  Antiperovskites are a promising candidate structure for the exploration of
new materials. We discovered an antiperovskite phosphide, LaPd$_{3}$P,
following our recent synthesis of $A$Pd$_{3}$P ($A$ = Ca, Sr, Ba). While
$A$Pd$_{3}$P and (Ca,Sr)Pd$_{3}$P were found to be tetragonal or orthorhombic
systems, LaPd$_{3}$P is a new prototype cubic system ($a$ = 9.0317(1) A) with a
noncentrosymmetric space group ($I-43m$). LaPd$_{3}$P exhibited
superconductivity with a transition temperature ($T_\mathrm{c}$) of 0.28 K. The
upper critical field, Debye temperature, and Sommerfeld constant ($\gamma$)
were determined as 0.305(8) kOe, 267(1) K, 6.06(4) mJ mol-1 K-2 f.u.-1,
respectively. We performed first-principles electronic band structure
calculations for LaPd$_{3}$P and compared the theoretical and experimental
results. The calculated Sommerfeld constant (2.24 mJ mol-1 K-2 f.u.-1) was much
smaller than the experimental value of $\gamma$ because the Fermi energy
($E_\mathrm{F}$) was located slightly below the density of states (DOS)
pseudogap. This difference was explained by the increase in the DOS at
$E_\mathrm{F}$ due to the approximately 5 at.% La deficiency (hole doping) in
the sample. The observed Tc value was much lower than that estimated using the
Bardeen-Cooper-Schrieffer equation. To explain the discrepancy, we examined the
possibility of an unconventional superconductivity in LaPd$_{3}$P arising from
the lack of space inversion symmetry.
