BCS-to-BEC evolution details

Again an article in Physics Today, (by Carlos Sá de melo October 2008, page 45 ), has incorrectly implied that Anthony Leggett was the first person to study the crossover from Bardeen-Cooper-Schrieffer to Bose–Einstein condensation. On page 47 of the article, it states that “a clear picture of the BCS-to-BEC evolution at zero temperature didn’t emerge until 1980, when Anthony Leggett realized that the physics could be captured by a simple description in real space of paired fermions with opposite spins.” Although the model I considered in my 1969 paper ¹ is slightly different from Leggett’s, figure 4 in my paper clearly shows regions where pairing without superconductivity occurs and where superconductivity is limited by the Bose- condensation temperature of pairs, and on page 458 I discuss a limit at which the diameter of pairs is small compared with the distance between them.

I also disagree with a statement in the box on page 47 of Sá de Melo’s article that “the evolution from a Bardeen-Cooper-Schrieffer superfluid to a Bose–Einstein condensation superfluid cannot be studied in … superconductors.” At least in ceramic samples of SrTiO₃ with 3% of the titanium replaced by zirconium, the transition has been studied by varying the carrier concentration via differing heat treatments to produce different concentrations of oxygen vacancies. ² It is possible that such a transition may be found in other superconducting semiconductors when people start to search for suitable materials. However, in three dimensions the pairing strength has to be above some threshold value to obtain the possibility of reaching the Bose-gas regime. Also, many authors think that the BEC regime occurs in underdoped cuprates, ^3,4 while the consensus is that overdoped samples are BCS-like.