For room-temperature superconductivity, abruptly diverging <i>T_c</i> over a transition pressure, 225 GPa, explained by Brinkman-Rice picture

For discovered room-temperature superconductivity of 287.7±12 K at 267±10 GPa in a H-S-C compound, T_c-discontinuity around P_transition=225 GPa and T_c-divergence over P_transition were observed [1]. Explaining T_c-divergence is a core problem for the mechanism of room-temperature superconductivity. ^~~The T_c-divergence results from 3D-density of states, N(0)^*, with diverging behavior of m^* induced by a large correlation strength of κ_BR=U/U_c near ρ≈1 [2].
This was analyzed by the strong-coupling-limit BCS T_c=(4/b)Θ_D^*exp(-1/λ^*)(1-exp(-2/λ^*))^-1=(4/b)ρ^1/3Θ_Dexp(-1/Aλ)(1-exp(-2/Aλ))^-1 with b≥3.5. Effective parameterts, Θ_D^*=ρ^1/3Θ_D, λ^*≡Aλ=A(N(0)V_e-phonon), A≡N(0)^*/N(0)=ρ^1/3/(1-ρ⁴) from N(0)^*∝m^*n^1/3, m^*=m/(1-ρ⁴) [2] are given.
^~~Here, n=ρn_tot, 0<ρ=n/n_tot<1 of band-filling factor, n_tot of the number of atoms in the measurement region are defined in an inhomogeneous system such as compounds with metal and insulator phases[2]. m^* is the effective mass obtained from the correlation strength in the Brinkman-Rice(BR) picture.
Moreover, with increasing pressure, n, ρ, T_c increase by insulator-metal transition, which is caused by the extension of the metal region (percolation). [1] Nature586(2020)373(Fig.1c). [2] arXiv/1710.07754.