Viyuela García, ÓscarFu, LiangMartín-Delgado Alcántara, Miguel Ángel2023-06-172023-06-172018-01-050031-900710.1103/PhysRevLett.120.017001https://hdl.handle.net/20.500.14352/11964© 2018 American Physical Society. We thank Leonid Glazman and Tharnier Oliveira for valuable conversations. M. A. M.-D. and O. V. thank the Spanish MINECO Grant No. FIS2012-33152, the CAM research consortium QUITEMAD+S2013/ICE-2801. O. V. thanks Fundación Rafael del Pino, Fundación Ramón Areces, and RCC Harvard. The research of M. A. M.-D. has been supported in part by the U.S. Army Research Office through Grant No. W911N F-14-1-0103. The work at MIT is supported by the DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award No. DE-SC0010526. L. F. is partly supported by the David and Lucile Packard Foundation.We study the phase diagram and edge states of a two-dimensional p-wave superconductor with longrange hopping and pairing amplitudes. New topological phases and quasiparticles different from the usual short-range model are obtained. When both hopping and pairing terms decay with the same exponent, one of the topological chiral phases with propagating Majorana edge states gets significantly enhanced by longrange couplings. On the other hand, when the long-range pairing amplitude decays more slowly than the hopping, we discover new topological phases where propagating Majorana fermions at each edge pair nonlocally and become gapped even in the thermodynamic limit. Remarkably, these nonlocal edge states are still robust, remain separated from the bulk, and are localized at both edges at the same time. The inclusion of long-range effects is potentially applicable to recent experiments with magnetic impurities and islands in 2D superconductors.engjournal articlehttp://dx.doi.org/10.1103/PhysRevLett.120.017001https://journals.aps.orgopen access53Non-abelian statisticsMajorana fermionsBound-statesZero modesInsulatorsVorticesImpurityLatticesFísica-Modelos matemáticos