Evolution of Superconducting-Transition Temperature with Superfluid Density and Conductivity in Pressurized Cuprate Superconductors

What factors fundamentally determine the value of superconducting transition temperature T_c in high temperature superconductors has been the subject of intense debate. Following the establishment of an empirical law known as Homes’ law, there is a growing consensus in the community that the T_c value of the cuprate superconductors is closely linked to the superfluid density (ρ_s) of its ground state and the conductivity (σ) of its normal state. However, all the data supporting this empirical law (ρ_s = AσT_c) have been obtained from the ambient-pressure superconductors. In this study, we present the first high-pressure results about the connection of the quantities of ρ_s and σ with T_c, through the studies on the Bi_1.74Pb_0.38Sr_1.88CuO_6+δ and Bi₂Sr₂CaCu₂O_8+δ, in which the value of their high-pressure resistivity (ρ = 1/σ) is achieved by adopting our newly established method, while the quantity of ρ_s is extracted using Homes’ law. We highlight that the T_c values are strongly linked to the joint response factors of magnetic field and electric field, i.e., ρ_s and σ, respectively, implying that the physics determining T_c is governed by the intrinsic electromagnetic fields of the system.