Pressure dependence of Tc from chemical equilibrium

Abstract

Chemical equilibrium theory analogous with dissociation of molecules is applied to high- T c superconductors. The starting point are preformed pairs, which exist in the normal state and can be treated as Coulomb bosons with charge 2 e. Above T c the pairs ( B 2+) decay into fermions ( h +) according to the equilibrium reaction B 2+⇌ 2h + . Using an approximate chemical equilibrium constant proportional to pressure P, we derive for the pressurized optimum transition temperature a universal two-parameter expression T c MAX( P)/ T c MAX(0)=(1+ β 1 P) 1/2(1− β 2 P) 2, where β 1(>0) and β 2 are parameters. We have applied this formula to the mercury compounds, where we obtain β 1=0.093 ( GPa) −1 . This then shows that in an interesting pressure range P>10 GPa , the expansion in powers of pressure diverges, due to the square root. One can also derive a more general doping formula T c( x, P)= A(1+ β 1 P) 1/2[ x− x 1( P)][ x 2( P)− x].