Boson-fermion duality and metastability in cuprate superconductors

Abstract

The intrinsic structural metastability in cuprate high-T c materials, evidenced in a checkerboard domain structure of the CuO 2 planes, locally breaks translational and rotational symmetry. Dynamical chargedeformation 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 ͑i͒ fermionic low-energy Bogoliubov branches for propagating Cooper pairs and ͑ii͒ 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.

Flow equation approach to the linear response theory of superconductors

“…They are mutually coupled through the charge exchange (Andreev-type) scattering. Such scenario (31) has been considered by various authors in the context of high T c superconductivity [14][15][16][17][18][19][20][21] and for description of the resonant Feshbach interaction in the ultracold fermion atom gasses [36][37][38].…”

“…More recently [19] we have also investigated evolution of the k-resolved pseudogap considering two-dimensional lattice dispersion with the nearest and next-nearest neighbor hopping integrals realistic for the cuprate superconductors. For temperatures slightly above T c we have found that the pseudogap starts to close around the nodal points restoring the Fermi arcs, whereas in the antinodal areas the pseudogap practically does not change.…”

“…Following the previous study [19] we have selfconsistently determined these renormalized energiesξ k ,Ẽ q by solving numerically the flow equations (34,35) for the tight-binding lattice model ε k = −2t [cos ak x + cos ak y ] − 2t z cos ck z assuming reduced mobility along z-axis t z = 0.1t. Initially (at l = 0) we have assumed bosons to be localized.…”

“…All l-dependent coefficients have to be determined applying the ansatz (19) in the flow equation (A7) for the current operatorsĵ σ q (l). On this basis we obtain the following set of equations…”

“…Adopting argumentation discussed in the literature on the microscopic [14][15][16][17][18][19] and the phenomenological grounds [20,21] we consider the system consisting of the preformed local pairs (of arbitrary origin) coexisting and interacting with the itinerant electrons. Using the flow equation approach we analyze the diamagnetism within such scenario.…”