Calculations with QuantumATK
MoS2, MoTe2, and WTe2 monolayers with different edges were constructed using QuantumATK NanoLab GUI. The novel surface Green’s function method  for studying truly semi-infinite systems and implementation of spin-orbit coupling (SOC) in QuantumATK made it possible to do fully self-consistent DFT calculations on a single isolated edge. This revealed breaking of the time-reversal symmetry in the band structure which would have been hidden by the spatial symmetry of a conventional calculation on a 2D slab. Response to electric fields was modelled by adding an external potential as a shift between the gate and the top of the cell, i.e., shifting the potential near the surface in the vacuum, and then running a self-consistent DFT calculation. This procedure of applying an electric field in QuantumATK resembles the real situation in which the device channel is modulated by external gates. Furthermore, the surface Green’s function method ensured that there was no change of the chemical potential of the surface in the presence of the electric field.
The results will be presented on July 4th in the 2D materials session at the 21st IVC Conference hosted in Malmö, Sweden.
The Surface Configuration method used in the paper is available in QuantumATK and is described in
· Tutorial: Green’s function surface calculations
 L. Jelver, D. Stradi, T. Olsen, K. Stokbro, and K.W. Jacobsen, “Spontaneous breaking of time-reversal symmetry at the edges of 1T’ monolayer transition metal dichalcogenides”, Phys. Rev. B 99, 155420 (2019).
 X. Qian, J. Liu, L. Fu, and J. Li, “Quantum spin Hall effect in two-dimensional transition metal dichalcogenides”, Science 346, 1344 (2014).
 S. Smidstrup, D. Stradi, J. Wellendorff, P.A. Khomyakov, U.G. Vej-Hansen, M.-E. Lee, E.J. T. Ghosh, H. Jónsson, and K. Stokbro, “First-principles Green’s function method for surface calculations: A pseudopotential localized basis sets approach”, Phys. Rev. B 96, 195309 (2017). arXiv:1707.02141 [cond-mat.mtrl-sci]