Cooper Pairs and BCS Theory

Electrical conductivity with exactly zero resistance.

Superconductivity, a phenomenon where certain materials exhibit zero electrical resistance and expulsion of magnetic fields at very low temperatures, is a fascinating field of study in quantum mechanics. One of the key concepts that underpin this phenomenon is the formation of Cooper pairs and the Bardeen–Cooper–Schrieffer (BCS) theory.

Introduction to Cooper Pairs

Cooper pairs, named after physicist Leon Cooper, are pairs of electrons that move through a superconductor without resistance. This is a surprising behavior because electrons, being like-charged particles, naturally repel each other according to Coulomb's law. However, in a superconductor, under certain conditions, they pair up and move together. This pairing mechanism is what allows superconductors to conduct electricity without resistance.

Formation and Properties of Cooper Pairs

The formation of Cooper pairs is a result of a subtle interplay between electrons and the lattice structure of the superconducting material. As an electron moves through the lattice, it causes nearby positive ions to move slightly towards it, creating a region of positive charge. This region can attract another electron, leading to the formation of a Cooper pair.

These pairs have some unique properties. They move through the superconductor as a single entity, and their motion is highly correlated. This means that the behavior of one electron in the pair is directly related to the behavior of the other, no matter how far apart they are. This is a quantum mechanical effect known as entanglement.

BCS Theory: Concept and Importance

The Bardeen–Cooper–Schrieffer (BCS) theory, proposed by John Bardeen, Leon Cooper, and John Robert Schrieffer, provides a theoretical explanation for superconductivity. The BCS theory describes how electrons in a superconductor form Cooper pairs and how these pairs contribute to superconductivity.

According to the BCS theory, the Cooper pairs form a quantum mechanical state in which they all occupy the lowest energy level. This state is resistant to perturbations, such as scattering by impurities, which normally cause electrical resistance. As a result, the Cooper pairs can move through the superconductor without resistance, leading to superconductivity.

Role of Cooper Pairs in Superconductivity

The formation of Cooper pairs is the fundamental reason why superconductors can conduct electricity without resistance. When electrons pair up to form Cooper pairs, they move in a coordinated way that allows them to avoid collisions with impurities and defects in the material. This coordinated movement is what allows superconductors to carry electrical current without loss of energy.

In conclusion, the concept of Cooper pairs and the BCS theory are fundamental to understanding superconductivity. They provide a theoretical framework that explains the unique properties of superconductors and pave the way for the development of new superconducting materials and technologies.