Planckian Dissipation and non-Ginzburg-Landau Type Upper Critical Field in Bi2201

Resistivity and Hall effect measurements have been carried out on a micro-fabricated bridge of Bi2201 single crystal at low temperatures down to 0.4 K under high magnetic fields. When superconductivity is crashed by a high magnetic field, the recovered "normal state" resistivity still shows a linear temperature dependence in low temperature region. Combining with the effective mass and the charge carrier density, we get a linear scattering rate $1/\tau = \alpha k_{B} T/\hbar$ with $0.77<\alpha<1.16$, which gives a strong evidence of the Planckian dissipation. Furthermore, our results reveal a new type of temperature dependence of upper critical field, $H_{c2}(T)=H^*\sqrt{(1-t)/(t+0.154)}$, which is totally different from the expectation of the Ginzburg-Landau theory, and suggests uncondensed Cooper pairs above $H_{c2}(T)$ line.