Thermally generated vortices, gauge invariance, and electron spectral function in the pseudogap regime

Starting from the classical vortex fluctuation picture, we study the single electron properties in the pseudogap regime. We show that it is the gauge invariant Green function of spinon which is directly related to ARPES data in the pseudogap regime instead of the nongauge invariant one. We find that the random gauge field from the thermally generated vortices destroys the coherent spinon motion. The energy distribution curves show broad peaks, while the momentum distribution curves show sharp peaks with Lorenz form. The local density of state at zero energy scales as the inverse of Kosterlitz-Thouless length. These results are qualitatively consistent with the ARPES data in the pseudogap regime.