EPJ B Colloquium - A colloquium on the variational method applied to excitons in 2D materials

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Published on 04 December 2020

Two-dimensional (2D) materials are condensed matter systems whose thickness varies from a single atom, as in graphene, to few atoms, as in transition metal dichalcogenides (TMDs). These exceedingly thin materials present, nevertheless, strong light-matter interaction.

Depending on the material, one can have an optical response from the terahertz (THz) to the ultraviolet, as in graphene, or an optical response starting only in the ultraviolet, as in hexagonal boron nitride (hBN), passing through other systems whose optical response starts in the infrared, as in phosphorene, or in the visible, as some transition metal dichalcogenides. Except for graphene, whose electronic spectrum has no gap, the other mentioned materials are either an insulator (hBN) or direct band-gap semiconductors (TMDs). As a consequence, their optical response is determined by a strong sub-gap optical absorption due to excitons. This type of quasi-particles are nothing but an electron and a hole, belonging to different bands, bound together by the electrostatic interaction. Being essentially a surface, most of the electrostatic field lines are outside the layer. Therefore, they are not screened. This leads to strongly bounded excitons and to their observation in an absorption experiment. The precise theoretical description of excitons in 2D materials requires the use of sophisticated and time consuming numerical methods. However, much can be understood from more simplified models, as the Wannier-Mott model. This model is an effective Schrödinger equation which can be treated using analytical variational methods.

In a new Colloquium published in EPJB, M.F.C. Martins Quintela and N.M.R. Peres (Universidade do Minho and International Iberian Nanotechnology Laboratory, Portugal) review the research on excitons in van der Waals heterostructures from the point of view of variational calculations, and discuss the Wannier-Mott exciton model and its application.