Dispersion anomalies in cuprate superconductors

We argue that the shape of the dispersion along the nodal and antinodal directions in the cuprates can be understood as a consequence of the interaction of the electrons with collective spin excitations. In the normal state, the dispersion displays a crossover at an energy where the decay into spin fluctuations becomes relevant. In the superconducting state, the antinodal dispersion is strongly affected by the (π,π) spin resonance and displays an S shape whose magnitude scales with the resonance intensity. For nodal fermions, relevant spin excitations do not have resonance behavior, rather they are better characterized as a gapped continuum. As a consequence, the S shape becomes a kink, and superconductivity does not affect the dispersion as strongly. Finally, we note that optical phonons typically lead to a temperature-independent S shape, in disagreement with the observed dispersion.