**2. Basic properties**

A superconductor exhibits two interesting properties: the first one is the electrical resistance of the material abruptly drops to zero at critical temperature T*c*. The superconductor is able to carry electrical current without resistance. This phenomenon is related to the perfect diamagnetism. The second feature of superconductivity is also known as Meissner effect. In this case a superconductor expels an external applied magnetic field into its interior.

This struggle between superconductivity and magnetic field penetration select two important behaviors. If a superconductor does not permit any applied magnetic flux, it is known as Type I superconductor. In this case, if the superconducting state is put in the presence of a too high magnetic field, the superconductivity is destroyed when the magnetic field magnitude exceeds the critical value H*c*. Other superconductor category is the Type II material in which the magnetic properties are more complex. For this material the superconductor switches from the Meissner state to a state of partial magnetic flux penetration. The penetration of magnetic flux starts at a lower field H*c*<sup>1</sup> to reach at an upper a higher field H*c*2.

In addition to the two limiting parameters T*c* and H*c*, the superconductivity is also broken down when the material carries an electrical current density that exceeds the critical current density J*c*. In the Ginzburg-Landau theory, the superconducting critical current density can be written as

$$J\_c = \left(\frac{2}{3}\right)^{2/3} \frac{H\_c}{\lambda}.\tag{1}$$

The current density given by Eq. (1) is sometimes called the *Ginzburg-Landau depairing current density*.

Once into the superconductor state, it is possible to cross the superconductor surface changing only the current. In this case, even for *T* < *Tc* and *H* < *Hc* with the material reaching its normal state, and with loss of its superconductor properties.
