  The Su, Schrieffer and Heeger (SSH) model, describing the soliton excitations
in polyacetylene due to the formation of antiphase domain walls (DW) from the
alternating bond pattern, has served as a paradigmatic example of
one-dimensional (1D) chiral topological insulators. While the SSH model has
been realized in photonic and plasmonic systems, there have been limited
analogues in three-dimensional (3D) electronic systems, especially regarding
the formation of antiphase DWs. Here, we propose that pristine bulk Bi, in
which the dimerization of $(111)$ atomic layers renders alternating covalent
and van der Waals bonding within and between successive $(111)$ bilayers,
respectively, serves as a 3D analogue of the SSH model. First, we confirm that
the two dimerized Bi structures belong to different Zak phases of 0 and $\pi$
by considering the parity eigenvalues and Wannier charge centers, while the
previously reported bulk topological phases of Bi remain invariant under the
dimerization reversal. Next, we demonstrate the existence of topologically
non-trivial $(111)$ and trivial $(11\bar{2})$ DWs in which the number of in-gap
DW states (ignoring spin) is odd and even respectively, and show how this
controls the interlinking of the Zak phases of the two adjacent domains.
Finally, we derive general criteria specifying when a DW of arbitrary
orientation exhibits a $\pi$ Zak phase based on the flip of parity eigenvalues.
An experimental realization of dimerization in Bi and the formation of DWs may
be achieved via intense femtosecond laser excitations that can alter the
interatomic forces and bond lengths.
