Physics electronics

The Lattice Dynamical Properties of High-Temperature Superconductor (LSCO)
There is strong coupling when the photon and electron interactions are coupled and
heated, leading to superconductivity. Ions in a metal have two states, static ionic lattice and
scattering of electrons by lattice. Vibration releases electrons. Static ionic lattice gives a
periodic potential for conduction electrons to move, hence evolution of plane wave states in
the Fermi gas into Bloch waves in the crystal. As the lattice vibrates, electrons are scattered
and create both Bloch and Simple long waves. By ignoring the Bloch waves and considering
only the phonons in the lattice interacting with Fermi gas, long-range Coulomb waves are
created (Müller & Bussmann-Holder, 2005).
If there is no Coulomb interaction then the phonon frequency will be equal to the
classical model of balls each with an ionic mass of M, and connected to the springs. If a 3D
solid has 1 atom per cell unit, then there are 3N normal modes and 3 acoustic phonon
branches. According to Dagoto (1994), if the electron-phonon coupling is neglected, and the
long range Coulomb interaction included, then the longitude acoustic ionic plasma frequency
will be achieved. The conditions for an acoustic mode in Goldstone theorem will have been

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breached. The long-range Coulomb force and the back and forth sloshing of the free-flowing
ion occur for the same reason and frequency as with electrons, i.e. charge.
The electron-phonon coupling charges the acoustic phonons. The electronic medium
controls the long range interaction, which diminishes becomes finite in interaction length and
recovery of the Goldstone or acoustic mode. Once the stationary phonon Hamiltonian is equal
to the sum of the independent harmonic oscillators, in their 2 nd quantized form, the electron-
phonon Hamiltonian becomes easy to quantize (Ashcroft & Mermin, 1976, p. 802).
Superconductivity is achieved through considering the polarization of the lattice and causing
it to attract the electors. The screened electron-phonon interacts with coupling constant,
through a normalized phonon frequency. Interaction between electrons polarizes the first
lattice, which charges the phonon. The second electron interacts with the polarized lattice,
thus completing the superconductivity.

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References

Ashcroft, N. W., & Mermin, N. D. (1976). Electron-phonon interaction. In Solid state
physics(pp. 1-10). New York [u.a.: Holt, Reinhart & Winston.
Dagoto, E. (1994, July). Correlated electrons in high-temperature superconductors. Retrieved
from http://inside.mines.edu/~Zhiwu/research/papers/RevModPhys.66.763.pdf
Müller, K., & Bussmann-Holder, A. (2005). Superconductivity in complex systems. Berlin:
Springer.