Implementation of a Semi-classical Theory for Superconductors: Scientific Explanation

When the temperature of certain materials is reduced to below a certain value known as the critical temperature, a state transition occurs, and the system transitions from the normal to superconducting state. A superconductor is defined by two fundamental physical properties: zero electrical resistance to direct current and the Meissner effect (the material repels any external magnetic flux). In the absence of a suitable theory, physicists have used phenomenological approaches to explicate the existence of this exotic low-temperature state. We present a semi-classical (non-phenomenological) theory of superconductors in this study. We then show that the existence of superconductors at high critical temperatures cannot be explained by anything other than the behavior of the gas of free electrons in response to temperature changes in the metal. The critical temperature then serves the same purpose as the liquefaction temperature in a gaseous-to-liquid transition and the Curie temperature in a paramagnetic-to-ferromagnetic transition.