Various properties of underdoped superconducting cuprates, including the momentum-dependent pseudogap opening, indicate a behavior which is neither BCS- nor Bose-Einstein condensation (BEC)– like. To explain this issue we introduce a two-gap model. This model assumes an anisotropic pairing interaction among two kinds of fermions with small and large Fermi velocities representing the quasiparticles near the M and the nodal points of the Fermi surface, respectively. We find that a gap forms near the M points resulting in incoherent pairing due to strong fluctuations. Instead, the pairing near the nodal points sets in with phase coherence at lower temperature. By tuning the momentum-dependent interaction, the model allows for a continuous evolution from a pure BCS pairing (in the overdoped and optimally doped regime) to a mixed boson-fermion picture (in the strongly underdoped regime).

The Magnitude–Frequency-Distribution (MFD) of earthquakes is typically modeled with the (tapered) Gutenberg–Richter relation. The main parameter of this relation, theb-value, controls the relative rate of small and large earthquakes. Resolving spatiotemporal variations of theb-value is critical to understanding the earthquake occurrence process and improving earthquake forecasting. However, this variation is not well understood. Here we present remarkable MFD variability during the complex 2016/17 central Italy sequence using a high-resolution earthquake catalog. Isolating seismically active volumes (‘clusters’) reveals that the MFD differed in nearby clusters, varied or remained constant in time depending on the cluster, and increased inb-value in the cluster where the largest earthquake eventually occurred. These findings suggest that the fault system’s heterogeneity and complexity influence the MFD. Our findings raise the question “b-value of what?”: interpreting and using MFD variability needs a spatiotemporal scale that is physically meaningful, like the one proposed here.