Charge 4$e$ superconductor: a wavefunction approach

We apply a wavefunction approach to study the charge 4$e$ superconductor. The wavefunction takes a similar structure to the BCS wavefunction for charge 2$e$ superconductors. The mean-field Hamiltonian and the Green's functions of charge 4$e$ are constructed. The physical properties including the density of states, gauge invariance, flux quantization, superfluid density and Josephson effects are systematically studied. All these results form a microscopic description of the charge 4$e$ SC and can be served as the hallmarks for experimental verifications.