Superconductivity under pressure in the Dirac semimetal PdTe₂

The Dirac semimetal PdTe₂ was recently reported to be a type-I superconductor (T _c   =  1.64 K, [Formula: see text] mT) with unusual superconductivity of the surface sheath. We here report a high-pressure study, [Formula: see text] GPa, of the superconducting phase diagram extracted from ac-susceptibility and transport measurements on single crystalline samples. T _c (p ) shows a pronounced non-monotonous variation with a maximum T _c   =  1.91 K around 0.91 GPa, followed by a gradual decrease to 1.27 K at 2.5 GPa. Surface superconductivity is robust under pressure as demonstrated by the large superconducting screening signal that persists for applied dc-fields [Formula: see text]. Surprisingly, for [Formula: see text] GPa the superconducting transition temperature at the surface [Formula: see text] is larger than T _c of the bulk. Therefore surface superconductivity may possibly have a non-trivial topological nature. We compare the measured pressure variation of T _c with recent results from band structure calculations and discuss the importance of a Van Hove singularity.