In the past couple of decades, the theoretical study of two-dimensional (2D) materials that could (hopefully) extend the miniaturization of semiconductor devices beyond the perceived limits of the Si CMOS technology has been affected by two major changes. On the one hand, these new materials are poorly known, so that one must rely almost exclusively on ‘basic’ physics (ab initio or ‘first principles”) to assess their properties. On the other hand, density functional theory (DFT) has reached the mature stage of being predictive, thus compensating for the poor practical and experimental knowledge we have of these materials. Sadly, however, a look at the literature shows that, in many cases, predictions made on carrier-transport properties of 2D materials are wildly inconsistent.

Starting from this consideration, here we will consider various groups of 2D materials: 1. Non-van der Waals (vdW) material, such as phosphorene; 2. ‘Pure’ van der Waals (vdW) planar (sp²) 2D materials, such as graphene; and 3. Non mirror-symmetric 2D crystals, such as silicene, germanene, and stanene. As an example of the first group, the problem of calculating the low-field carrier mobility in monolayer phosphorene will be reviewed and critically discussed, since values for the mobility reported in the literature span almost three orders of magnitude and clarifications are needed. Therefore, we shall pay attention to the drawbacks and advantages of various ab initio models that can be used to calculate charge-transport properties. Regarding planar vdW materials, we will consider the specific case of graphene (and its nanoribbons) as an example in which the supporting substrate plays the beneficial role of stabilizing the crystal and damping the out-of-plane vibrational modes, but also has the detrimental effect of reducing the carrier mobility via scattering with interface hybrid optical-phonon/plasmon modes. In addition, we shall discuss the strong effect that line-edge roughness has on electron transport in armchair-edge graphene nanoribbons (AGNRs). For non-mirror-symmetric crystals, the strong coupling of electrons with acoustic flexural modes (ZA-phonons) causes major concerns, often ignored. We will discussed this, showing that the problem regarding thermodynamic stability of 2D crystals (the ‘Mermin-Wagner theorem’) can bear strong consequences also on electronic transport.

Pseudopotential-based quantum-transport simulations of 5 nm-long field-effect transistors (FETs) will also be shown, comparing devices based on graphene and phosphorene nanoribbons to Si nanowire-FETs.

Finally, the intriguing properties of 2D topological insulators will be discussed, considering the cases of monolayer tin and bismuth and their potential applications in spintronics and low-power high-performance devices.