The materials that conduct electricity when it's cooled to extremely low temperatures in a quantum computer are called superconductors. For example :- Lead, Niobium, Magnesium Diboride.
The reason why this is possible is because the material's chemical structure, the attractive property between the electrons is quite enough to have near to no resistance offering huge amount of electronic current generation.
For quantum computers to work, there is need for the materials to be stored in temperature which is close to absolute zero kelvin in order to support the mentioned property.