Quasiparticle and Spin Excitation Spectra in the Normal and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-Wave Superconducting State of the Two-Dimensional Hubbard Model

Abstract

The quasiparticle and spin excitation spectra in the 2D Hubbard model are calculated self-consistently as functions of momentum on the real frequency axis. Near half filling we obtain in the normal state a pseudogap in the density of states. The pairing state has ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ symmetry. Below ${T}_{c}$, gaps open rapidly in the frequency spectra of the gap function, the quasiparticle scattering rate, and the density of states. The scattering rate and spin-lattice relaxation rate drop abruptly below ${T}_{c}$. Our results are consistent with experiments on ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Cu}{\mathrm{O}}_{4}$.