A study of lattice and magnetic interactions of conduction electrons

Abstract

Using basic theoretical considerations we show that the elastic continuum and conduction electrons interact via a vector field, to first order. This interaction must therefore be closely related to a magnetic interaction. We then study the magnetic interaction between conduction electrons using the Darwin approach and the free electron gas model. We show that pairing of conduction electrons may result and we calculate the total energy lowering due to the Darwin term in the Hamiltonian. The relevance of the results to superconductivity is considered.

Classical Electrodynamics without Fields and the Aharonov-Bohm effect

“…The relativistic invariance of this approach was established in [24]. The Darwin-Breit Hamiltonian was successfully applied to various electromagnetic problems, such as the fine structure in atomic spectra [25,26], superconductivity and properties of plasma [27,28,29].…”

Spin currents, relativistic effects and the Darwin interaction in the theory of hole superconductivity

“…According to Essen's treatment the interaction would be repulsive for spin currents, and in contrast to our work there is no charge inhomogeneity in his description of superconductors. Furthermore, in Essen's treatment electrons move at non-relativistic speeds and hence the magnitude of the Darwin energy is small, and certainly cannot account for high T c superconductivity [10]. Instead we argue here that the interaction is in fact attractive for spin currents and repulsive for charge currents, and in addition that electrons in spin currents move at relativistic speeds.…”

Electrodynamic model connecting superconductor response to magnetic field and to rotation

“…Electrons inside the surface are not able to change their state of motion. The relevant electrons are thus those with the largest energies and velocities [24], essentially the Fermi energy and Fermi velocity, v F . In a normal metal, such electrons are scattered and have a short mean free path .…”

“…The conduction electrons and thus also the superconducting condensate consist of electrons from a thin layer at the Fermi surface in momentum space. Since this is a two-dimensional object the number of relevant electrons must obey N ∝ R 2 (Essén [24]). Incidentally, this gives the physical result that the surface charge density σ − = −Ne/4πR 2 , of our model, can remain constant as R increases.…”