Anyon Bosonization of 2D Fermions and Single Boson Phase Diagram Implied from Experiment on Visualizing Pair Formation in Superconductor Bi_2Sr_2CaCu_2O_{8+\delta}

摘要

Recently, Gomes et al. [1] have visualized the gap formation in nanoscaleregions (NRs) above the critical temperature T_c in the high-T_c superconductorBi_2Sr_2CaCu_2O_{8+\delta}. 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 ofthe NR [1] leads to a conclusion that the superconducting phase is a result ofthese overlapped NRs. In the present paper we perform the charge andpercolation regime analysis of NRs and show that at the first critical dopingx_{c1}, when the superconductivity starts on, each NR carries the positiveelectric charge one in units of electron charge, thus we attribute the NR to asingle hole boson, and the percolation lines connecting these bosons emerge. Atthe second critical doping x_{c2}, when the superconductivity disappears, ouranalysis demonstrates that the charge of each NR equals two. The origin ofx_{c2} can be understood by introducing additional normal phase hole fermionsin NRs, whose concentration appearing above x_{c1} increases smoothly with thedoping and breaks the percolation lines of bosons at x_{c2}. The last oneresults 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 [1] has demonstrated the absence of NRs at the PG boundary one canconclude that along this boundary, as well as in x_{c2}, all bosons disappear.As justification of appearance of single bosons, the bosonization of 2Dfermions is rigorously proven using the concept of anyons. The linear densitydependence of the energy gap between excited fermionic and bosonic groundstates describes the Uemura relation for 2D superconductors.