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Thermoelectric effects in silicene nanoribbons

Transport and thermoelectric coefficients (including also spin thermopower) of silicene nanoribbons with zigzag edges are investigated by {\it ab-initio} numerical methods. Local spin density of such nanoribbons reveals edge magnetism. Like in graphene, one finds antiferromagnetic and ferromagnetic ordering, with spin polarization at one edge antiparallel or parallel to that at the other edge, respectively. Thermoelectric properties, especially the Seebeck coefficient, significantly depend on the electronic band structure and are enhanced when the Fermi level is in the energy gap. However, these thermoelectric properties are significantly reduced when the phonon contribution to the heat conductance is included. This phonon contribution has been calculated numerically by two different methods. Transition from antiferromagnetic to ferromagnetic states leads to a large magnetoresistance as well as to a considerable magnetothermopower. Thermoelectric parameters in the antiparallel configuration, when spin polarization in the left part of the nanoribbon is opposite to that in the right part, are also analyzed.