Criticality in electronic structure of two graphene layers containing praseodymium superhydride doped molecules

Compressed hydrogen-rich compounds have been verified extensively by theoretical scientists for finding high-temperature superconductivity. Although some experiments confirm these findings, their requirement of extremely high critical pressure condition ( $$ 100\ \text {GPa }\lesssim P_c$$ 100 GPa ≲ P c ) makes them impossible to apply in daily life. The main purpose of present work is to help finding materials with high-temperature superconductivity at low pressures. For this purpose, we consider two graphene sheets with sine form corrugations whose honeycomb patterns are exactly on top of each other with some doped molecules intercalated into sheets. The free energy of valence electrons of total atoms is computed for doped molecules PrH $$ _{6}$$ 6 , PrH $$ _{7}$$ 7 , PrH $$ _{8}$$ 8 , and PrH $$ _{9}$$ 9 , separately. Our calculations indicate a second-order phase transition for PrH $$ _{9}$$ 9 at critical temperature $$T_c =179.01 \ \text {K}$$ T c = 179.01 K with applying no external pressure, while no phase transition is observed for other doped molecules. This high-temperature electronic structural stability is $$46 \ \text {K} $$ 46 K greater than the $$T_c$$ T c of the cuprate materials which are the highest-temperature superconductors at low pressures. We guess this phase transition is a superconductivity transition due to the observation of Meissner effect in magnetic susceptibility diagram. Graphic abstract