A model of coexistence of antiferromagnetism and superconductivity in electron- and hole-doped cuprates

The evolution of the high temperature superconductors containing Cu 2O plane(s) (known as cuprates) from the Mott insulating state in the parent composition to the superconducting phase with insertion or extraction of electrons (doping) remains an important unsolved problem. This issue is tied to attempts to understand the pairing mechanism of these materials. Current models fall into two categories: (1) the pairing arises due to a bound state formation of the two electrons without the need of any pairing glue and (2) a magnetic mechanism for superconductivity in which the magnetic excitations provide the glue. In scenario 1, the bound state of the electron pairs originates due to the strong electron-electron interactions which can be described by Mott physics. On the other hand, the magnetic mechanism for superconductivity is best described in terms of magnetic excitations which originate from a competing phase with long-range magnetic order (Slater physics) in a weak or intermediate coupling regime. Interestingly, cuprates exhibit two energy scales, low-energy coherent spectra near the Fermi level and the high energy incoherent region, which support scenario 1 and 2 respectively and make it very hard to choose the right model to start with.;To elaborate upon the above controversies, angle-resolved photoemission spectro-scopies (ARPES) and other experimental probes find evidence for a magnetic order which appears as a pseudogap in the low-energy coherent spectra and decreases with doping to a quantum critical point (where a phase transition occurs at zero temperature). The magnetic order is a manifestation of weak coupling theory. On the contrary, the optical experiments exhibit an absorption peak beyond the coherent region which persists above the quantum critical point, in fact shifting to higher rather than lower energies with doping. This absorption peak is characteristic of a Mott gap (not to be confused with the pseudodap), a clear signature of strong coupling effects. Here I present an intermediate coupling model stating from the weak coupling region, which will be called the quasiparticle-GW (QP-GW) model.;The model is based on the mean-field theory in the Hartree-Fock formalism to describe the low-energy pseudogap physics. Then the strong correlation effects are accounted for through a self-energy calculation due to magnetic fluctuations (magnetic fluctuations are called 'magnons' in the field theory terminology). These magnon modes are observed in neutron scattering in various cuprates and are believed to provide the pairing glue. I have included the superconductivity though a phenomanological form of pairing potential and solved in the Bardeen-Cooper-Schrieffer (BCS) theory. The superconductivity coexists with the pseudogap state in a uniform phase and explains the salient features of the two-gap behavior in both electron and hole doped cuprates, consistent with ARPES, scanning tunneling microscopy (STM) and penetration depth measurements.;The model also describes both parts of the spectra and the opposite doping dependencies of the pseudogap and Mott gap in both electron and hole doped cuprate in a consistent way. Some of the significant predictions of the model are mentioned here as (1) Fermi surface topological transitions as observed in ARPES, scanning tunneling microscopy (STM), Hall effect etc.;(2) high-energy 'kink' or 'waterfall' physics as observed in ARPES and quantum Monte Carlo (QMC) calculations; (3) the entire doping and energy dependence of the optical spectra and the microscopic mechanism of the mid-infrared peak and Mott gap features; (4) Mott gap collapse and anomalous spectral weight transfer consistently explained in a series of experiments including ARPES, x-ray absorption spectroscopy, optical experiments; (5) the opposite doping behavior of the spectral weight and dispersion renormalization features in cuprates.