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

Abstract

a b s t r a c tRecently, Gomes et al. [1] have visualized the gap formation in nanoscale regions (NRs) above the critical temperature T c in the high-T c superconductor Bi 2 Sr 2 CaCu 2 O 8+d . 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 x c1 , 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 x c2 , when the superconductivity disappears, our analysis demonstrates that the charge of each NR equals two. The origin of x c2 can be understood by introducing additional normal phase hole fermions in NRs, whose concentration appearing above x c1 increases smoothly with the doping and breaks the percolation lines of bosons at x c2 . 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 x c2 , 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.

Normal state pair nematicity and hidden magnetic order and metal-insulator (fermionboson) crossover origin of pseudogap phase of cuprates II

“…While their evolution with doping (see Refs. [28][29][30]) qualitatively coincides with that of the NRs, described in [3]. However, minimal size NRs are single bosons, therefore, the IUC hidden magnetic order objects are also single bosons and PG and HTS pairs.…”

“…The theoretical calculation, shown in the Ref. [3], has further justified the possible existence of single bosons in two-dimensional systems as a − b planes of cuprates. The QPs, PG and HTS pairs-single bosons, have become the fundamental particles in our semi-phenomenological Coulomb single boson and single fermion two liquid model, which positions are formulated in the following list [7].…”

“…The minimal size for square form nanoregions (NRs) (or of pseudogap (PG) and high T c superconductivity (HTS) pairs), recently measured in the scanning tunneling microscopy (STM) experiments of Gomes et al [1] and Pan et al [2] for visualization of the energy gap formation in the cuprate Bi 2 Sr 2 CaCu 2 O 8+δ , has varied between nearly 4.5 a and 2.6 a of the a − b plane crystal spacing constant a, when doping varies between two critical values in the doping-temperature phase diagram. Electric charge analysis of these NRs, made by Abdullaev et al [3], reveals that at the first critical doping we have one boson inside of each NR, while at the second critical doping, one boson and one fermion. The wide spatial spreading of particle-charge in the underdoped region indicates that the role of the dielectric parent compound of cuprates is unimportant, which leads to universality of the properties of all underdoped copper-oxides with the same a.…”

“…With an increase of doping in the interval between two critical levels and close to the optimal one, the spatial sizes of NRs decrease and single bosons transform into single fermions [3].…”

“…The seminal STM experiments of Gomes et al [1] and Pan et al [2] on the visualization of the real space PG and HTS NRs, which exhibited an energy gap, together with their electric charge and percolation analysis, made by Abdullaev et al [3], have deeply extended our understanding of the HTS cuprate physics. The theoretical calculation, shown in the Ref.…”