Superconductivity

Discovery of Superconductivity

H. Kammerlingh Onnes discovered superconductivity in 1911 when it was observed that the resistance of Mercury (Hg) dropped to zero at approximately 4.2K. After this was observed, many other metals exhibited the same phenomena when they reached a certain critical temperature T_c. Creating a loop and inducing a current onto a superconductor with zero resistivity will result in that current being sustained almost infinitely, so long as the metal remains at zero resistivity. This is known as a persistent current. Compared to an ordinary metal with an induced current going around in a loop, the current in the ordinary metal ring will decay quickly because of resistance.

Critical Temperature of Superconductors

The critical temperature for superconductors T_c is the temperature where the electrical resistivity of a metal drops to zero. This occurs quite suddenly once the temperature is reached and is thought to have undergone some kind of phase transition. This phase of superconductivity is described by BCS theory.

BCS Theory

John Bardeen, Leon Cooper, and Robert Schrieffer modeled the properties of Type 1 superconductors, which eventually became known as BCS Theory. An important part of this theory requires the pairing of the electrons in the superconductor into what are known as Cooper pairs. The pairing of these electrons is a result of attraction from distorted lattice vibrations, which in turn causing a phonon interaction. What happens is one of the electrons comes in contact with the lattice and causes the distortion. This results in a net positive charged localized at that location and then attracts the other electron in the pair. These pairs of electrons behave differently compared to a single electron. The electrons in a Cooper pair have opposite spins and momentum. Because they are also in a superconductor, they have zero resistance as well and do no scatter. These electrons behave somewhat like bosons, which are able to condense into the same energy level. The Pauli Exclusion principle doesn't allow electrons to occupy the same energy level so theoretically there could have been a phase transition to induce this behavior. Compared to a normal electron's, the electrons in a Cooper pair have less energy and leave an energy gap. This energy gap is one of the things that sets these electrons apart and prevents collisions with other electrons which could lead to resistivity.

Meissner Effect

The transition from a normal metal to a superconductor causes the Meissner Effect, which is a state of perfect diamagnetism. In this state, the superconductor excludes magnetic fields from its interior. In other words, it expels magnetic flux completely.

London Equation

The London Equation describes the Meissner Effect. It describes the decay of a magnetic field inside a superconductor in terms of a parameter known as the London penetration depth $\lambda \,\!$.

${\overrightarrow {B}}=-{\frac {m}{n_{s}e^{2}}}\nabla \ \times \ {\overrightarrow {J}}_{s}$

Coherence Length

The coherence length $\zeta \,\!$of a superconductor is related to the Fermi Velocity v_F of the material as well as the energy gap.

Types of Superconductors

Type 1

Type 1 superconductors are modeled by BCS theory.

Type 2

Type 2 superconductors are made from alloys, which are solid solutions that consist of one or more elements.