Electron-pair Waves

In superconductors the resistanceless current is carried by pairs of electrons, known as Cooper Pairs. Each pair can be treated as a single particle with a mass and charge twice that of a single electron, whose velocity is that of the center of mass of the pair.

In a normal conductor the coherence length of the conduction electron wave is quite short due to scattering. Cooper pairs, however, are not scattered hence their wavefunctions are coherent over very long distances.

Each pair can be represented by a wavefunction of the form[12]

$$\Phi_{P} = \Phi e^{i(\boldsymbol{P}.\boldsymbol{r})/\hbar}$$ (3.15)

where $\boldsymbol{P}$ is the net momentum of the pair whose center of mass is at $\boldsymbol{r}$. In a uniform current density all the electron wavelengths will be equal with the superposition of these coherent waves producing a single wave of the same wavelength, meaning all of the electron-pairs in a superconductor can be described by a single wavefunction

$$\Psi_{P} = \Psi e^{i(\boldsymbol{P} \centerdot \boldsymbol{r})/\hbar}$$ (3.16)

This electron-pair wave retains its phase coherence over long distances and it is this characteristic which leads to interference and diffraction phenomena. As they are macroscopic manifestations of quantum interactions the phenomena are collectively termed ``Quantum Interference''.