In this paper we demonstrate the necessity of including the generally omitted collective-mode contributions in calculations of the Meissner effect for nonuniform superconductors. We consider superconducting pairing with nonzero center-of-mass momentum, as is possibly relevant to high transition temperature cuprates, cold atoms, and color superconductors in quantum chromodynamics. For the concrete example of the Fulde-Ferrell phase we present a quantitative calculation of the superfluid density, showing not only that the collective-mode contributions are appreciable but also that they derive from the amplitude mode of the order parameter. This latter mode is generally viewed as being invisible in conventional superconductors. However, our analysis shows that it is extremely important in pair-density-wave-type superconductors, where it destroys stable superfluidity well before the mean-field order parameter vanishes.
It is generally believed that the BCS-BEC evolution in fermionic systems with
s-wave pairing is a smooth crossover. However, for nonzero orbital-angular-momentum pairing such as
p- or
d-wave pairing, the system undergoes a quantum phase transition at the point where the chemical potential $\ensuremath{\mu}$ vanishes. In this paper, we study the BCS-BEC quantum phase transition and the collective excitations associated with the order-parameter fluctuations in two-dimensional fermionic systems with
p- and
d-wave pairings. We show that the quantum phase transition in such systems can be generically traced back to the infrared behavior of the fermionic excitation at $\ensuremath{\mu}=0$: ${E}_{\mathbf{k}}\ensuremath{\sim}{k}^{l}$, where
l=1,2 is the quantum number of the orbital angular momentum. The nonanalyticity of the thermodynamic quantities is due to the infrared divergence caused by the fermionic excitation at $\ensuremath{\mu}=0$. As a result, the evolution of the Anderson-Bogoliubov mode is not smooth: Its velocity is nonanalytical across the quantum phase transition.