Planck quantization pseudogap in high-temperature superconductors

The behavior of the pseudogap phase is a major enigma in the superconductivity mechanism. It can either aid or hinder superconductivity, and the origins of the two gaps in high-temperature superconductors are still unknown. Based on Planck's quantum theory and polyhedral quantum well confinement in real space, we theoretically derived an inverse-square superconducting equation like Newton's and Coulomb's laws. This equation accurately predicts the superconducting transition temperatures of almost all copper- and iron-based superconducting materials, with theoretical and experimental results in agreement. This paper details the relationships among the superconducting nematic phase, the pseudogap phase, and doping concentration. We argue that the superconducting state corresponds to Planck's ground state, while the pseudogap state is Planck's excited state. Theoretical results show the pseudogap has no linear relation with doping concentration. Instead, as doping concentration drops, the pseudogap changes stepwise like the quantum Hall effect, with step depth determined by the Planck energy level. We also clarify the relationship among the specific heat jump near the superconducting transition temperature, doping concentration, and Planck energy level. These findings offer profound insights into the correlation between the pseudogap phase and superconductivity in cuprate superconductors. Given that both the superconducting and pseudogap stem from Planck's energy quantization, it is inferred that all superconductors may share the same superconducting mechanism.