Concentration of Charge Carriers and Anomalous Gap Parameter in the Normal State of High-$T_c$ Superconductors

TL;DR

This paper introduces a model using Fermi-Dirac statistics with an added ionization energy gap to analyze charge carrier concentration and resistivity in high-$T_c$ superconductors, revealing gapless charge dynamics and anomalous Fermi liquid behavior.

Contribution

It presents a novel approach incorporating ionization energy as an anomalous gap to derive charge carrier concentration and resistivity in high-$T_c$ superconductors.

Findings

Charge carrier concentration ranges from 10$^{16}$ m$^{-2}$ to 9 meV ionization energy.

Resistivity model aligns with gapless charge dynamics and nested Fermi liquid theory.

Charge carriers exhibit anomalous Fermi liquid behavior.

Abstract

Fermi-Dirac statistics has been utilized by introducing the average ionization energy ($E_I$) as an additional anomalous energy gap in order to derive the two-dimensional concentration of charge carriers and the phenomenological resistivity model for the superconducting polycrystalline materials. The best fitted values of $E_I$ and the charge carriers' concentration ranges in the vicinity of 4 to 9 meV and 10$^{16}$ m$^{-2}$ respectively for the superconducting single crystal samples and polycrystalline compounds synthesized with various compositions via solid-state reactions. The phenomenological resistivity model is further redefined here based on the gapless nature of charge-carriers' dynamics within the Cu-O$_2$ planes that corresponds to anomalous Fermi liquid behavior, which is in accordance with the nested Fermi liquid theory.