Electron Number Density and Coherence Length of Boson-Fermion Pair in HTSC

Abstract

A Bose-Einstein Condensate (BEC) of a nonzero momentum Cooper pair constitutes a composite boson or simply a boson. Previously, it has been shown that the quantum coherence of the two-component BEC (boson and fermion condensates) is controlled by plasmons where $<1\%$ of plasmon energy mediates the charge pairing but most of the plasmon energy is used to overcome the modes that compete against superconductivity such as phonons, charge density waves, antiferromagnetism, and damping effects. The dependence of plasmon frequency on the material of a superconductor reveals that modes within a specific range of frequency enhance superconductivity and therefore affect the critical temperature of a particular superconducting material. Against this background, we study the effect on doping on boson-fermion pairing energy and hence the critical temperature. While most hole doping agents are atoms lighter than copper, many of the electron doping agents are materials heavier than copper. This property defines the doping effect on the plasma frequency. Heavier dopants lower the critical temperature while lighter dopants increase the critical temperature of a superconductor. The number density of electrons is also found to be proportional to the square of critical temperature $\left(T_c\right)$ while the size of a boson-fermion pair condensate (BFPC) is proportional to $T_c^{-2/3}$ . The size of a BFPC particle is less than boson-fermion (BF) coherence length by almost an order.