The catalog of available 2D materials keeps growing since the seminal discovery and exfoliation of graphene. Today this catalog includes semiconductors and semimetals, topological insulators, superconductors, as well as 2D magnets. We are using statistical mechanics, quantum field theory approaches, first-principles calculations and tight-binding models to unveil the physical mechanisms underlying the main properties of these exotic materials. Thereby, we focus on new physical phenomena that emerge, for example, at the interface of heterostructures made of these layered materials and twisted bilayers, which may find use on different applications such as capacitors, optoelectronic devices, or magnetic memory devices (such as MRAMS).
Ferromagnetism in 2D materials
The recent discovery of ferromagnetism in monolayer CrI3 and CrGeTe3 has revolutionized the field of 2D materials. These materials defy the Mermin-Wagner theorem and become ferromagnetic at low temperatures due to their magnetic anisotropy.
Understanding how Coulomb interactions affect magnetism in 2D ferromagnets may help to get a deeper insight into the mechanisms leading to magnetic order, and to design new devices based on these novel materials. In this context, we combine density functional theory, many body lattice models, and the magnetic force theorem to address several open issues regarding magnetic exchange interactions (J) and magnetic anisotropy in chromium trihalides . For instance, this will allow us to predict the effect of substrate screening, external fields, and doping in the magnon spectrum of these materials.
 Orbitally-resolved ferromagnetism of monolayer CrI3, I. V. Kashin, V. V. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, 2D Materials 7, 025036 (2020)
Electric field switching of bilayer CrI 3
Bulk CrI3 is a ferromagnetic material. However, in thin films, the interlayer exchange interaction becomes antiferromagnetic . This seems to be related to changes in the stacking configuration when going from bulk to the 2D limit . This antiferromagnetism is very weak and can be tuned by small perturbations. We have demonstrated that the electron doping of bilayer CrI3 favors the formation of magnetic polarons, which helps to undergo the antiferromagnetic to ferromagnetic transition , which has been already observed experimentally and may allow for fully electrical control of interlayer magnetism.
 Probing magnetism in 2D van der Waals crystalline insulators via electron tunneling, D. R. Klein, D. MacNeill, J. L. Lado, D. Soriano, E. Navarro-Moratalla, K. Watanabe, T. Taniguchi, S. Manni, P. Canfield, J. Fernández-Rossier, and P. Jarillo-Herrero. Science 360, 1218 (2018)
 Interplay between interlayer exchange and stacking in CrI3 bilayers, D. Soriano, C. Cardoso, and J. Fernández-Rossier. Sol. Stat. Comm. 299, 113662 (2019)
 Magnetic polaron and antiferromagnetic-ferromagnetic transition in doped bilayer CrI3, D. Soriano and M. I. Katsnelson.Phys. Rev. B 101, 041402(R) (2020)
Multiscale modeling of 2D materials
To deeply understand the physical properties of quantum systems we need to study them on various length scales. Especially at the mesoscopic and macroscopic level new quantum phenomena emerge, such as interference, quantum confinement, or charging effects. To study the electronic, transport, and optical properties of various systems, including graphene and its derivatives, semiconducting 2D materials, artificial quantum structures, and quantum spin systems on these length scales, we develop new methods and software for the simulation of a quantum system up to billion atoms [1-2]. For more details and recent updates see the website of Prof. dr. S. (Shengjun) Yuan here .
 Modeling electronic structure and transport properties of graphene with resonant scattering centers, S. Yuan, H. De Raedt, and M. I. Katsnelson, PRB. 82, 115448 (2010)
 Excitation spectrum and high energy plasmons in single- and multi-layer graphene, S. Yuan, R. Roldán, and M. I. Katsnelson, PRB 84, 035439 (2011)
Semiclassical Study of Chiral Tunneling
Because of its high charge carrier mobility, graphene is a promising candidate for future electronics. In contrast to conventional semiconductors, its charge carriers obey an effective Dirac equation. This gives rise to the phenomenon of Klein tunneling: electrons normally incident on a potential barrier will always be transmitted, in contrast to the Schrödinger case, where the transmission is exponentially small. Thus graphene electronics cannot copy the standard semiconductor one, since it is not possible to lock a graphene transistor based on an n-p-n junction.
Using different semiclassical methods, we have studied n-p-n junctions in graphene in great detail. It turns out that, for a generic asymmetric barrier, the side resonances, that occur due to quasibound hole states within the barrier, decay exponentially with the angle of incidence. By comparison with numerical results, we find that our analytical predictions for the transmission and reflection coefficients are uniformly valid in the entire range of incidence angles.
Our numerical studies show that, in contrast to the case of a single layer, the side resonances in bilayer graphene always give rise to total transmission.
 Chiral tunnelling and the Klein paradox in graphene, M.I. Katsnelson, K.S. Novoselov, and A.K. Geim, Nat. Phys. 2, 620 (2006)
 Chiral tunneling in single-layer and bilayer graphene, T. Tudorovskiy, K.J.A. Reijnders, and M.I. Katsnelson, Physica Scripta T 146, 014010 (2012)
 Semiclassical theory of potential scattering for massless Dirac fermions, K.J.A. Reijnders, T. Tudorovskiy, M.I. Katsnelson, Annals of Physics 333, 155 (2013)
Thermal fluctuations inevitably induce ripples and perturbations in the structure of freely-suspended crystalline membranes. The description of these ripples within statistical mechanics is controlled by a strongly-nonlinear theory, and it constitutes a challenging theoretical problem. Graphene and atomically-thin two-dimensional materials are extreme realizations of an elastic membrane. When free-standing and subject to very weak external tension, they constitute an ideal platform for the observation of intriguing phenomena, such as anomalous scale invariance. In our group, we combine elasticity theory, quantum field theory techniques, and numerical simulations to describe experimentally-relevant membrane phenomenology.
 The structure of suspended graphene sheets, J. C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth, Nature 446, 60 (2007)
 Intrinsic ripples in graphene, A. Fasolino, J. H. Los, and M. I. Katsnelson, Nature Mater. 6, 858 (2007)
 Scaling properties of flexible membranes from atomistic simulations: application to graphene, J. H. Los, M. I. Katsnelson, O. V. Yazyev, K. V. Zakharchenko, and A. Fasolino, PRB 80, 121405(R) (2009)
 Graphene as a prototype crystalline membrane, M. I. Katsnelson and A. Fasolino, Accounts Chem. Res. 46, 97 (2013)
 Scaling behavior and strain dependence of in-plane elastic properties of graphene, J. H. Los, A. Fasolino, and M. I. Katsnelson, PRL 116, 015901 (2016
 Scaling behavior of crystalline membranes: an ε-expansion approach, A. Mauri and M. I. Katsnelson, Nucl. Phys. B 956, 115040 (2020)