High temperature superconductivity: The mystery we are ever after

Superconductivity was an unanticipated property of matter. Perhaps no history of a scientific subject is as impressive as the history of superconductivity. Over the past nine decades the history remains exciting, where some of our best minds were and are engaged on understanding how this remarkable property is manifested in some materials under certain conditions. In 1986 Alex Müller and Georg Bednorz from IBM, Zurich reported Ba-doped lanthanum cuprate is a superconductor with an onset temperature of 35K. Since then an unprecedented race continues. High T_c superconductors are difficult to understand because they involve a number of electronic and structural phase transitions between anti-ferromagnetic insulators, highly correlated metals, superconductors and normal metals. The general consensus is that the parent materials are Mott insulators, where strong electronic Coulomb repulsion suppresses charge fluctuations on the Cu sites. Upon doping the holes/electrons become mobile and exhibit various mysterious phases. At present the key issue remains to be resolved - how do we understand a variety of anomalies in the normal state, particularly in the underdoped part of the density-temperature (n∼T) phase diagram? What do these anomalies indicate towards the microscopic mechanism of superconducting pairing?