106 research outputs found
The Isotope Effect in d-Wave Superconductors
Based on recently proposed anti-ferromagnetic spin fluctuation exchange
models for -superconductors, we show that coupling to harmonic
phonons {\it{cannot}} account for the observed isotope effect in the cuprate
high- materials, whereas coupling to strongly anharmonic multiple-well
lattice tunneling modes {\it{can}}. Our results thus point towards a strongly
enhanced {\it{effective}} electron-phonon coupling and a possible break-down of
Migdal-Eliashberg theory in the cuprates.Comment: 12 pages + 2 figures, Postscript files, all uuencoded Phys. Rev.
Lett. (1995, to be published
Berry phases and pairing symmetry in Holstein-Hubbard polaron systems
We study the tunneling dynamics of dopant-induced hole polarons which are
self-localized by electron-phonon coupling in a two-dimensional antiferro-
magnet. Our treatment is based on a path integral formulation of the adia-
batic approximation, combined with many-body tight-binding, instanton, con-
strained lattice dynamics, and many-body exact diagonalization techniques. Our
results are mainly based on the Holstein- and, for comparison, on the
Holstein-Hubbard model. We also study effects of 2nd neighbor hopping and
long-range electron-electron Coulomb repulsion. The polaron tunneling dynamics
is mapped onto an effective low-energy Hamiltonian which takes the form of a
fermion tight-binding model with occupancy dependent, predominant- ly 2nd and
3rd neighbor tunneling matrix elements, excluded double occupan- cy, and an
effective intersite charge interactions. Antiferromagnetic spin correlations in
the original many-electron Hamiltonian are reflected by an attractive
contribution to the 1st neighbor charge interaction and by Berry phase factors
which determine the signs of effective polaron tunneling ma- trix elements. In
the two-polaron case, these phase factors lead to polaron pair wave functions
of either -wave symmetry or p-wave symme- try with zero and
nonzero total pair momentum, respectively. Implications for the doping
dependent isotope effect, pseudo-gap and Tc of a superconduc- ting polaron pair
condensate are discussed/compared to observed in cuprates.Comment: 23 pages, revtex, 13 ps figure
Screened-interaction expansion for the Hubbard model and determination of the quantum Monte Carlo Fermi surface
We develop a systematic self-consistent perturbative expansion for the self
energy of Hubbard-like models. The interaction lines in the Feynman diagrams
are dynamically screened by the charge fluctuations in the system. Although the
formal expansion is exact-assuming that the model under the study is
perturbative-only if diagrams to all orders are included, it is shown that for
large-on-site-Coulomb-repulsion-U systems weak-coupling expansions to a few
orders may already converge. We show that the screened interaction for the
large-U system can be vanishingly small at a certain intermediate electron
filling; and it is found that our approximation for the imaginary part of the
one-particle self energy agrees well with the QMC results in the low energy
scales at this particular filling. But, the usefulness of the approximation is
hindered by the fact that it has the incorrect filling dependence when the
filling deviates from this value. We also calculate the exact QMC Fermi
surfaces for the two-dimensional (2-D) Hubbard model for several fillings. Our
results near half filling show extreme violation of the concepts of the band
theory; in fact, instead of growing, Fermi surface vanishes when doped toward
the half-filled Mott-Hubbard insulator. Sufficiently away from half filling,
noninteracting-like Fermi surfaces are recovered. These results combined with
the Luttinger theorem might show that diagrammatic expansions for the
nearly-half-filled Hubbard model are unlikely to be possible; however, the
nonperturbative part of the solution seems to be less important as the filling
gradually moves away from one half. Results for the 2-D one-band Hubbard model
for several hole dopings are presented. Implications of this study for the
high-temperature superconductors are also discussed.Comment: 11 pages, 12 eps figures embedded, REVTeX, submitted to Phys. Rev. B;
(v2) minor revisions, scheduled for publication on November 1
Superconducting instability in the Holstein-Hubbard model: A numerical renormalization group study
We have studied the d-wave pairing-instability in the two-dimensional
Holstein-Hubbard model at the level of a full fluctuation exchange
approximation which treats both Coulomb and electron-phonon (EP) interaction
diagrammatically on an equal footing. A generalized numerical renormalization
group technique has been developed to solve the resulting self-consistent field
equations. The -wave superconducting phase diagram shows an optimal T_c at
electron concentration ~ 0.9 for the purely electronic Hubbard system. The
EP interaction suppresses the d-wave T_c which drops to zero when the
phonon-mediated on-site attraction becomes comparable to the on-site
Coulomb repulsion . The isotope exponent is negative in this model
and small compared to the classical BCS value or compared
to typical observed values in non-optimally doped cuprate superconductors.Comment: 4 pages RevTeX + 3 PS figures include
d_{x^2-y^2} Symmetry and the Pairing Mechanism
An important question is if the gap in the high temperature cuprates has
d_{x^2-y^2} symmetry, what does that tell us about the underlying interaction
responsible for pairing. Here we explore this by determining how three
different types of electron-phonon interactions affect the d_{x^2-y^2} pairing
found within an RPA treatment of the 2D Hubbard model. These results imply that
interactions which become more positive as the momentum transfer increases
favor d_{x^2-y^2} pairing in a nearly half-filled band.Comment: 9 pages and 2 eps figs, uses revtex with epsf, in press, PR
An alternative approach for the dynamics of polarons in one dimension
We developed a new method based on functional integration to treat the
dynamics of polarons in one-dimensional systems. We treat the acoustical and
the optical case in an unified manner, showing their differences and
similarities. The mobility and diffusion coefficients are calculated in the
Markovian approximation in the strong coupling limit.Comment: 57 page
Raman Response in Doped Antiferromagnets
The resonant part of the electronic Raman scattering response is
calculated within the model on a planar lattice as a function of
temperature and hole doping, using a finite-temperature diagonalization method
for small systems. Results, directly applicable to experiments on cuprates,
reveal on doping a very pronounced increase of the width of the two-magnon
Raman peak, accompanied by a decrease of the total intensity. At the same time
the peak position does not shift substantially in the underdoped regime.Comment: 11 pages revtex, 3 postscript figures. Minor corrections and changes
from previous version, to be published in Phys. Rev.
- …