  Recent theoretical advances have proposed a new class of topological
crystalline insulator (TCI) phases protected by rotational symmetries. Distinct
from topological insulators (TIs), rotational symmetry-protected TCIs are
expected to show unique topologically protected boundary modes: First, the
surface normal to the rotational axis features unpinned Dirac surface states
whose Dirac points are located at generic k points. Second, due to the
higher-order bulk boundary correspondence, a 3D TCI also supports 1D helical
edge states. Despite the unique topological electronic properties, to date,
purely rotational symmetry-protected TCIs remain elusive in real materials.
Using first-principles band calculations and theoretical modeling, we identify
the van der Waals material $\alpha$-Bi4Br4 as a TCI purely protected by
rotation symmetry. We show that the Bi4Br4's (010) surface exhibits a pair of
unpinned topological Dirac fermions protected by the two-fold rotational axis.
These unpinned Dirac fermions show an exotic spin texture highly favorable for
spin transport and a band structure consisting of van Hove singularities due to
Lifshitz transition. We also identify 1D topological hinge states along the
edges of an $\alpha$-Bi4Br4 rod. We further discuss how the proposed
topological electronic properties in $\alpha$-Bi4Br4 can be observed by various
experimental techniques.
