Dipolon theory of energy gap parameters in high-temperature superconductors at zero temperature - art. no. 054506

Many-body field-theoretic techniques involving dipolon propagator and elect ron Green's function have been used to derive the general expressions at ze ro temperature for the renormalized energy gap parameter Delta((k) over rig ht arrow,omega), the gap renormalization parameter Z((k) over right arrow,o mega), and energy band renormalization parameter chi((k) over right arrow,o mega) for momentum (k) over right arrow and frequency omega. The present th eory takes into account explicitly the dressed dipolons as mediators of sup erconductivity, the screened Coulomb repulsion, and nonrigid electron energ y bands considering retardation and damping effects and electron-hole asymm etry. For superconducting cuprates it has been shown by symmetry considerat ions that, in the lowest order approximations, there exists two energy gap parameters, one being antisymmetric (as) with respect to the exchange of th e k(x) and k(y) components of vector (k) over right arrow and the other bei ng symmetric (s) with respect to the exchange of k(x) and k(y). The antisym metric solution is a d(x2-y2) wave (i.e., proportional to [cos(k(x))-cos(k( y))]) which changes sign with respect to the exchange of k(x) and k(y), and the symmetric solution which is highly asymmetric s wave or equivalently, a combination of a symmetric s wave and absolute value of d(x2-y2) wave (i. e. proportional to \ [cos(k(x))-cos(k(y))] \) which does not change sign wi th respect to the exchange of k(x) and k(y). Our self-consistent calculatio ns of the real and imaginary parts of Delta((k) over right arrow,omega), Z( (k) over right arrow,omega), and chi((k) over right arrow,omega) verify the existence of these two (different) solutions and lead to the conclusion th at the antisymmetric solution of the gap parameter corresponds to the obser ved regular (reg) superconducting energy gap whereas the symmetric solution corresponds to the observed pseudo (pse) energy gap.Calculations have been made for Bi2Sr2CaCu2O8 + delta as well as Bi2Sr2CaCu2O8. Explicitly, for B i2Sr2CaCu2O8 + delta superconductor our calculated values of the antisymmet ric and symmetric energy gap parameters are Delta (as)(0) = 22+/-15 meV and Delta (s)(1) = 30 +/-10 meV with Delta (s)(0) = 1.5+/-1.5 meV, where Delta (as)((k) over right arrow) = Delta (as)(0) [cos(k(x))-cos(k(y))] and Delta (s)((k) over right arrow) = Delta (s)(0) + Delta (s)(1)\ [cos(k(x)) -cos(k (y))] \, in agreement with the corresponding experimental results Delta (re g)(0) = 16.5+/-1.5 meV, Delta (pse)(1) approximate to 24 meV, and Delta (ps e)(0) = -0.5+/-2.5 meV. For Bi2Sr2CaCu2O8 superconductor our calculated val ues of the antisymmetric and the symmetric energy gap parameters are Delta (as)(0) = 24+/-13 meV and Delta (s)(1) = 29+/-15 meV with Delta (s)(0)appro ximate to0 which also agree with the corresponding experimental results Del ta (reg)(0) = 16.5+/-1.5 meV and Delta (pse)(1) = 30 -40 meV with Delta (ps e)(0) = -0.5+/-2.5 meV. Our calculations also indicate that the bosonic energy relevant to supercon ductivity in Bi2Sr2CaCu2O8 + delta superconductor is about 60 meV arising f rom O-1.2 dipolon excitations and that the broad bands observed in optical experiments are due to O-1.1, O-1.2, and O-3 dipolon excitations. Relative contributions from the various dipolon modes have been analyzed. One finds that the symmetric longitudinal modes of oxygen dipolons contribute dominan tly in energy gap parameters. The uncertainties in the calculated values of the various parameters are due to uncertainties in the values of the polar izability particularly of oxygen ions, the shielding parameter, the repulsi ve Coulomb energy, and due to the calcula tional errors. The origin of the experimentally deduced T* values has been discussed in terms of the present theory which reveals that T* is greater than T-c and that they have the sa me physical origin.