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We analyze the electric field driven topological field effect transition on2D-xene materials with the addition of momentum relaxation effects, in order toaccount for dephasing processes. The topological field effect transitionbetween the quantum spin Hall phase and the quantum valley Hall phase isanalyzed in detail using the Keldysh non-equilibrium Green's function techniquewith the inclusion of momentum and phase relaxation, within the self-consistentBorn approximation. Details of the transition with applied electric field areelucidated for the ON-OFF characteristics with emphasis on the transportproperties along with the tomography of the current carrying edge states. Wenote that for moderate momentum relaxation, the current carrying quantum spinHall edge states are still pristine and show moderate decay with propagation.To facilitate our analysis, we introduce two metrics in our calculations, thecoherent transmission and the effective transmission. In elucidating thephysics clearly, we show that the effective transmission, which is derivedrigorously from the quantum mechanical current operator is indeed the rightquantity to analyze topological stability against dephasing. Exploring further,we show that the insulating quantum valley Hall phase, as a result of dephasingcarries band-tails which potentially activates parasitic OFF currents, therebydegrading the ON-OFF ratios. Our analysis sets the stage for realistic modelingof topological field effect devices for various applications, with theinclusion of scattering effects and analyzing their role in the optimization ofthe device performance.

Momentum relaxation effects in 2D-Xene field effect device structures