  The link between crystal and electronic structure is crucial for
understanding structure-property relations in solid-state chemistry. In
particular, it has been instrumental in understanding topological materials,
where electrons behave differently than they would in conventional solids.
Herein, we identify 1D Bi chains as a structural motif of interest for
topological materials. We focus on Sm$_3$ZrBi$_5$, a new quasi-one-dimensional
(1D) compound in the Ln$_3$MPn$_5$ (Ln = lanthanide; M = metal; Pn = pnictide)
family that crystallizes in the P$6_{3}$/mcm space group. Density functional
theory calculations indicate a complex, topologically non-trivial electronic
structure that changes significantly in the presence of spin-orbit coupling.
Magnetic measurements show a quasi-1D antiferromagnetic structure with two
magnetic transitions at 11.7 and 10.7 K that are invariant to applied field up
to 9 T, indicating magnetically frustrated spins. Heat capacity, electrical,
and thermal transport measurements support this claim and suggest complex
scattering behavior in Sm$_3$ZrBi$_5$. This work highlights 1D chains as an
unexplored structural motif for identifying topological materials, as well as
the potential for rich physical phenomena in the Ln$_3$MPn$_5$ family.
