  Theoretically, the helical edge states of two-dimensional topological
insulators are protected from coherent backscattering due to nonmagnetic
disorder provided electron interactions are not too strong. Experimentally, the
edges typically do not demonstrate the systematic and robust quantization, at
the same time little is known about the sub-Kelvin temperature behavior. Here,
we report the surprising localization of the edge states in an 8 nm HgTe
quantum well in zero magnetic field at millikelvin temperatures. Additionally,
the magnetoresistance data at 0.5 K for the edges few micrometers long suggests
the field-dependent localization length $l_B\propto B^{-\alpha}$, with $\alpha$
ranging approximately from $1.6$ to $2.8$ at fields $B\lesssim0.1\,\text{T}$
and $\alpha\approx1.1$ at higher fields up to $0.5\,\text{T}$. In the frame of
disordered interacting edge, these values of $\alpha$ correspond to the
Luttinger liquid parameters $K\approx 0.9-1.1$ and $K\approx 0.6$,
respectively. We discuss possible scenarios which could result in the zero
magnetic field localization.
