Vortex Glass Transition and Quantum Vortex Liquid at Low Temperature in a Thicka-MoxSi1−xFilm

We present measurements of ac complex resistivity, as well as dc resistivity, for a thick amorphous ${\mathrm{Mo}}_x{\mathrm{Si}}_{1-x}$ film at low temperatures ( $T>\mathrm{}0.04\mathrm{K}$) in various constant fields $B$. We find that the vortex glass transition (VGT) persists down to $T\sim {0.04T}_{c0\mathrm{}}$ up to $B\sim {0.9B}_{c2\mathrm{}}\left(0\right)$, where $T_{c0\mathrm{}}$ and $B_{c2\mathrm{}}\left(0\right)$ are the mean-field transition temperature and upper critical field at $T=0\mathrm{}$, respectively. In the limit $T\to 0$, the VGT line $B_g\left(T\right)$ extrapolates to a field below $B_{c2\mathrm{}}\left(0\right)$, while the dc resistivity $\rho \left(T\right)$ tends to the finite nonzero value in fields just above $B_g\left(0\right)$. These results indicate the presence of a metallic quantum vortex liquid at $T=0\mathrm{}$ in the regime $B_g\left(0\right)<B<\mathrm{}{B}_{c2\mathrm{}}\left(0\right)$.