Anomalous magnetoresistance near the superconductor-insulator transition in ultrathin films of $a-{\mathrm{Mo}}_x{\mathrm{Si}}_{1-x}$

We have made systematic studies for both the zero-field and field-driven superconductor-insulator transitions in a series of 4-nm-thick films of amorphous ${\mathrm{Mo}}_x{\mathrm{Si}}_{1-x}$ at temperatures $T$ down to ∼0.05 K and fields $B$ up to 15 T. For superconducting films, we have observed an anomalous peak in the magnetoresistance $R\left(B\right)\mathrm{}$ and a subsequent decrease in $R\left(B\right)\mathrm{}$ with increasing $B$ at low temperatures in fields higher than the critical field $B_{\mathrm{xxC}}.$ This result, together with finding that the magnetoresistance is always positive for insulating films, may suggest the presence of localized Cooper pairs even at $B>\mathrm{}{B}_{\mathrm{xxC}}$ in the limit of $\overrightarrow{T}0.$