Fig. 2: Summary of the method developed to simulate electron transport through WS₂-Al₂O₃ stacks.

a After constructing a unit cell containing both materials³⁰, its Hamiltonian H_U and overlap S_U matrices are calculated with the CP2K package²⁸ (left). The unit cell Hamiltonian H_U is decomposed into its in-cell coupling matrix H₀ (highlighted in orange) and its coupling to the next cell, H₁ (green). Similar blocks can be extracted from S_U. b All these blocks are repeated to create the Hamiltonian H_D and overlap S_D matrices of the device of interest. The latter is composed of N repetitions of the same super cell, with N between 3 and 5. Pristine monolayer WS₂ cells are then added on both sides of the generated structure to form semi-infinite contacts and enable the scattering-free injection of electrons into the resulting open system. Python scripts are used for that purpose. The final Hamiltonian H_D is shown in the middle. c The atomic lattice of the full device is depicted at the bottom. The unit cell Hamiltonian blocks H₀ and H₁ are indicated by arrows and colors. (d) Once H_D and S_D are available, the quantum transport properties of the constructed device can be computed with the OMEN solver³⁹. The detailed procedure is explained in the Method section.