Magnetic-field-induced normal state in a stripe-ordered cuprate La$_{1.7}$Eu$_{0.2}$Sr$_{0.1}$CuO$_{4}$ in the zero-temperature limit

Charge orders have been discovered in all hole-doped cuprates, but their precise interplay with the high-temperature superconductivity (SC), especially under extreme conditions of high magnetic fields ($H$), is not well understood. We have studied the magnetotransport properties of the stripe-ordered cuprate La$_{1.7}$Eu$_{0.2}$Sr$_{0.1}$CuO$_{4}$ [$T_{c}(H=0)=5.9$~K] at high fields ($H$ ${\le}$ 35 T) and very low temperatures ($T$ ${\ge}$ 16 mK). Our results reveal, for the first time in stripe-ordered cuprates, a full sequence of ground states as a function of $H$: a vortex solid [$T_c(H)\neq 0$], a vortex glass ($T_c=0$), a possible coexistence region of the vortex glass and the high-$H$ normal phase, and the high-$H$ normal phase in which SC is suppressed. The high-$H$ normal state is characterized by the negative magnetoresistance and a $\ln(1/T)$ dependence of the resistivity, which becomes weaker with increasing $H$ and disappears for $H >$ 55 T. Thus the results strongly suggest that the high-field ground ($T=0$) state in stripe-ordered cuprates is a metal.