Boson-fermion duality and metastability in cuprate superconductors

The intrinsic structural metastability in cuprate high-T_c materials, evidenced in a checkerboard domain structure of the CuO₂ planes, locally breaks translational and rotational symmetry. Dynamical charge-deformation fluctuations of such nanosize unidirectional domains, involving Cu-O-Cu molecular bonds, result in resonantly fluctuating diamagnetic pairs embedded in a correlated Fermi liquid. As a consequence, the single-particle spectral properties acquire simultaneously (i) fermionic low-energy Bogoliubov branches for propagating Cooper pairs and (ii) bosonic localized glassy structures for tightly bound states of them at high energies. The partial localization of the single-particle excitations leads to a fractionation of the Fermi surface as the strength of the exchange coupling between itinerant fermions and partially localized fermion pairs increases upon moving from the nodal to the antinodal point. This is also the reason why bound fermion pairs accumulate near the antinodal points and thereby control the doping dependence of the cuprates upon approaching the singular universal optimal doping rate.