  The notion of topological insulators (TIs), characterized by an insulating
bulk and conducting topological surface states, can be extended to higher-order
topological insulators (HOTIs) hosting gapless modes localized at the
boundaries of two or more dimensions lower than the insulating bulk1-5. In this
work, by performing high-resolution angle-resolved photoemission spectroscopy
(ARPES) measurements with submicron spatial and spin resolutions, we
systematically investigate the electronic structure and spin texture of
quasi-one-dimensional (1D) HOTI candidate Bi4Br4. In contrast to the
bulk-state-dominant spectra on the (001) surface, we observe gapped surface
states on the (100) surface, whose dispersion and spin-polarization agree well
with our ab initio calculations. Moreover, we reveal in-gap states connecting
the surface valence and conduction bands, which is an explicit signature of the
existence of hinge states inside the (100) surface gap. Our findings provide
compelling evidence for the HOTI phase of Bi4Br4. The identification of the
higher-order topological phase will lay the promising prospect of applications
based on 1D spin-momentum locked current in electronic and spintronic devices.
