**3.3. Theory of anti-proximity effect**

### *3.3.1. Superconductivity in nanowires enhanced by applied magnetic field*

Unlike the bulk superconductors, a nanoscale system can have externally applied magnetic field *H* to penetrate it with essentially no attenuation at all throughout the whole sample.

But it has been observed that the application of a small magnetic field *H* can decrease the resistance in even simple narrow superconducting wires (i.e., negative magnetoresistance) [12, 13], while larger applied magnetic field *H* can increase the critical current (*I*C) significantly [14]. These indicate an enhancement of superconductivity in nanowires by the application of magnetic field. But to understand the enhancement of superconductivity by magnetic field in nanoscale systems is very challenging currently in the science community.
