Pressure-dependent upper critical field of FeSe superconductor

In FeSe, the superconducting transition temperature $T_c $ ($\approx 9\,$K at ambient pressure) has a complicated pressure dependence with a local maximum near $p_1\approx$\,0.8\,GPa and a local minimum at $p_2\approx$\,1.2GPa. In this work, we study the upper critical field, $H_{c2,c}(T)$, of FeSe using c-axis resistivity measurements under hydrostatic pressure up to 1.56\,GPa with the magnetic field H$\parallel$c. Application of both current and magnetic field along the same axis reduces the flux flow motion and give sharper transition in applied fields. We observe a non-monotonic evolution of the slope of $H_{c2,c}(T)$$\mid_{T_c}$ with pressure, with changes around $p_1$ and $p_2$. We employ two-band orbital $H_{c2,c}$ calculation to show that the data can be explained using the Fermi velocities extracted from the recent quantum oscillations study\,$[1]$ over the whole pressure range. \linebreak $[1]$ Terashima {\it et al.} arXiv:1510.01840v1 [cond-mat.supr-con] (2015)