Bi_2Sr_2CaCu_2 O_{8+δ}超导体中电子对形成实验所揭示的二维费米子的任意子玻色子化和单玻色子Phase Diagram
Anyon Bosonization of 2D Fermions and Single Boson Phase Diagram Implied from Experiment on Visualizing Pair Formation in Superconductor Bi_2Sr_2CaCu_2O_{8+δ}
摘要：
最近，Gomes等人[1]在高T_c超导体Bi_2Sr_2CaCu_2 O_{8+δ}中观察到了临界温度T_c以上纳米尺度区域（NR）的能隙形成。已经发现，随着温度的降低，NR在由不均匀性组成的体超导状态下膨胀。不均匀性[2]的尺寸接近NR [1]的最小尺寸的事实导致超导相是这些重叠NR的结果的结论。本文对NR的电荷和渗流态进行了分析，结果表明，在第一临界掺杂x_{c1}时，当超导开始时，每个NR都带有正的电荷（单位为电子电荷），因此我们将NR归结为一个空穴玻色子，并出现了连接这些玻色子的渗流线。在第二临界掺杂x_{c2}，当超导性消失时，我们的分析表明，每个NR的电荷等于2。x_{c2}的起源可以通过在NR中引入额外的正常相空穴费米子来理解，其出现在x_{c1}上方的浓度随着掺杂而平滑地增加，并且破坏了x_{c2}处玻色子的渗透线。最后一个导致赝隙（PG）区域的体玻色子性质消失，这解释了能斯特效应中涡旋存在的上限[3]。由于[1]已经证明了在PG边界处没有NR，我们可以得出结论，沿着这个边界，以及在x_{c2}中，所有的玻色子都消失了。作为单玻色子出现的合理性证明，利用任意子的概念严格证明了二维费米子的玻色子化。激发态费米子和玻色子基态之间的能隙的线性密度依赖性描述了二维超导体的Uemura关系。
英文摘要：
Recently, 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_2Sr_2CaCu_2O_{8+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 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 [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.
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