  Axion electrodynamics in condensed matter could emerge from the formation of
charge density waves (CDWs) in Weyl semimetals. (TaSe$_4$)$_2$I was proposed to
be the first material platform for realizing axionic CDW that may host
topological defects with one-dimensional in-gap modes. The real-space
modulation of the CDW phase and the existence of in-gap modes remain elusive.
Here, we present a comprehensive scanning tunneling microscopic and
spectroscopic study of a CDW on a (TaSe$_4$)$_2$I (110) surface. The tunneling
spectroscopic measurements reveal a CDW gap of $\sim 200$ meV, in good
agreement with prior studies, while the spectroscopy of CDW edge dislocation
shows no indication of in-gap states. The bias-dependent scanning tunneling
microscopy images indicate that the CDW in(TaSe$_4$)$_2$I is dominated by a
large periodic lattice distortion instead of charge modulation, suggesting a
non-Peierls mechanism of the CDW instability.
