Antiferromagnetism and charged vortices in high-Tc superconductors

We present the results of a detailed mean-field study of the effect of the long-range Coulomb interaction on charge accumulation in antiferromagnetic vortices in high-$T_c$ superconductors. We have found that antiferromagnetism is associated with an accumulation of charge in the vortex core, even in the presence of the long-range Coulomb interaction and that the local density of states in the vortex core, as described by a simple theory of competing $d$SC and AFM orders, is in excellent qualitative agreement with experimental data. We also touch on the manifestation of $\Pi$-triplet pairing in the presence of coexisting $d$SC and AFM order, and the intriguing appearance of one-dimensional stripe-like ordering.