There are materials that have zero electrical resistance if the temperature is sufficiently low. Also the current density and the magnetic field should not be too high. In 1908 Heike Kamerlingh-Onnes and his laboratory accomplished to liquify helium whose boiling temperature is about 4.2 K under atmospheric pressure. Thus he could discover the superconductivity of mercury in 1911.
In the following years many other superconductors have been discovered, even high temperature superconductors (HTS). HTS has the advantage that liquid nitrogen (77 K) is sufficient.
Superconducting magnets often consist of niobium titanium (NbTi) that has a critical temperature of approximately 10 K.
The colder part of current leads is frequently built with HTS for very large currents.
Current leads are a cryo-electrical component of the circuit of a superconducting magnet, a pair for each electrical circuit. One end, the warm terminal, has ambient temperature, about 300 K (Kelvin). The other end, the cold terminal, has the temperature of liquid helium, approximately 4 K.
If the cross-section of the conductor is too large, a lot of heat comes from the warm to the cold terminal. On the other hand, if the cross-section is too small, the electrical current will cause a significant heating and the current leads may burn through. The designer has to find a compromise.
There are current leads which are only cooled at the cold terminal. This is the conduction cooled type. The vapour cooled current leads guide the helium vapour all along the whole length from the cold to the warm terminal. Sometimes the temperature is fixed in between with liquid nitrogen (77 K) by the employment of a thermal anchor.