  Harnessing topological phases with their dissipationless edge-channels
coupled with the effective engineering of quantum phase transitions is a spinal
aspect of topological electronics. The accompanying symmetry protection leads
to different kinds of topological edge-channels which include, for instance,
the quantum spin Hall phase, and the spin quantum anomalous Hall phase. To
model realistic devices, it is important to ratify the robustness of the
dissipationless edge-channels, which should typically exhibit a perfect quantum
of conductance, against various disorder and dephasing. This work is hence
devoted to a computational exploration of topological robustness against
various forms of dephasing. For this, we employ phenomenological dephasing
models under the Keldysh non-equilibrium Green's function formalism using a
model topological device setup on a 2D-Xene platform. Concurrently, we also
explicitly add disorder via impurity potentials in the channel and averaging
over hundreds of configurations. To describe the extent of robustness, we
quantify the decay of the conductance quantum with increasing disorder under
different conditions. Our analysis shows that these topological phases are
robust to experimentally relevant regimes of momentum dephasing and random
disorder potentials. We note that Rashba mixing worsens the performance of the
QSH phase and point out a mechanism for the same. Further, we observe that the
quantum spin Hall phase break downs due to spin dephasing, but the spin quantum
anomalous Hall phase remains robust. The spin quantum anomalous Hall phase
shows stark robustness under all the dephasing regimes, and shows promise for
realistic device structures for topological electronics applications.
