  Superconductivity in noncentrosymmetric compounds has attracted sustained
interest in the last decades. Here we present a detailed study on the
transport, thermodynamic properties and the band structure of the
noncentrosymmetric superconductor La$_7$Ir$_3$ ($T_c$ $\sim$2.3 K) that was
recently proposed to break the time-reversal symmetry. It is found that
La$_7$Ir$_3$ displays a moderately large electronic heat capacity (Sommerfeld
coefficient $\gamma_n$ $\sim$ 53.1 mJ/mol $\text{K}^2$) and a significantly
enhanced Kadowaki-Woods ratio (KWR $\sim$ 32 $\mu\Omega$ cm mol$^2$ K$^2$
J$^{-2}$) that is greater than the typical value ($\sim$ 10 $\mu\Omega$ cm
mol$^2$ K$^2$ J$^{-2}$) for strongly correlated electron systems. The upper
critical field $H_{c2}$ was seen to be nicely described by the single-band
Werthamer-Helfand-Hohenberg model down to very low temperatures. The
hydrostatic pressure effects on the superconductivity were also investigated.
The heat capacity below $T_c$ reveals a dominant s-wave gap with the magnitude
close to the BCS value. The first-principles calculations yield the
electron-phonon coupling constant $\lambda$ = 0.81 and the logarithmically
averaged frequency $\omega_{ln}$ = 78.5 K, resulting in a theoretical $T_c$ =
2.5 K, close to the experimental value. Our calculations suggest that the
enhanced electronic heat capacity is more likely due to electron-phonon
coupling, rather than the electron-electron correlation effects. Collectively,
these results place severe constraints on any theory of exotic
superconductivity in this system.
