Signature of optimal doping in Hall-effect measurements on a high-temperature superconductor

High-temperature superconductivity is achieved by doping copper oxide insulators with charge carriers. The density of carriers in conducting materials can be determined from measurements of the Hall voltage--the voltage transverse to the flow of the electrical current that is proportional to an applied magnetic field. In common metals, this proportionality (the Hall coefficient) is robustly temperature independent. This is in marked contrast to the behaviour seen in high-temperature superconductors when in the 'normal' (resistive) state; the departure from expected behaviour is a key signature of the unconventional nature of the normal state, the origin of which remains a central controversy in condensed matter physics. Here we report the evolution of the low-temperature Hall coefficient in the normal state as the carrier density is increased, from the onset of superconductivity and beyond (where superconductivity has been suppressed by a magnetic field). Surprisingly, the Hall coefficient does not vary monotonically with doping but rather exhibits a sharp change at the optimal doping level for superconductivity. This observation supports the idea that two competing ground states underlie the high-temperature superconducting phase.