Mechanism of pseudogap probed by a local impurity

The response to a local strong nonmagnetic impurity in the pseudogap phase is examined in two distinctly different scenarios: phase fluctuation (PF) of pairing field and d-density-wave (DDW) order. In the PF scenario, the resonance state is generally double peaked near the Fermi level, and is abruptly broadened by vortex fluctuations slightly above the transition temperature. In the DDW scenario, the resonance is single peaked and remains sharp up to gradual intrinsic thermal broadening, and the resonance energy is analytically determined to be at minus of the chemical potential.