Scaling law of the Hall coefficient in cuprates

One parameter scaling of the Hall coefficient of cuprates has been well known for almost three decades, but still lacks a simple mathematical expression. Motivated by the recent phenomenological prediction of the universal scaling of the thermal Hall conductivity, we propose here a simple scaling function for the Hall coefficient in cuprates that varies exponentially with the temperature. Comparison with experimental data in La$_{2-x}$Sr$_{x}$CuO$_{4}$, YBa$_2$Cu$_3$O$_{6+\delta}$, and Bi$_{2}$Sr$_{2-x}$La$_{x}$CuO$_{6+\delta }$ confirms its validity over a wide temperature and doping range. The scaling is independent of microscopic details and arises as long as the hole carriers have nonzero Berry curvature density within a finite energy window, possibly due to their interaction with the spin liquid. This differs from the activation model proposed previously to explain the Hall coefficient at low doping and high temperatures, and suggests a unified picture in line with the one parameter scaling observed in many physical quantities of cuprates.