  We studied the millihertz quasi-periodic oscillation (mHz QPO) in the 2020
outburst of the Be/X-ray binary 1A 0535+262 using Insight-HXMT data over a
broad energy band. The mHz QPO is detected in the 27-120 keV energy band. The
QPO centroid frequency is correlated with the source flux, and evolves in the
35-95 mHz range during the outburst. The QPO is most significant in the 50-65
keV band, with a significance of ~ 8 sigma, but is hardly detectable (<2 sigma)
in the lowest (1-27 keV) and highest (>120 keV) energy bands. Notably, the
detection of mHz QPO above 80 keV is the highest energy at which mHz QPOs have
been detected so far. The fractional rms of the mHz QPO first increases and
then decreases with energy, reaching the maximum amplitude at 50-65 keV. In
addition, at the peak of the outburst, the mHz QPO shows a double-peak
structure, with the difference between the two peaks being constant at ~0.02
Hz, twice the spin frequency of the neutron star in this system. We discuss
different scenarios explaining the generation of the mHz QPO, including the
beat frequency model, the Keplerian frequency model, the model of two jets in
opposite directions, and the precession of the neutron star, but find that none
of them can explain the origin of the QPO well. We conclude that the
variability of non-thermal radiation may account for the mHz QPO, but further
theoretical studies are needed to reveal the physical mechanism.
