Fermionic Bogoliubov quasiparticle ($E_{\mathbf{k}}=\sqrt{{\xi }_{\mathbf{k}}^2+|\Delta {|}^2}$)

A fermionic excitation obtained by a canonical particle–hole Bogoliubov transformation of a paired mean-field Hamiltonian. The uniform spin-singlet problem has the displayed positive energy and weights $|u{|}^2=(1+\xi /E)/2$, $|v{|}^2=(1-\xi /E)/2$. It interpolates between particle-like and hole-like excitations across the Fermi surface. These single-particle excitations differ from collective phase and amplitude modes of the order parameter.