Evidence of Strong Relationship Between Carrier States in Fractional Quantum-Hall Effect and in High- Temperature Superconductivity Found in Dielectric Measurement of La_2−xSr_xCuO₄ Film

Abstract

The capacitance measurement of Pd/La_2−xSr_xCu0₄/(100)SrTiO₃/Pd multi-layer structure at low ac frequency 40Hz–100kHz shows the increase of its capacitance C _t at Sr-doping factor x =1/2k with the decrease at x =1/(2k+1) where k is integer. Strong correspondence is found between the observed x − C _t relationship and the v − ΔE relationship known in the fractional quantum Hall effect, where y is the electron filling factor and ΔE is the 2D electron energy. The correspondence exists in the following points. (i) Both x and v are the filling factor of carriers in quantum sites. (ii) Peaks are found when the factors are 1/(even integer). (iii) Sharp valleys are found when the factors are 1/(odd integer). The origin of the correspondence is discussed based on the similarity between the 2D electron state in strong magnetic field and the hole carrier state in the presence of space charge in La_2−xSr_xCuO₄ with periodic block-layer potential.