.org/



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