THE PAIRON PROBLEM IN HIGH TEMPERATURE SUPERCONDUCTIVITY

Abstract

The historic discovery of fascinating phenomenon of superconductivity by H. Kamerlingh Onnes promptly creates a striking impression among the Physics community. The two most important turning points of theoretical understanding of superconductivity are (i) phenomenological theory of superconductivity developed by Ginzburg and Landau known as Ginzburg-Landau (GL) theory and (ii) microscopic theory of superconductivity developed by J. Bardeen, L. N. Cooper, and J. R. Schrie er known as BCS theory. Another breakthrough appears as a milestone when G. Bednorz and K. A. M uller discover the high-temperature superconductor (HTS) La2􀀀xSrxCuO4 with transition temperature (Tc) up to 30 K. In the subsequent year the superconductor YBa2Cu3O7􀀀 is discovered with critical temperature Tc = 93 K. Of many models proposed after the discovery of HTS, some of the worth mentioning are: RVB theory of HTS by P. W. Anderson and gauge theory of HTS for strongly correlated Fermi system by P. W. Anderson and G. Baskaran. It is identi ed that in cuprate HTS the charge carriers are holes and located in the same copper-oxide plane and it increases with the increasing number of copper-oxide layers. The role of the exchange of antiferromagnetic spin uctuations in high-temperature superconductivity (HTSC) worked out by Moriya et al. and C. M. Varma. The understanding of several unusual properties of HTS, namely; anisotropy of superconducting gap (SG), the high value of 2 =kBTc (5 to 8), dx2􀀀y2 pairing symmetry, co-existence of superconducting and antiferromagnetic (AF) phases, etc. become i ii a challenge for theorists. None of these unusual properties could be explained by the BCS theory, and this enforced the researchers to think beyond the BCS model. To understand the mechanism of HTSC in cuprate superconductors Fujita et al. used the idea of attractive potential between two electrons from the BCS theory and showed the formation of d-wave Cooper-pair (pairon) in the copper-oxide plane. William et al. recently revealed that the holes in the cuprate superconductor get coupled to its local AF environment and creates the pairons. It is shown that pairon formation in cuprate superconductor is direction dependent due to anisotropic phonon exchange attraction which leads to anisotropic SG formation. Though the mechanism of HTSC is not fully understood, it appears that the understanding of pairons can provide some insight into the strange behaviour of HTS. The electron-phonon interaction emerged as a key factor in the theoretical development of conventional superconductivity as well as HTSC. The e ects of doping (impurity/defect)and that of anharmonicity, also has been noticed to be signi cant in the superconducting phenomenon. In the present work using a generalized (non- BCS) Hamiltonian, the contribution due to electrons, phonons, electron-phonon interactions, anharmonicity, and defects is taken care. The HTS has a very complex structure e.g., La2􀀀xSrxCuO4 and YBa2Cu3O7􀀀 , which have layered structure with the di erent layer of copper-oxide planes that introduced a complex network interactions channels and are precisely taken care of by the modi ed form of Born- Mayer-Huggins potential (MBMHP). The Green's functions method based on many body quantum dynamics of electrons and phonons, has been adopted to investigate the properties of the SG. Using the generalized EDOS of HTS followed by BCS formalism the two SG equations have been obtained which shows dependence on temperature, Fermi energy and renormalized electron, and phonon energies. The e ect of AF spin uctuations on the SG and pairing symmetry also seen. The expressions for pairing potential are iii also obtained by utilizing the SG equations. Using Green's functions technique the renormalized electron-phonon dispersion is obtained from which the behaviour of SG, nodal and antinodal gap with doping are studied. The renormalized electronphonon dispersion further used to analyze the anisotropy of the SG and pairing symmetry as well as a theory of renormalized phonon group velocity for HTS has been formulated using phonon Green's functions.