Precursor effects of the superconducting state caused by d-wave   phase-fluctuations above Tc
  One of the hallmarks of high-temperature superconductors is a pseudogap regime appearing in the underdoped cuprates above the superconducting transition temperature Tc. The pseudogap continously develops out of the superconducting gap. In addition, high-frequency conductivity experiments show a superconducting scaling of the optical response in the pseudogap regime, pointing towards a superconducting origin of the pseudogap. The phase-fluctuation vortex scenario is further supported by the measurement of an unusually large Nernst signal above Tc and the recently observed field-enhanced diamagnetism which scales with the Nernst signal. In this paper, we use a simple phenomenological model to calculate the paraconductivity and magnetic response caused by phase fluctuations of the superconducting order parameter above Tc. Our results are in agreement with experiments such as the superconducting scaling of the optical response and the spin (or Pauli) susceptibility, and further strengthen the idea of a phase-fluctuation origin of the pseudogap. 
Thomas Eckl and Werner Hanke