Graphene, Dirac Fermions and Topological Matter

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Graphene, Dirac fermions and topological matter Teacher : Pascal SIMON ECTS 3 Language Anglais Web site : https://sites.google.com/site/pascalsimonphysics/ Volume : 30 hours of main lecture and around four exercices sheets Exam : At least one oral presentation of a research article Description In the past years, condensed matter physics has witnessed tremendous progress with the synthesis of new carbon based materials such as nanotubes and graphene and more recently with the emergence of new exotic materials named topological insulators. The electronic properties of all these materials share the property that they are largely described by solutions of Dirac equations in low dimensions. Simulating Dirac matter in situ with cold atoms in specific optical lattices is also an important direction followed in quantum optics. This course aims at introducing these new emerging concepts to Master 2 students. Outlook of the course : 0) A short general introduction to topological effects in matter. I) Graphene and graphene-like materials : the massless Dirac equation in two dimensions - Tight-binding model on the honeycomb lattice and the 2D massless Dirac equation - Relativistic Landau levels and quantum Hall effect in graphene - How to generate a gap in graphene - A graphene-like material in 3D : the Weyl semi-metal and its experimental realization II) Berry phases and topological invariants - Berry phases and Berry curvatures : generalities - Study of various examples such as the Aharonov-Bohm effect, the semi-classical equation of motion of a Bloch electron, the Berry phase in quantum spin systems. - Berry phases in Bloch space: Application to Graphene-like systems - Chern invariants and Chern insulators (and its experimental realizations) III) Introduction to topological insulators and superconductors - The integer quantum Hall effect and chiral edge states - 2D topological insulators and helical edge states - 3D topological insulators and topological magnetoelectric effects - Majorana fermions as edge states of topological superconductors .

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Arxiv:1803.11480V3 [Cond-Mat.Str-El] 23 May 2020 Submitted To: J
Interacting Dirac Materials S. Banerjee1;2;3, D.S.L. Abergel2, H. Ågren3;4, G. Aeppli5;6;7, A.V. Balatsky2;8 1 Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, 86135 Augsburg Germany 2Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden 3Division of Theoretical Chemistry and Biology, Royal Institute of Technology, SE-10691 Stockholm, Sweden 4 Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden 5 Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland 6 Laboratory for Solid State Physics, ETH Zurich, Zurich, CH-8093, Switzerland 7 Institut de Physique, EPF Lausanne, Lausanne, CH-1015, Switzerland 8 Department of Physics, University of Connecticut, Storrs, Connecticut 06269, USA E-mail: [email protected] 26 May 2020 Abstract. We investigate the extent to which the class of Dirac materials in two-dimensions provides general statements about the behavior of both fermionic and bosonic Dirac quasiparticles in the interacting regime. For both quasiparticle types, we find common features for the interaction induced renormalization of the conical Dirac spectrum. We perform the perturbative renormalization analysis and compute the self-energy for both quasiparticle types with different interactions and collate previous results from the literature whenever necessary. Guided by the systematic presentation of our results in Table 1, we conclude that long- range interactions generically lead to an increase of the slope of the single-particle Dirac cone, whereas short-range interactions lead to a decrease. The quasiparticle statistics does not qualitatively impact the self-energy correction for long-range repulsion but does affect the behavior of short-range coupled systems, giving rise to different thermal power-law contributions.
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Dirac Fermion Optics and Plasmonics in Graphene Microwave Devices
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Strained Hgte: a Textbook 3D Topological Insulator ClÉment Bouvier, Tristan Meunier, Philippe Ballet, Xavier Baudry, Roman Kramer, Laurent LÉvy
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