Anyon bosonization of 2D fermions and single boson phase diagram implied from experiment on visualizing pair formation in superconductor Bi2Sr2CaCu2O8+δ

• Published in: Physica. C, Superconductivity Superconductivity, 2011-08, Vol.471 (15-16), p.486-491
• Main Authors: Abdullaev, B., Park, C.-H., Musakhanov, M.M.
• Format: Article
• Language: English
• Subjects: Anyon; Charge of hole; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Cuprate; Exact sciences and technology; Phase diagram; Phase diagrams; Physics; Properties of type I and type II superconductors; Single boson; Superconductivity; Uemura relation
• ISSN: 0921-4534; 1873-2143
• DOI: 10.1016/j.physc.2011.04.001

► STM experiment shows minimal size nanoscale regions with energy gaps in cuprate B2212. ► In the present paper one performs charge and percolation analysis of these regions. ► It shows that a charge equals unity at first critical doping and two at second one. ► It demonstrates also the appearance of a percolation in the first critical doping. ► Existence of single hole bosons is rigorously proved and it is explained a Uemura scale. Recently, Gomes et al. [1] have visualized the gap formation in nanoscale regions (NRs) above the critical temperature Tc in the high-Tc superconductor Bi2Sr2CaCu2O8+δ. It has been found that, as the temperature lowers, the NRs expand in the bulk superconducting state consisted of inhomogeneities. The fact that the size of the inhomogeneity [2] is close to the minimal size of the NR [1] leads to a conclusion that the superconducting phase is a result of these overlapped NRs. In the present paper we perform the charge and percolation regime analysis of NRs and show that at the first critical doping xc1, when the superconductivity starts on, each NR carries the positive electric charge one in units of electron charge, thus we attribute the NR to a single hole boson, and the percolation lines connecting these bosons emerge. At the second critical doping xc2, when the superconductivity disappears, our analysis demonstrates that the charge of each NR equals two. The origin of xc2 can be understood by introducing additional normal phase hole fermions in NRs, whose concentration appearing above xc1 increases smoothly with the doping and breaks the percolation lines of bosons at xc2. The last one results in disappearing the bulk bosonic property of the pseudogap (PG) region, which explains the upper bound for existence of vortices in Nernst effect [3]. Since Gomes et al. [1] has demonstrated the absence of NRs at the PG boundary one can conclude that along this boundary, as well as in xc2, all bosons disappear. As justification of appearance of single bosons, the bosonization of 2D fermions is rigorously proven using the concept of anyons. The linear density dependence of the energy gap between excited fermionic and bosonic ground states describes the Uemura relation for 2D superconductors.