Are Symmetry Protected Topological Phases Immune to Dephasing?

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.