Field-Induced Quantum Critical Route to a Fermi Liquid in Overdoped Tl$_2$Ba$_2$CuO$_{6+x}$

In high temperature superconductivity, charge doping is a natural tuning parameter that takes copper oxides from the antiferromagnet through the superconducting `dome'-shaped region. In the metallic state above $T_{\rm c}$ the standard Landau's Fermi-liquid theory of metals, as typified by the temperature squared ($AT^2$) dependence of resistivity, appears to break down. The expected recovery of the usual Fermi-liquid metal on the high doping side is fundamental but ill understood. Here we uncover a new transformation in an overdoped superconducting copper oxide Tl$_2$Ba$_2$CuO$_{6+x}$ from the non-Fermi to a Fermi-liquid state driven by magnetic field [1]. From the $c$-axis resistivity measured up to 45~T, we show that the Fermi-liquid $AT^2$ features, accompanied by a field-linear magnetoresistance, appear above a field $H_{\rm FL}$. This crossover field $H_{\rm FL}$ decreases linearly with decreasing temperature $T$ and lands at a quantum critical point (QCP) near the upper critical field $H_{\rm c2}(0)$. The Fermi-liquid coefficient $A(H)$ shows a power-law diverging behavior on the approach to the QCP, indicating the second-order quantum phase transition at this field. The connection between the field-induced QCP and the pseudogap observed in the underdoped regime will be discussed. \\ \\ \noindent [1] T. Shibauchi {\it et al.}, Proc. Natl. Acad. Sci. USA {\bf 105}, 7120 (2008).