Is there a quantum critical point controlled by pressure in the superconducting borocarbides RNi2B2C (R = Y, Ho, Er, Tm)?

A decade ago, Alleno et al. [Physica C 242 169 (1995)] reported measurements under hydrostatic pressure P of the superconducting temperature T-c(P), with P < 2 GPa, in the compounds RNi2B2C, where R = Y, Ho, Er, Tm. We utilise an extrapolation they propose for their data to higher pressures to address the question posed in the title. We then find critical pressures Pc ranging from similar to 23GPa for Y down to similar to 12GPa for Ho. The corresponding slopes dT(c)/dP\(P=) range from similar to-2GPa/GPa for Er to similar to-1GPa/GPa for Tm. Crucial to the discussion is whether a structural phase transition is induced in RNi2B2C by pressure before this critical pressure P-c is reached. Theory presently cannot answer such a question, but the compound for say R = Er should be experimentally accessible. Though dT(c)/dP\(P=P) is predicted to be finite above, all important is whether T-c(P) is proportional to (P-c - P) as P-c is approached, or whether the behaviour is non-analytic, such as (P-c - P)(gamma) where gamma is non-integer. If the former situation obtains, important consequences follow from the Ehrenfest relation for dT(c)/dP in terms of (a) thermal expansion, and (b) specific heat.