Mode-coupling model of Mott gap collapse in the cuprates: Natural phase boundary for quantum critical points

A simple antiferromagnetic approach to the Mott transition was recently shown to provide a satisfactory explanation for the Mott gap collapse with doping observed in photoemission experiments on electron-doped cuprates. Here this approach is extended in a number of ways. Random phase approximation, mode coupling (via self-consistent renormalization), and (to a limited extent) self-consistent Born approximation calculations are compared to assess the roles of hot-spot fluctuations and interaction with spin waves. When fluctuations are included, the calculation satisfies the Mermin-Wagner theorem (Neel transition at T=0 only-unless interlayer coupling effects are included), and the mean-field gap and transition temperature are replaced by pseudogap and onset temperature. The model is in excellent agreement with experiments on the doping dependence of both photoemission dispersion and magnetic properties. The magnetic phase terminates in a quantum critical point (QCP), with a natural phase boundary for this QCP arising from hot-spot physics. Since the resulting T=0 antiferromagnetic transition is controlled by a generalized Stoner factor, an ansatz is made of dividing the Stoner factor up into a material-dependent part, the bare susceptibility and a correlation-dependent part, the Hubbard U, which depends only weakly on doping. From the material-dependent part of the interaction, it is possible to explain the striking differences between electron and hole doping, despite an approximate symmetry in the doping of the QCP. The slower divergence of the magnetic correlation length in hole-doped cuprates may be an indication of more Mott-like physics.