Magnetic field induced transition from a vortex liquid to Bose metal in ultrathin a -MoGe thin film

We find transport and spectroscopic signatures that are consistent with a magnetic field induced transition from a vortex liquid to Bose metal in a two-dimensional amorphous superconductor, $a$-MoGe, using a combination of magnetotransport and scanning tunneling spectroscopy (STS). Below the superconducting transition, $\phantom{\rule{4pt}{0ex}}{T}_c\ensuremath{\sim}1.36\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, the magnetoresistance isotherms cross at a nearly temperature independent magnetic field, ${H}_c^* \ensuremath{\sim}36\phantom{\rule{0.16em}{0ex}}\mathrm{kOe}$. Above this field, the temperature coefficient of resistance is weakly negative, but the resistance remains finite as $T\ensuremath{\rightarrow}0$, as expected in a bad metal. From STS conductance maps and transport measurements at 450 mK we observe a very disordered vortex lattice at very low fields that melts into a vortex liquid above 3 kOe. Up to ${H}_c^*$ the tunneling spectra display a superconducting gap and coherence peak over a broad background caused by electron-electron interactions, as expected in a vortex liquid. However, above ${H}_c^*$ the tunneling spectra continue to display the gap but the coherence peak gets completely suppressed, suggesting that Cooper pairs lose their phase coherence. We conclude that ${H}_c^*$ demarcates a transition from a vortex liquid to Bose metal, that eventually transforms to a regular metal at a higher field ${H}^*$ where the gap vanishes in the electronic spectrum.