Self-consistent electronic structure of a $d_{x^2-y^2}$ and a $d_{x^2-y^2}+i{d}_{xy}$ vortex

Abstract

We investigate quasiparticle states associated with an isolated vortex in a d-wave superconductor using a self-consistent Bogoliubov-de Gennes formalism. For a pure $d_{x^2-y^2}$ superconductor we find that there exist no bound states in the core; all the states are extended with continuous energy spectrum. This result is inconsistent with the existing experimental data on cuprates. We propose an explanation for this data in terms of a magnetic-field-induced $d_{x^2-y^2}+i{d}_{xy}$ state recently invoked in connection with the thermal conductivity measurements on Bi${}_2$Sr${}_2$CaCu${}_2$O${}_8$.

arXiv comment4 pages REVTeX, 3 .ps figures included. Version to appear in PRL, May 24, 1998. Minor changes, references added

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