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Bulletin of the American Physical Society

Maximization of a Superconductor's Transition Temperature in a Boson - Fermion Model by Variation of the Boson Density of States and the Boson - Fermion Coupling Constants or for Spin Vector or Scalar Couplings Respective

A. P. Kampf, J. R. Schrieffer

Published Mar 23, 2005• 0 citations
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We study the effect of gapless quasiparticles in a d-wave superconductor on the T=0T=0T=0 end point of the Kosterlitz-Thouless transition line in underdoped high-temperature superconductors. Starting from a lattice model that has gapless fermions coupled to three-dimensional XY\mathrm{XY}XY phase fluctuations of the superconducting order parameter, we propose a continuum field theory to describe the quantum phase transition between the d-wave superconductor and the spin-density-wave insulator. Without fermions, the theory reduces to the standard Higgs scalar electrodynamics (HSE), which is known to have the critical point in the inverted XY\mathrm{XY}XY universality class. Extending the renormalization group calculation for the HSE to include the coupling to fermions, we find that the qualitative effect of fermions is to increase the portion of the space of coupling constants where the transition is discontinuous. The critical exponents at the stable fixed point vary continuously with the number of fermion fields N, and we estimate the correlation length exponent $(\ensuremath{\nu}=0.65)$ and the vortex field anomalous dimension $({\ensuremath{\eta}}_{\ensuremath{\Phi}}=\ensuremath{-}0.48)$ at the quantum critical point for the physical case N=2.N=2.N=2. The stable critical point in the theory disappears for the number of Dirac fermions N>Nc,N>{N}_{c},N>Nc​, with ${N}_{c}\ensuremath{\approx}3.4$ in our approximation. We discuss the relationship between the superconducting and the chiral (SDW) transitions, and point to some interesting parallels between our theory and the Thirring model.
A ground state energy variational calculation of anyon gas with Hamiltonian included the interaction of spins of particles with anyon vector potential induced, i.e. statistical, magnetic field exhibits exact cancelation of terms connected with fractional statistics. This leads to bosonization of anyons due to coupling of their spins with statistical magnetic field. We presume that at the dense gas fluctuations of effective spins destroy the coupling and bosons become anyons. At the assumption that pseudogap (PG) boundary is temperature independent and when anyons are fermions we use this model to interpret experimental phase diagrams of Tallon and Loram hole and electron doped High-T_c superconductors below PG energy E_g and find the qualitative and quantitative agreement. We do the hypothesis that phase transition (PT) of bosons into Bose-Einstein condensate is not of second order, but of first order, close to second one, PG regime is meta stable phase of bosons, and E_g=0 is the critical point of this PT. Bosons undergo PT into fermions on PG boundary. Described in the literature non-Fermi quasi-particles might be related to bosons with effective spins.
After reminding of properties of the condensate of the complex scalar field in the external uniform magnetic field HHH, focus is made on the study of phases of the complex neutral vector-boson fields coupled with magnetic field by the Zeeman coupling and phases of the charged vector-boson fields. The systems may behave as nonmagnetic and ferromagnetic superfluids and ordinary and ferromagnetic superconductors. Response of these superfluid and superconducting systems occupying half of space on the external uniform static magnetic field HHH is thoroughly studied. Then the spin-triplet pairing of neutral fermions at conserved spin is considered. Novel phases are found. In external magnetic field, the phase with zero mean spin proves to be unstable to the formation of a phase with a nonzero spin. For a certain parameter choice ferromagnetic superfluid phases are formed already for H=0H=0H=0, characterized by an own magnetic field hhh. For H>Hcr2H>{H}_{\mathrm{cr}2}H>Hcr2​, the spin-triplet pairing and ferromagnetic superfluidity continue to exist above the ``old'' phase transition critical temperature Tcr{T}_{\mathrm{cr}}Tcr​. Formation of domains is discussed. Next, spin-triplet pairing of charged fermions is studied. Novel phases are found. Then, the 3P23{\mathrm{P}}_{2}3P2​ nnnnnn pairing in neutron star matter is studied. Also, a 3P23{\mathrm{P}}_{2}3P2​ pppppp pairing is considered. Numerical estimates are performed in the BCS weak-coupling limit and beyond it for the 3P23{P}_{2}3P2​ nnnnnn and pppppp pairings, as well as for the 3S13{\mathrm{S}}_{1}3S1​ npnpnp pairing.