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The search for non-centrosymmetric superconductors that may exhibit unusualphysical properties and unconventional superconductivity has yielded thesynthesis of a non-centrosymmetric phosphide Mg$_2$Rh$_3$P with anAl$_2$Mo$_3$C-type structure. Although stoichiometric Mg$_2$Rh$_3$P does notexhibit superconductivity at temperatures above 2 K, we found that an Mgdeficiency of approximately 5 at.% in the Mg$_2$Rh$_3$P inducedsuperconductivity at 3.9 K. Physical properties such as the lattice parameter a= 0.70881 nm, Sommerfeld constant $\gamma_n$ = 5.36 mJ mol$^{-1}$ K$^{-2}$,specific heat jump $\Delta$C$_{el}$/$\gamma_n$Tc = 0.72, electron-phononcoupling constant $\lambda$$_{e-p}$ = 0.58, upper critical field H$_{c2}$(0) =24.3 kOe, and pressure effect dTc/dP = -0.34 K/GPa were measured for thesuperconducting Mg$_{2-\delta}$Rh$_3$P ($\delta$ $\sim$ 0.1). Band-structurecalculations indicate that exotic fermions, which are not present inhigh-energy physics, exist in Mg$_2$Rh$_3$P. Since Mg, Rh, and P are the firstelements used at each crystal site of Al$_2$Mo$_3$C-type compounds, thediscovery of Mg$_2$Rh$_3$P may guide the search for new related materials.

Superconductivity induced by Mg deficiency in non-centrosymmetric phosphide Mg$_2$Rh$_3$P