[Paper Review] Relativistic mechanism of superconductivity

H. Y. Cui|ArXiv.org|Dec 17, 2002

Relativity and Gravitational Theory1 references3 citations

TL;DR

This paper proposes a relativistic quantum mechanism for superconductivity, where the relativistic Coulomb force between electron pairs includes an attractive component under specific conditions, enabling Cooper pair formation. By modeling electron interactions via relativistic quantum theory, the framework reproduces key superconducting phenomena—quantized flux, London equation, Meissner effect, and Josephson effect—offering a unified explanation for both conventional and high-Tc superconductivity through collective electron-lattice and electron-electron dynamics.

ABSTRACT

According to the theory of relativity, the relativistic Coulomb's force between an electron pair is composed of two parts, the main part is repulsive, while the rest part can be attractive in certain situations. Thus the relativistic attraction of an electron pair provides an insight into the mechanism of superconductivity. In superconductor, there are, probably at least, two kinds of collective motions which can eliminate the repulsion between two electrons and let the attraction being dominant, the first is the combination of lattice and electron gas, accounting for traditional superconductivity; the second is the electron gas themselves, accounting for high $T_c$ superconductivity. In usual materials, there is a good balance between the repulsion and attraction of an electron pair, the electrons are regarded as free electrons so that Fermi gas theory plays very well. But in some materials, when the repulsion dominates electron pairs, the electron gas will has a behavior opposite to superconductivity. In the present paper the superconducting states are discussed in terms of relativistic quantum theory in details, some significant results are obtained including quantized magnetic flux, London equation, Meissner effect and Josephson effect.

Motivation & Objective

• To resolve the theoretical challenge of unifying conventional and high-Tc superconductivity under a single mechanism.
• To explore whether the relativistic Coulomb force between electron pairs can yield an effective attractive interaction despite the dominant repulsive component.
• To derive established superconducting effects (e.g., London equation, Meissner effect) from relativistic quantum field theory.
• To propose that two distinct collective motions—electron-lattice coupling and electron gas self-organization—can suppress repulsion and enable superconductivity.

Proposed method

• Derives the relativistic Coulomb force between two electrons using 4-velocity orthogonality and Lorentz-invariant force formulation, showing it acts perpendicular to the 4-velocity and lies in the plane of the other particle’s 4-velocity and separation vector.
• Expresses the force in terms of a relativistic potential using the 4-potential $ A_{ u} = \frac{kq'}{c^2} \frac{u'_{ u}}{r} $, satisfying the Lorentz gauge condition $ \partial_{\mu}A^{\mu} = 0 $.
• Applies the relativistic path integral formalism to calculate phase differences in electron wavefunctions, incorporating vector potentials and magnetic flux, leading to interference conditions for the Aharonov-Bohm effect.
• Uses the relativistic wave equation and phase coherence to derive the London equation and the Meissner effect via the requirement of gauge invariance and minimal coupling.
• Models the Josephson junction by comparing path integrals across and around an insulating barrier, deriving the tunneling current as a function of applied voltage and phase difference.
• Treats electron pairs in atoms and in diffraction experiments as superconducting states, suggesting a universal mechanism based on relativistic attraction.

Experimental results

Research questions

• RQ1 Can the relativistic Coulomb force between two electrons produce an effective attractive interaction under certain kinematic conditions?
• RQ2 How can the same relativistic mechanism account for both conventional superconductivity (via electron-lattice coupling) and high-Tc superconductivity (via electron gas self-organization)?
• RQ3 Can the London equation, Meissner effect, and Josephson effect be derived from a relativistic quantum field-theoretic framework without relying on BCS-type electron-phonon coupling?
• RQ4 What role does the 4-velocity orthogonality play in generating a non-classical, transverse force that enables binding of electron pairs?
• RQ5 How does the Aharonov-Bohm effect emerge as a consequence of relativistic phase coherence in superconducting states?

Key findings

• The relativistic Coulomb force between two electrons contains a repulsive main component and a potentially attractive residual component, depending on the relative motion and orientation of their 4-velocities.
• The force is orthogonal to the 4-velocity of the electron, resembling a centripetal force, and is derived from a relativistic potential satisfying the Lorentz gauge condition.
• Quantized magnetic flux is reproduced via the relativistic path integral, where phase differences depend on enclosed magnetic flux $ \phi $, leading to $ \psi \propto \cos(\frac{q\phi}{\hbar} + \cdots) $.
• The London equation and Meissner effect emerge naturally from the relativistic wavefunction formalism, with the supercurrent proportional to the vector potential and phase gradient.
• The Josephson effect is derived as a tunneling current oscillating at frequency $ \omega = \frac{2eV}{\hbar} $, with amplitude modulated by the phase difference between wavefunctions across and around the insulator.
• The theory suggests that electron pairs in atoms and in coherent electron diffraction experiments are also in a superconducting state, indicating a universal mechanism based on relativistic attraction.