*3.3.2. Proximity effect*

6 Superconductors – Materials, Properties and Applications

electron spins also feel zero in total field.

**3.2. Theory of spin fluctuation effect** 

seen from a typical *H-T* phase diagram shown in Fig. 2.

*T***c (K)**

case without local spin fluctuation moments as a reference.

**0**

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

applied magnetic field.

field in total that the conduction electron spins experience becomes zero (also a complete suppression of the Zeeman effect), and thus the superconductivity is induced in this case.

Certainly, superconductivity could also be possible in this case (as a stable phase), even if without the external field *H* (i.e. *H* = 0). This is because the magnetic moments point to random directions (without *H*) and cancel each other, i.e., *H***J** = 0, and thus the conduction

This theory was mainly reported by Maekawa, S. and Tachiki, M. [7] in 1970s, with the discovery of field-induced superconductors EuxSn1-xMo6S8-ySey. These types of materials have rare-earth 4f-ions and paired conduction electrons from the 4d-Mo-ions. The rare-earth 4f-ions have large fluctuating magnetic moments, while the conduction electrons from the

Without externally applied magnetic field (*H* = 0), the fluctuating magnetic field from the rare-earth 4f-ion moments at the 4d-Mo conduction electrons are so strong that it weakens the BCS coupling of the Mo-electrons. Thus there is no superconductivity without externally

However, when external magnetic field is applied (*H* ≠ 0) it suppresses the spin uctuation, causing an increase of the BCS coupling among the conduction electrons. Thus, superconductivity appears in the presence of an applied magnetic field. This scenario can be

**Figure 2.** A possible *H-T* phase diagram for the spin fluctuation effect. The thin-red line represents a

*H* **(T)**

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.

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

4d-Mo-ions have strong electron–electron interactions and they form Cooper pairs.

On the other hand, when a superconducting nanowire is connected to two normal metal electrodes, generally a fraction of the wire is expected to be resistive, especially when the wire diameter is smaller than the superconducting coherence length. This is called the proximity effect [10].

Similarly, when a superconducting nanowire is connected to two bulk superconducting (BS) electrodes, the combined sandwiched system is expected to be superconducting (below the *TC* of the superconducting nanowire and the BS electrodes), and the superconductivity of the nanowire is then expected to be more supportive and more robust through its coupling with the superconducting reservoirs. This is also actually what is theoretically expected [15].
