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, $T_c\sim 1.36\mathrm{K}$, the magnetoresistance isotherms cross at a nearly temperature independent magnetic field, $H_c^{*} \sim 36\mathrm{kOe}$. Above this field, the temperature coefficient of resistance is weakly negative, but the resistance remains finite as $T\to 0$, 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.

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• Magnetoresistance
• Pseudogap
• Superconductivity
• Vortex lattices
• Disordered alloys
• Low-temperature superconductors
• Thin films
• Resistivity measurements
• Scanning tunneling spectroscopy