In recent years, novel two-dimensional (2D) materials have attracted much attention due to their unique properties and numerous possible applications [1]. In particular, one of the key domains that can be addressed with the 2D materials refers to the energy conversion and storage [2]. In this context, the novel monolayer group-VI B transition metal dichalcogenides (MX2, where M = Mo, W and X = S, Se, Te) are of special interest. Specifically, the MX2 monolayers are characterized by the high charge mobility [3] and direct electronic band gaps in the visible spectrum range [4], which allows their use in the low-dimensional tunneling transistors [3], [5], photodetectors [6], [7], or solar cells [8], [9].

In such electronic and optoelectronic applications, the electronic transport processes play a pivotal role. In particular, the functionality and efficiency of the low-dimensional systems are highly influenced by the quantum effects that forbid their investigation within the classical regime [10], [11]. From the theoretical point of view, the quantum transport phenomenon is usually described in the framework of the Landauer-Büttiker theory [12], [13], which relates the scattering theory to the quantum electronic conductance. In what follows, the central role in Landauer-Büttiker formalism is played by the transmission probabilities, familiar in the scattering theory, which can be expressed in the terms of the bulk solutions of the Schrodinger equation.

These bulk solutions of the Schrodinger equation incorporate both the propagating and evanescent electronic states that compose the so-called complex band structures (CBSs) of the solids. However, the importance of the CBSs is not only restricted to the quantum transport simulations, where they are used as a complete basis set of the electronic states for calculations. Notably, CBSs allow for capturing the properties of solids that are beyond the typical electronic band structure analysis, e.g. the surface states [14], [15], the localized edge states [16], [17] or decay characteristics of localized states [18], [19].

In the present communication we report the recent calculations of the CBSs of monolayer MX2 materials (where M = Mo, W and X = S, Se, Te) [20]. Herein, the basic electronic properties of MX2 systems are described by using the tight-binding (TB) model [21] which permits the spin-orbit coupling (SOC) effects. The adopted TB model allows describing the most important features of the MX2 systems, presenting at the same time predictive capabilities of more advanced theories. Next, the CBSs of MX2 materials are calculated from the developed nonlinear generalized eigenvalue problem (NGEP) method. The electronic states obtained from the NGEP method are characterized and classified due to their functional behavior in the momentum space. It is shown that the calculated CBSs strongly depend on the SOC interaction and present the band spin splitting of the electronic branches. Moreover, the complex loops, which describe the tunneling currents at the direct band gaps, are observed. Their characterization is given regarding the decay behavior of the corresponding evanescent states that create the complex loops. The discussion is supplemented by the analysis of the importance of CBSs in quantum transport calculations for MX2 monolayers, and by the perspectives for further research in this domain.


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