Hall effect and Fermi surface reconstruction via electron pockets in the high-$T_c$ cuprates

The mechanism by which the Fermi surface of high-$T_c$ cuprates undergoes a dramatic change from a large hole-like barrel to small arcs or pockets on entering the pseudogap phase remains a question of fundamental importance. Here we calculate the normal-state Hall coefficient from the resonating-valence-bond spin-liquid model developed by Yang, Rice and Zhang. In this model, reconstruction of the Fermi surface occurs via an intermediate regime where the Fermi surface consists of both hole- and electron-like pockets. We find that the doping $(x)$ dependence of the Hall number transitions from $1+x$ to $x$ over this narrow doping range. At low temperatures, a switch from a downturn to an upturn in the Hall coefficient signals the departure of the electron-like pockets from the Fermi surface.