The Ginzburg-Landau parameter $\alpha$, representing the energy competition between ordering ($U_{\text{ord}}$) and disordering ($U_{\text{dis}}$) energies, serves as the fundamental driving force for superconducting transitions. While its phenomenological role is well-established, a microscopic mechanism connecting $\alpha$ to quantum mechanical first principles remains elusive.
This work develops a unified microscopic framework by establishing matter wave (de Broglie wave) interference as the fundamental origin of energy competition in superconductors. We demonstrate that constructive interference of electronic wavefunctions at specific wavevectors—corresponding to Fermi surface nesting or electron-boson coupling vectors—leads to periodic charge density modulations in real space. These modulations, manifesting as charge density wave (CDW) or spin density wave (SDW) fluctuations, dynamically redistribute interaction energies among electron-phonon coupling, Coulomb repulsion, and exchange correlation terms.
The central finding reveals that under specific interference conditions, this energy redistribution can reverse the net electron-electron interaction from repulsive to attractive in particular momentum channels, corresponding to $U_{\text{ord}} > U_{\text{dis}}$ and thus $\alpha < 0$. We establish scaling relations between interference conditions (Fermi surface geometry, coupling strength) and the macroscopic energy competition parameter $\alpha$, providing a quantum mechanical foundation for understanding diverse superconducting mechanisms—from conventional electron-phonon coupling to unconventional spin-fluctuation mediation—as different manifestations of matter wave interference under varying material conditions.