Spin-charge separation and its relevance to the high-temperature superconductors

A phenomenological model of spin-charge separated phases is explored with emphasis on applications to the quasi-two-dimensional cuprate superconductors. 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 these degrees of freedom; the electron spectral function is calculated in three phases: (1) AF*, a fractionalized antiferromagnet where the spinons are paired into a state with long-ranged Néel 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. Comparison with angle-resolved photoeinission spectroscopy data in the undoped, pseudogapped, and superconducting regions is made. The contribution of deconfined spinons to inelastic neutron scattering (INS) in AF* is also calculated. It is found that the presence of free spin-1/2 chargeless excitations leads to a continuum INS signal above the Néel gap. This signal is found above and in addition to the usual spin-1 magnon signal, which to lowest order is the same as in the more conventional confined antiferromagnet. Working within the Z₂ gauge theory of fractionalized phases, our results should be valid at scales below the energy gap of the vison—the basic vortex excitfitiorn in the theory. However, on a phenomenological level, our results should apply to any spin-charge separated system where the excitations have these low-energy effective forms. Finally, a zero-temperature phase transition between a d-wave superconductor and a Mott insulator in two dimensions is studied. In this quantum transition; spinon and chargon are confined to form the electron in the Mott insulator. Within a dual formulation, direct transitions from d-wave superconductors at half-filling to insulators with spin-Peierls (as well as other) order emerge naturally. The transition is described by nodal fermions and bosonic vortices; interacting via a long-ranged statistical interaction modeled by two, coupled Chern-Simons gauge fields, and the critical properties of this model are discussed.