Electronic properties of 2D materials and its heterostructures: a minimal review

Abstract

An overview of two-dimensional (2D) materials electronic properties is presented, including research in multilayered heterostructures. An emphasis is made on simple models that contain the representative physical features seen among 2D materials, while presenting dierent and important perspectives that have been ignored or overlooked in other reviews. Starting with a short section on the crystallographic and diraction properties, the review continues with a discussion of the theoretical models needed to describe the electronic properties. An special emphasis is made on the rise of the Dirac equation in terms of the electronic wavefunctions frustration due to the underlying triangular symmetry of graphene. Then a new method to deal with such problems in other systems is presented. Also, a section concerning the less known graphene's free-electron bands is presented, which is important to describe interactions with metals and liquids as water. These bands are explained in terms of the electron interaction with its charge image, resulting in an effective Hydrogen like model leading to
a Rydberg series. We also discuss the effects of disorder, exural modes, strain and electromagnetic waves, using novel techniques developed in collaborations with other groups in Mexico. Using all of the previous techinques, other exotic matter phases are studied like Kekule and Moire patterns, at bands, topological insulators and time dependent topological states. Finally, heterostructures made by stacking layers of 2D materials are studied. An special section is devoted to the latest discovered superconductivity of graphene over graphene at magic angles, including our latest reduction of the problem onto a simple 2 2 Hamiltonian which describes the phenomena. Moreover, any other stacking of graphene layers like trilayer graphene, can be reduced using such method.