Evgeniĭ Ivanovich Zababakhin (Obituary)

Pairing of bosons in the condensed state of the boson-fermion model

“…Soon after Anderson [17] and Street and Mott [22] introduced localized pairs in amorphous semiconductors, a two component model of negative U centers coupled with the Fermi sea of itinerant fermions was employed to study superconductivity in disordered metalsemiconductor alloys [23,24]. When the attractive potential U is large, the model is reduced to localized hardcore bosons spontaneously decaying into itinerant electrons and vice versa, different from a non-converting mixture of mobile charged bosons and fermions [25,26]. This boson-fermion model (BFM) was applied more generally to describe pairing electron processes with localizationdelocalization [27], and a linear resistivity in the normal state of cuprates [28].…”

Converting boson–fermion mixtures

“…The model attracted more attention in connection with exotic [5], and high-temperature superconductors [6,7,8,9,10,11,12,13,14,15,16,17,18]. When the attractive potential U is large, the model is reduced to localised bosons spontaneously decaying into itinerant electrons and vice versa, different from a non-converting mixture of mobile charged bosons and fermions [19,20]. More recently this boson-fermion model has been adopted for a description of superfluidity of atomic fermions scattered into bound (molecular) states [21].…”

“…It means that the phase transition is never a BCS-like second-order phase transition even at large E 0 and small g. In fact, the transition is driven by the Bose-Einstein condensation of real bosons with q = 0, which occur due to the complete softening of their spectrum at T c in 3D BFM. Remarkably, the conventional upper critical field, determined as the field, where a non-trivial solution of the linearised Gor'kov equation (19) occurs, is zero in BFM, H c2 (T ) = 0. It is not a finite H c2 (T ) found in Ref.…”