The average kinetic energy density of Cooper pairs above $T_c$ in ${\rm YBa_2Cu_3O_{7-x}}$, ${\rm Bi_2Sr_2CaCu_2O_{8+\delta}}$, and ${\rm Nb}$

TL;DR

This study investigates the kinetic energy density of Cooper pairs in high-temperature superconductors and Nb, revealing a persistent superconducting condensate above the critical temperature in high-$T_c$ materials.

Contribution

It provides the first detailed comparison of kinetic energy density curves in high-$T_c$ superconductors and conventional Nb, highlighting the existence of a superconducting condensate above $T_c$ in high-$T_c$ materials.

Findings

High-$T_c$ superconductors show a superconducting condensate above $T_c$.

Nb exhibits a different behavior with no such condensate above $T_c$.

Kinetic energy density curves reflect the nature of the superconducting state.

Abstract

We have obtained isofield curves for the square root of the average kinetic energy density of the superconducting state for three single crystals of underdoped $YBa_2Cu_3O_{7-x}$, an optimally doped single crystal of $Bi_2Sr_2CaCu_2O_{8+\delta}$, and Nb. These curves, determined from isofield magnetization versus temperature measurements and the virial theorem of superconductivity, probe the order parameter amplitude near the upper critical field. The striking differences between the Nb and the high-$T_c$ curves clearly indicate for the latter cases the presence of a unique superconducting condensate below and above $T_c$.