Origin of magnetic resonance spectrum in cuprate high-temperature superconductors and related issues

A distinct low energy magnetic mode has been observed in almost all the cuprate materials in a broad range of experiments including ARPES, Raman, optical, STM, RIXS, as well as neutron scattering. This mode is enhanced in the superconducting (SC) state and its energy scales universally as $\omega_{res} \propto2\Delta$, suggesting that these modes play an important role in the mechanism of superconducting pairing. Here we study this resonance via first-principle susceptibility calculations in a Hubbard model with $d-$wave superconductivity [1]. The resulting excitation mode produces the universal $\omega_{res}\propto 2\Delta$ relation as well as the puzzling `hour-glass' dispersion and the 45$^{\circ}$ rotation of the spin excitations with energy in a series of cuprates in accord with experiments [2]. Work supported by US DOE.\\[4pt] [1] Tanmoy Das, R.S. Markiewicz, and A. Bansil, Phys. Rev. B {\bf 81}, 174504 (2010).\\[0pt] [2] A. Bansil, {\it et al.} Journal of Physics and Chemistry of Solids (2010).