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Pseudogap state in superconductors

Pratap Raychaudhuri

4 July 2011

The ability of certain materials to conduct electricity without any resistance was discovered a hundred years ago when Kammerlingh Onnes found that the resistance of solid mercury dropped to zero below 4.2K, its so called transition temperature (Tc). Studies based on this spectacular phenomenon, coined as "superconductivity" , are now a century old, but they continue to thrive both from the point of view of newer applications as well as that of throwing up challenges on the fundamental physics governing the collective behavior of electrons in solids.

All superconductors discovered in the first seven decades after Kammerleigh Onnes discovery had low transition temperatures (highest one being Nb3Ge with Tc~23K), well below the liquefaction temperature of nitrogen (77K). The physics behind these conventional superconductors has been well understood over the past 50 odd years based on Bardeen-Cooper-Schrieffer (BCS) theory. In these materials, an indirect attractive force mediated by vibrations of the crystalline lattice (phonons) bind pairs of electrons with opposing spin into what is called Cooper pairs . Once formed, Cooper pairs collapse into a phase-coherent state that can carry current without any resistance. The binding energy of the Cooper pairs is observed as a gap in the density of states at the Fermi energy called the superconducting energy gap. BCS theory successfully predicts the relationship between transition temperature, superconducting energy gap and the change in transition temperature when an element is substituted by a different isotope of the same element.

While the 'holy grail' of superconductivity, namely a material that superconducts at or close to room temperature has not been discovered yet, a major breakthrough happened in 1986 with the discovery of a new class of ceramic materials, all of them containing Copper and Oxygen. Known as High-Temperature superconducting cuprates , several members in this class of materials become superconducting at temperatures well above that of liquid nitrogen (YBa2Cu3O7, Tc~90K; Bi2Sr2CaCu2O8, Tc~85K and HgBa2Ca2Cu3O8 with the highest Tc of 135K), making them useful for diverse applications such as superconducting magnets and levitated trains. However, as far as fundamental physics is concerned, these materials also pose one of the greatest unsolved mysteries in condensed matter physics today.

High-temperature cuprate superconductors are completely different from their conventional counterparts. The normal state does not follow the " Fermi liquid theory " as expected in a normal metal. Unlike conventional superconductors, the wave-function describing the Copper pair is highly anisotropic and changes sign when rotated by 90 degree. But the most intriguing feature is the observation of a "pseudogap" state above the transition temperature where the zero resistance is destroyed, but a gap in the electronic density of state, commonly associated with the existence of Cooper pairs, continues to persist up to a much higher temperature. Arguably the hottest debate in this field relates to the nature of the pseudogap, i.e. whether it is persistent superconductivity or whether it arises from some competing magnetic order. A number of recent experiments on these and other related materials have tried to resolve this issue, but the debate continues.

Now experiments performed in TIFR on superconducting NbN thin films, show that the "pseudogap" state can also appear in conventional superconductors when the superconductor is made "dirty" enough, by introducing disorder in the form of structural defects in the crystalline lattice. Clean NbN is a conventional superconductor whose properties are well described by the BCS theory. However, the situation becomes different in the dirty-limit when the electronic mean free path approaches the de-Broglie wavelength of the electron. Experiments such as scanning tunneling spectroscopy performed at low temperature using a scanning tunneling microscope reveal that the gap in the electronic density of states extends up to a temperature, T*, which is well above Tc. The origin of this pseudogap state in NbN can be traced back to phase fluctuations, which are directly observed in the complimentary measurement of magnetic penetration depth . In the pseudogap state between Tc and T* (Fig. 1), the electrons bind into Cooper pairs. However, these Cooper pairs do not condense into a phase-coherent state, due to thermal phase-fluctuations between nanometer-sized domains that spontaneously form in the presence of strong disorder. It is interesting to note that a novel phenomenon once thought to be uniquely associated to the physics of High Temperature superconducting cuprates has ended up enriching our understanding of conventional superconductors.

To what extent the same mechanism is also responsible for the pseudogap state in High Temperature superconducting cuprates is currently still open to debate. Further experiments on the role of the underlying magnetic order and the role of disorder that is inevitably present in these doped materials, are needed to conclusively end this debate in cuprates. However, as newer materials are discovered, the older ones are understood deeper, clearing some mysteries while new mysteries continue to unfold throwing up newer challenges for days to come!

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