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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 Tc (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 ∼ 23 GPa for Y down to ∼ 12 GPa for Ho. The corresponding slopes range from ∼ −2 GPa/GPa for Er to ∼ −1 GPa/GPa for Tm. Crucial to the discussion is whether a structural phase transition is induced in RNi2B2C by pressure before this critical pressure Pc is reached. Theory presently cannot answer such a question, but the compound for say R = Er should be experimentally accessible. Though is predicted to be finite above, all important is whether Tc (P) is proportional to (Pc −P) as Pc is approached, or whether the behaviour is non-analytic, such as (Pc −P)γ , where γ is non-integer. If the former situation obtains, important consequences follow from the Ehrenfest relation for dTc/dP in terms of (a) thermal expansion, and (b) specific heat.