Impurity induced renormalized phonon spectrum of cuprate superconductors

Abstract

The potential problem of anharmonic lattice vibrations in high-temperature superconductors (HTS) using the most suitable Born–Mayer–Huggins (BMH) potential has been taken up to investigate the renormalized phonon density of states (RPDOS). In order to develop the suitable results, the many body theory using quantum dynamical approach of Green’s function (GF) via an almost complete Hamiltonian (without using BCS type Hamiltonian) has been incorporated which includes harmonic electron and phonon Hamiltonian, electron–phonon interaction Hamiltonian, anharmonic and defect Hamiltonian. The derivation of anharmonic phonon GF for modified form of BMH potential enables to evaluate the renormalized and perturbed mode phonon frequencies of solids. The expressions obtained for the RPDOS can be resolved into diagonal and nondiagonal parts of which the nondiagonal part chiefly depends on impurities and disappears in pure crystals. A large number of new features are investigated in the light of this formulation followed by the numerical analysis for the energy spectrum of representative cuprate HTS YBa2Cu3O[Formula: see text]. The inclusion of defects, anharmonicities and electron–phonon interactions in the cuprate superconductors substantially modifies the scenario of RPDOS and reveals a large number of unexplained peaks in the spectrum.

A New Approach to the Potential Energy of Solids

“…Next, we figure out the PDOS corresponding to the peak energy values set side by side the PDOS estimated by A. Gupta et. al [19] and experimental observations as shown in Table 3.…”

“…Also, Q ¼ k þ q (k; q represent phonon and electron wave vectors, respectively), u c q and u c Q are pairon frequencies with pairon distribution functions n c ðqÞ and n c ðQÞ. All the other details of above symbols are available in the references elsewhere [14e16, 18,19] and the reproduction of them is needless. The renormalized, perturbed mode frequencies, as well as the life-times, depend on the various orders of potential functions f II ðrÞ, f III ðrÞ and f IV ðrÞ which evidently reveal the dependence of PDOS on potential energy.…”