Evidence for Field-Induced Quantum Criticality in an Overdoped Cuprate

In current views, the putative quantum phase transitions in high-$T_{\rm c}$ superconductors are deemed driven by charge doping. Here we uncover an unanticipated transition from a non-Fermi- to a Fermi-liquid state driven by magnetic field in a highly overdoped Tl$_2$Ba$_2$CuO$_{6+x}$ with $T_{\rm c}\approx 15$~K. From the $c$-axis resistivity measured up to 45~T, we show that the Fermi-liquid $\rho_c = \rho_c(0)+ AT^2$ features, accompanied by a (quantum) field-linear magnetoresistance, appear above a temperature-dependent field $H_{\rm FL}$, which decreases linearly with decreasing temperature and points to a quantum critical point near the upper critical field $H_{\rm c2}(0)$. The observed field-induced quantum criticality with a power-law diverging $A(H)$ bears a striking resemblance to that of heavy-fermion superconductor CeCoIn$_5$, suggesting a common underlying physics in these strongly correlated electron systems.