Superconductor–insulator transition

The superconductor–insulator transition is an example of a quantum phase transition, whereupon tuning some parameter in the Hamiltonian, a dramatic change in the behavior of the electrons occurs. The nature of how this transition occurs is disputed, and many studies seek to understand how the order parameter, ${\displaystyle \Psi =\Delta \exp(i\theta )}$, changes. Here ${\displaystyle \Delta }$ is the amplitude of the order parameter, and ${\displaystyle \theta }$ is the phase. Most theories involve either the destruction of the amplitude of the order parameter - by a reduction in the density of states at the Fermi surface, or by destruction of the phase coherence; which results from the proliferation of vortices.