  The intermetallic compound TlBi$_2$ crystallizes in the MgB$_2$ structure and
becomes superconducting below 6.2 K. Considering that both Tl and Bi have heavy
atomic masses, it is puzzling why TlBi$_2$ is a conventional phonon-mediated
superconductor. We have performed comprehensive first-principles calculations
of the electronic structures, the phonon dispersions and the electron-phonon
couplings for TlBi$_2$. The $6p$ orbitals of bismuth dominate over the states
near the Fermi level, forming strong intra-layer $p_{x/y}$ and inter-layer
$p_z$ $\sigma$ bonds which is known to have strong electron-phonon coupling. In
addition, the large spin-orbit coupling interaction in TlBi$_2$ increases its
electron-phonon coupling constant significantly. As a result, TlBi$_2$, with a
logarithmic phonon frequency average one tenth that of MgB$_2$, is a
phonon-mediated superconductor.
