An important paper for understanding the pseudogap state of the cuprates is Diamagnetism and Cooper pairing above Tc in cuprates by Lu Li, Yayu Wang, Seiki Komiya, Shimpei Ono, Yoichi Ando, G. D. Gu, and N. P. Ong.
Physics has a helpful commentary by Kivelson and Fradkin.
Diamagnetic response of the superconducting state is orders of magnitude larger than other states of matter. [Due to the Meissner effect superconductors are sometimes said to be perfect diamagnets]. A state with no long range superconducting order but large fluctuations can produce a significant diamagnetic response. The authors find that for a wide range of underdoped cuprates that there is significant diamagnetism for a wide temperature regime above Tc. Moreover, this signal co-exists with a large Nernst signal.
This is important because it tends to rule out a proposed alternative explanation for the large Nernst signal that it could be produced by quasi-particles in small hole pockets associated with a density wave state.
A key signature of superconducting fluctuations is a non-linear dependence of the magnetisation on the magnitude of the magnetic field. For small fields it must be linear in field, but there must be some field scale, of the order of the upper critical mean-field H_c2 above which there is no diamagnetic response. This means there is some field scale H_min at which the magnetisation is a minimum. The non-linearity of the field dependence is seen in the Figure below. (The different curves correspond to different temperatures).
PRB). The authors argue that if it is due to quasi-particles it should be linear in field up to a much higher field scale, e.g. comparable to the band width.
Aside: Are there any measurements of non-linear diamagnetism on organic charge transfer salts?