The Electron Spectral Function in Two-Dimensional Fractionalized Phases

We study the electron spectral function of various zero-temperature spin-charge separated phases in two dimensions. In these phases, the electron is not a fundamental excitation of the system, but rather ``decays'' into a spin-1/2 chargeless fermion (the spinon) and a spinless charge e boson (the chargon). Using low-energy effective theories for the spinons (d-wave pairing plus possible N\'{e}el order), and the chargons (condensed or quantum disordered bosons), we explore three phases of possible relevance to the cuprate superconductors: 1) AF*, a fractionalized antiferromagnet where the spinons are paired into a state with long-ranged N\'{e}el order and the chargons are 1/2-filled and (Mott) insulating, 2) the nodal liquid, a fractionalized insulator where the spinons are d-wave paired and the chargons are uncondensed, and 3) the d-wave superconductor, where the chargons are condensed and the spinons retain a d-wave gap. Working within the $Z_2$ gauge theory of such fractionalized phases, our results should be valid at scales below the vison gap. However, on a phenomenological level, our results should apply to any spin-charge separated system where the excitations have these low-energy effective forms. Comparison with ARPES data in the undoped, pseudogapped, and superconducting regions is made.