Enhancement of commensurate magnetic resonance energy by the additional second neighbor hopping t′ in cuprate superconductors

Within the t-t′-J model, the effect of the additional second neighbor hopping t′ on the spin response of doped cuprates in the superconducting-state is discussed under the kinetic energy driven superconducting mechanism. It is shown that the additional second neighbor hopping t′ is systematically accompanied with the enhancement of the commensurate magnetic resonance energy, and therefore it plays an important role in quantitatively determining the commensurate magnetic resonance energy. The incommensurate magnetic scattering peaks are found at [(1±δ)π,π] and [π,(1±δ)π] at low energy and [(1±δ′)π,(1±δ′)π] at high energy, with the magnetic excitations at high energy disperse almost linearly with energy, and have energies greater than the superconducting gap energy, and are present at the superconducting transition temperature. These incommensurate magnetic scattering peaks from both low and high energies converge to the commensurate [π,π] magnetic resonance peak at intermediate energy, with the commensurate magnetic resonance energy increases with increasing doping in the underdoped regime, and reaches a maximum in the optimal doping, then decreases in the overdoped regime.