  Electronic topological phases are renowned for their unique properties, where
conducting surface states exist on the boundary of an insulating
three-dimensional bulk. While the transport response of the surface states has
been extensively studied, the response of the topological hinge modes remains
elusive. Here, we investigate a layered topological insulator
$\alpha$-Bi$_4$Br$_4$, and provide the first evidence for quantum transport in
gapless topological hinge states existing within the insulating bulk and
surface energy gaps. Our magnetoresistance measurements reveal pronounced h/e
periodic (where h denotes Planck's constant and e represents the electron
charge) Aharonov-Bohm oscillation. The observed periodicity, which directly
reflects the enclosed area of phase-coherent electron propagation, matches the
area enclosed by the sample hinges, providing compelling evidence for the
quantum interference of electrons circumnavigating around the hinges. Notably,
the h/e oscillations evolve as a function of magnetic field orientation,
following the interference paths along the hinge modes that are allowed by
topology and symmetry, and in agreement with the locations of the hinge modes
according to our scanning tunneling microscopy images. Remarkably, this
demonstration of quantum transport in a topological insulator can be achieved
using a flake geometry and we show that it remains robust even at elevated
temperatures. Our findings collectively reveal the quantum transport response
of topological hinge modes with both topological nature and quantum coherence,
which can be directly applied to the development of efficient quantum
electronic devices.
