| Abstract: | The sign of the Hall conductivity σxy in metals corresponds to the sign of the charge carriers. In type II superconductors σxy was predicted to have the same sign as in the normal state; that is, the same as the charge carriers. However, Hall measurements showed that σxy changes sign as a function of temperature in cuprate high temperature superconductors such as YBCO shortly after their discovery, contradicting the existing models. Recently, another anomaly in the form of a transition from σxy ∝ 1+p to σxy ∝ p, where p is the hole doping was measured in YBCO. We show that both of these effects are exhibited by a simple model for a d-wave superconductor. We solve this model using self-consistent mean field, and calculate its Hall conductivity via the relation between σxy and Chern numbers. We show that the sign of σxy corresponds to the sign of excess charge in the vortex core, while the transition from σxy ∝ 1+p to σxy ∝ p is triggered by the appearance of antiferromagnetism in the core. We then proceed to study the t-J model, widely considered to be a minimal model for the cuprates, using variational Monte Carlo. Once again we find both effects, suggesting that the peculiarities of the Hall conductivity in the cuprates may be entirely explained by their vortex cores' structure.
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