  Gapless helical edge modes are a hallmark of the quantum spin Hall effect.
Protected by time-reversal symmetry, each edge contributes a quantized
zero-temperature conductance quantum $G_0 \equiv e^2/h$. However, the
experimentally observed conductance in WTe$_2$ decreases below $G_0$ per edge
already at edge lengths around 100 nm, even in the absence of explicit
time-reversal breaking due to an external field or magnetic impurities. In this
work, we show how a time-reversal breaking excitonic condensate with a
spin-spiral order that can form in WTe$_2$ leads to the breakdown of
conductance quantization. We perform Hartree-Fock calculations to compare
time-reversal breaking and preserving excitonic insulators. Using these
mean-field models we demonstrate via quantum transport simulations that weak
non-magnetic disorder reproduces the edge length scaling of resistance observed
in the experiments. We complement this by analysis in the Luttinger liquid
picture, shedding additional light on the mechanism behind the quantization
breakdown.
