A generalization of the random-phase approximation of the theory of Coulomb correlation energy is applied to the theory of superconductivity. With no further approximations it is shown that most of the elementary excitations have the Bardeen-Cooper-Schrieffer energy gap spectrum, but that there are collective excitations also. The most important of these are the longitudinal waves which have a velocity ${v}_{F}{{\frac{1}{3}[1\ensuremath{-}4N(0)|V|]}}^{\frac{1}{2}}$ in the neutral Fermi gas, and are essentially unperturbed plasma oscillations in the charged case. Other collective excitations resembling higher bound pair states may or may not exist but do not seriously affect the energy gap. The theory obeys the sum rules and is gauge invariant to an adequate degree throughout.A generalization of the random-phase approximation of the theory of Coulomb correlation energy is applied to the theory of superconductivity. With no further approximations it is shown that most of the elementary excitations have the Bardeen-Cooper-Schrieffer energy gap spectrum, but that there are collective excitations also. The most important of these are the longitudinal waves which have a velocity ${v}_{F}{{\frac{1}{3}[1\ensuremath{-}4N(0)|V|]}}^{\frac{1}{2}}$ in the neutral Fermi gas, and are essentially unperturbed plasma oscillations in the charged case. Other collective excitations resembling higher bound pair states may or may not exist but do not seriously affect the energy gap. The theory obeys the sum rules and is gauge invariant to an adequate degree throughout.

Physical ReviewDec 15, 19581,380 citations

Collective Excitations in the Extended Hubbard Model with Intrasite Attraction

T. Kostyrko

Abstract Collective excitations in the superconducting state of an extended Hubbard model with an intrasite attraction are investigated using the random phase approximation method. The results for the energy of gapless excitations are consistent with the well known result of Anderson in the limit of weak attraction and the result of the perturbation theory (with respect to the band term) in the limit of strong attraction. Investigating the dependence of the excitation energy on the density of electrons in the band conditions are found of instability of the singlet superconducting state with respect to the disordered state (for attractive intersite interactions) and to the charge ordered superconducting state (for intersite repulsion).Abstract Collective excitations in the superconducting state of an extended Hubbard model with an intrasite attraction are investigated using the random phase approximation method. The results for the energy of gapless excitations are consistent with the well known result of Anderson in the limit of weak attraction and the result of the perturbation theory (with respect to the band term) in the limit of strong attraction. Investigating the dependence of the excitation energy on the density of electrons in the band conditions are found of instability of the singlet superconducting state with respect to the disordered state (for attractive intersite interactions) and to the charge ordered superconducting state (for intersite repulsion).

physica status solidi (b)Sep 1, 198711 citations

Doping induced spinless collective excitations of charge 2e in doped Mott insulators

W. Vincent Liu

Based on the Hubbard model description of the doped Mott insulator, we prove that there must exist a spinless collective excitation of charge $2e$ and of energy $U-2μ$ peaked at momentum $(π/a,π/a)$ in the non-superconducting state due to doping. Such a collective excitation arises from the electron pair correlation. Its existence is related to the breakdown of an approximate SU(2) particle-hole symmetry, from which an effective field theory of the new excitations is constructed.Based on the Hubbard model description of the doped Mott insulator, we prove that there must exist a spinless collective excitation of charge $2e$ and of energy $U-2μ$ peaked at momentum $(π/a,π/a)$ in the non-superconducting state due to doping. Such a collective excitation arises from the electron pair correlation. Its existence is related to the breakdown of an approximate SU(2) particle-hole symmetry, from which an effective field theory of the new excitations is constructed.

arXiv:cond-mat/0010470Oct 29, 20000 citations

Based on the Hubbard model description of the doped Mott insulator, we prove that there must exist a spinless collective excitation of charge

2e

and of energy

U-2μ

peaked at momentum

(π/a,π/a)

in the non-superconducting state due to doping. Such a collective excitation arises from the electron pair correlation. Its existence is related to the breakdown of an approximate SU(2) particle-hole symmetry, from which an effective field theory of the new excitations is constructed.