Atomically inspired k · p approach and valley Zeeman effect in transition metal dichalcogenide monolayers

We developed a six-band k·p model that describes the electronic states of monolayer transition metal dichalcogenides (TMDCs) in K valleys. The set of parameters for the k·p model is uniquely determined by decomposing tight-binding (TB) models in the vicinity of K± points. First, we used TB models existing in literature to derive systematic parametrizations for different materials, including MoS2,WS2,MoSe2, and WSe2. Then, by using the derived six-band k·p Hamiltonian we calculated effective masses, Landau levels, and the effective exciton g-factor gX0 in different TMDCs. We showed that TB parametrizations existing in literature result in small absolute values of gX0, which are far from the experimentally measured gX0≈−4. To further investigate this issue we derived additional sets of k·p parameters for different TMDCs by developing our own TB parametrizations based on simultaneous fitting of ab initio calculated, within the density functional theory (DFT) and GW approaches, energy dispersion, and the value of gX0. We showed that the change in TB parameters, which only slightly affects the dispersion of higher conduction and deep valence bands, may result in a significant increase of |gX0|, yielding close-to-experiment values of gX0. Such a high parameter sensitivity of gX0 opens a way to further improvement of the description of TMDCs electronic structures by DFT and/or TB models.