title: Topological degeneracy (Majorana zero-mode) and 1 + 1D fermionic topological order in a magnetic chain on superconductor via spontaneous Z₂(f) symmetry breaking.
abstract: We study a chain of ferromagnetic sites, ie nano-particles, molecules or atoms, on a substrate of fully gapped superconductors. We find that under quite realistic conditions, the fermion-number-parity symmetry Z₂(f) can spontaneously break. In other words, such a chain can realize a 1  +  1D fermionic topologically ordered state and the corresponding two-fold topological degeneracy on an open chain. Such a topological degeneracy becomes the so called Majorana zero mode in the non-interacting limit.
authors.affiliation: Department of Physics, University of Guelph, 50 Stone Road East, Guelph, Ontario, Canada. Institute for Quantum Computing, 200 University Avenue West, Waterloo, Ontario, Canada.
authors.forename: Joel
authors.initials: J
authors.lastname: Klassen
authors.forename: Xiao-Gang
authors.initials: XG
authors.lastname: Wen