142 research outputs found
Double fluctuations on the attractive Hubbard model: ladder approximation
We explore, for the first time, the effect of double fluctuations on both the
diagonal and off-diagonal self-energy. We use the T-Matrix equations below
, developed recently by the Z\"urich group (M.H. Pedersen et al) for the
local pair attraction Hamiltonian. Here, we include as well the effect of
fluctuations on the order parameter (beyond the BCS solution) up to second
order in . This is equivalent to approximating the effective interaction
by in the off-diagonal self-energy. For , , and , we find four peaks both for the diagonal,
, and off-diagonal, ,
spectral functions. These peaks are not symmetric in pairs as previously found.
In addition: (a) in , the far left peak has a
vanishing small weight; (b) in the far left and
far right peaks have very small weights. The physical picture is, then, that
the pair physics in the normal phase () is still valid below .
However, the condensation of the e-h pairs produces an additional gap around
the chemical potential as in BCS, in other words, superconductivity opens a gap
in the lower branch of a Hubbard-type-I solution.Comment: LaTeX, 7 pages. 8 figures available on request. To appear in Z.
Physik
Self-consistent calculation of particle-hole diagrams on the Matsubara frequency: FLEX approximation
We implement the numerical method of summing Green function diagrams on the
Matsubara frequency axis for the fluctuation exchange (FLEX) approximation. Our
method has previously been applied to the attractive Hubbard model for low
density. Here we apply our numerical algorithm to the Hubbard model close to
half filling (), and for , in order to study the
dynamics of one- and two-particle Green functions. For the values of the chosen
parameters we see the formation of three branches which we associate with the a
two-peak structure in the imaginary part of the self-energy. From the imaginary
part of the self-energy we conclude that our system is a Fermi liquid (for the
temperature investigated here), since Im
around the chemical potential. We have compared our fully self-consistent FLEX
solutions with a lower order approximation where the internal Green functions
are approximated by free Green functions. These two approches, i.e., the fully
selfconsistent and the non-selfconsistent ones give different results for the
parameters considered here. However, they have similar global results for small
densities.Comment: seven pages, nine figures as ps files. Accepted in Int. J. Modern
Phys. C (1997
Diquark Bose-Einstein condensation
Bose-Einstein condensation (BEC) of composite diquarks in quark matter (the
color superconductor phase) is discussed using the quasi-chemical equilibrium
theory at a relatively low density region near the deconfinement phase
transition, where dynamical quark-pair fluctuations are assumed to be described
as bosonic degrees of freedom (diquarks). A general formulation is given for
the diquark formation and particle-antiparticle pair-creation processes in the
relativistic flamework, and some interesting properties are shown, which are
characteristic for the relativistic many-body system. Behaviors of transition
temperature and phase diagram of the quark-diquark matter are generally
presented in model parameter space, and their asymptotic behaviors are also
discussed. As an application to the color superconductivity, the transition
temperatures and the quark and diquark density profiles are calculated in case
with constituent/current quarks, where the diquark is in bound/resonant state.
We obtained MeV for constituent quarks and MeV
for current quarks at a moderate density (). The method
is also developed to include interdiquark interactions into the quasi-chemical
equilibrium theory within a mean-field approximation, and it is found that a
possible repulsive diquark-diquark interaction lowers the transition
temperature by nearly 50%.Comment: 21 pages, 23 figure
Optimal interlayer hopping and high temperature BoseâEinstein condensation of local pairs in quasi 2D superconductors
Both FeSe and cuprate superconductors are quasi 2D materials with high transition temperatures and local fermion pairs. Motivated by such systems, we investigate real space pairing of fermions in an anisotropic lattice model with intersite attraction, V, and strong local Coulomb repulsion, U, leading to a determination of the optimal conditions for superconductivity from BoseâEinstein condensation. Our aim is to gain insight as to why high temperature superconductors tend to be quasi 2D. We make both analytically and numerically exact solutions for two body local pairing applicable to intermediate and strong V. We find that the BoseâEinstein condensation temperature of such local pairs pairs is maximal when hopping between layers is intermediate relative to in-plane hopping, indicating that the quasi 2D nature of unconventional superconductors has an important contribution to their high transition temperatures
Metal-Insulator Transition in the Two-Dimensional Hubbard Model at Half-Filling with Lifetime Effects within the Moment Approach
We explore the effect of the imaginary part of the self-energy,
, having a single pole, ,
with spectral weight, , and quasi-particle lifetime,
, on the density of states. We solve the set of parameters,
), , and by means of
the moment approach (exact sum rules) of Nolting. Our choice for
, satisfies the Kramers - Kronig relationship automatically.
Due to our choice of the self - energy, the system is not a Fermi liquid for
any value of the interaction, a result which is also true in the moment
approach of Nolting without lifetime effects. By increasing the value of the
local interaction, , at half-filling (), we go from a
paramagnetic metal to a paramagnetic insulator, (Mott metal - insulator
transition ()) for values of of the order of ( is
the band width) which is in agreement with numerical results for finite
lattices and for infinity dimensions (). These results settle down
the main weakness of the spherical approximation of Nolting: a finite gap for
any finite value of the interaction, i.e., an insulator for any finite value of
. Lifetime effects are absolutely indispensable. Our scheme works better
than the one of improving the narrowing band factor, , beyond the
spherical approximation of Nolting.Comment: 5 pages and 5 ps figures (included
Phenomenological theory of cuprate superconductivity
Reasonably good agreement with the superconducting transitiontemperatures of the cuprate highâT c superconductors can be obtained on the basis of an approximate phenomenological theory. In this theory, two criteria are used to calculate the superconducting transitiontemperature. One is that the quantum wavelength is of the order of the electronâpair spacing. The other is that a fraction of the normal carriers exist as Cooper pairs at T c . The resulting simple equation for T c contains only two parameters: the normal carrier density and effective mass. We calculate specific transition temperatures for 12 cuprate superconductors
Superconducting properties of the attractive Hubbard model
A self-consistent set of equations for the one-electron self-energy in the
ladder approximation is derived for the attractive Hubbard model in the
superconducting state. The equations provide an extension of a T-matrix
formalism recently used to study the effect of electron correlations on
normal-state properties. An approximation to the set of equations is solved
numerically in the intermediate coupling regime, and the one-particle spectral
functions are found to have four peaks. This feature is traced back to a peak
in the self-energy, which is related to the formation of real-space bound
states. For comparison we extend the moment approach to the superconducting
state and discuss the crossover from the weak (BCS) to the intermediate
coupling regime from the perspective of single-particle spectral densities.Comment: RevTeX format, 8 figures. Accepted for publication in Z.Phys.
Theory of a Higher Order Phase Transition: Superconducting Transition in BKBO
We describe here the properties expected of a higher (with emphasis on the
order fourth) order phase transition. The order is identified in the sense
first noted by Ehrenfest, namely in terms of the temperature dependence of the
ordered state free energy near the phase boundary. We have derived an equation
for the phase boundary in terms of the discontinuities in thermodynamic
observables, developed a Ginzburg-Landau free energy and studied the
thermodynamic and magnetic properties. We also discuss the current status of
experiments on and other based superconductors,
the expectations for parameters and examine alternative explanations of the
experimental results.Comment: 18 pages, no figure
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