Nodal quasiparticle dispersion in strongly correlated d-wave superconductors

We analyze the effects of a $\mathbf{k}$-dependent self-energy on the photoemission momentum distribution curve (MDC) line shape and dispersion and, in particular, show that this modifies the “high-energy” dispersion $v_F^{\mathrm{high}}$ of the MDC’s in an essential way. These general results are illustrated by a detailed examination of nodal quasiparticles in the superconducting state of the high-$T_c$ cuprates. Using variational results for the nodal quasiparticle weight Z, which vanishes with the hole doping x, and the low energy dispersion $v_F^{\mathrm{low}},$ which is independent of x, we show that the “high-energy” dispersion $v_F^{\mathrm{high}}{=v}_F^{\mathrm{low}}/Z$ is much larger than the band structure value and exhibits a striking doping dependence in good agreement with recent data. These results provide strong evidence for an electronic origin of all the nodal dispersion anomalies, including the much-studied kink.