Edge superconductivity in Nb thin film microbridges revealed by integral and spatially resolved electric transport

The resistance $R$ vs perpendicular external magnetic field $H$ was measured for superconducting Nb thin--film microbridges with and without microholes [antidots (ADs)]. Well below the transition temperature, integral $R(H)$ measurements of the resistive transition to the normal state on the plain bridge show two distinct regions, which can be identified as bulk and edge superconductivity, respectively. The latter case appears when bulk superconductivity becomes suppressed at the upper critical field $H_{c2}$ and below the critical field of edge superconductivity $H_{c3}\approx 1.7\, H_{c2}$. The presence of additional edges in the AD bridge leads to a different shape of the $R(H)$ curves. We used low-temperature scanning laser microscopy (LTSLM) to visualize the current distribution in the plain and AD bridge upon sweeping $H$. While the plain bridge shows a dominant LTSLM signal at its edges for $H > H_{c2}$ the AD bridge also gives a signal from the inner parts of the bridge due to the additional edge states around the ADs. LTSLM reveals an asymmetry in the current distribution between left and right edges, which confirms theoretical predictions. Furthermore, the experimental results are in good agreement with our numerical simulations (based on the time-dependent Ginzburg--Landau model) yielding the spatial distribution of the order parameter and current density for different bias currents and $H$ values.