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Universal Description of Motion and Merging of Dirac Points in 2D Crystals

Explore the impact of artificial graphenes, microwaves, and cold atoms on condensed matter physics in the 21st century through Jacques Friedel's influence. Discover the manipulation of Dirac cones, topological transitions, and merging scenarios in a variety of experimental setups. Learn about the universal Hamiltonian, the transition between valleys, and the coupling of Dirac points, as well as the creation, movement, and merging of Dirac points utilizing Fermi gases in honeycomb lattices. Uncover the evolution of Dirac points under strain and the emergence of black phosphorus as a condensed matter candidate. Delve into new thermodynamic, transport, and interaction properties in 2D crystals, paving the way for interference effects, Berry phase phenomena, and advancements in orbital magnetism. Envision a future where coupled bands effects and polaritons in honeycomb semiconductor structures shape the realm of physics to come.

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Universal Description of Motion and Merging of Dirac Points in 2D Crystals

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  1. Les graphènes artificiels, des microondes aux atomes froids Gilles Montambaux, Orsay Physique de la matière condensée au 21e siècle - L'impact de Jacques Friedel 26 janvier 2016 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  2. … … (2011)

  3. Les graphènes artificiels, des microondes aux atomes froids Gilles Montambaux, Orsay K’ K Graphene electronic spectrum

  4. Les graphènes artificiels, des microondes aux atomes froids Gilles Montambaux, Orsay K’ K « Dirac point » Relativistic quantum physics in a benchtop experiment (A. Geim) QED in a pencil trace… (K. Novoselov)

  5. Les graphènes artificiels, des microondes aux atomes froids Gilles Montambaux, Orsay Winding of the wave function K’ K W=+1 W=-1 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA

  6. Manipulation of Dirac cones in artificial graphenes W=1 0 W=1 W=-1 W=-1 « Life and death of Dirac points » deformation of honeycomb lattice Artificial graphenes Graphene-Dirac physics with microwaves Graphene-Dirac physics with cold atoms in an optical lattice More systems…

  7. Motion and merging of Dirac points

  8. Motion and merging of Dirac points

  9. Motion and merging of Dirac points massive ! massless ! « Semi-Dirac » spectrum

  10. Motion and merging of Dirac points

  11. The merging scenario is universal Honeycomb Brick wall merging point at a symmetry point of the reciprocal lattice

  12. The merging scenario is universal Universal Hamiltonian The parameter drives the topological transition 1 0 -1 This Hamiltonian describes the topological transition, the coupling between valleys and the merging of the Dirac points

  13. Topological transition of Dirac points in a microwave experiment M. Bellec, U. Kuhl, F. Mortessagne (NICE), G. M. Honeycomb lattice of dielectric resonators Evanescent propagation between the dots -> Tight-binding description Measure of the reflexion coefficient  LDOS ~ 50cm (2nd and 3rd nearest neighbor couplings not negligeable) ~ 250 « atoms » High flexibility 1) Look for the merging transition 2) Probe the edge states

  14. Topological transition of Dirac points in a microwave experiment New edge states Uniaxial strain P. Delplace, D. Ullmo, G.M., PRB 2011 See also photonic crystals

  15. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice L.Tarruell et al. Nature, 483, 302 (2012)Tilman Esslinger (Zürich) Atoms are trapped in an optical lattice potential and form an artifical crystal Honeycomb « brickwall »

  16. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice Bloch oscillations = uniform motion in reciprocal space

  17. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice Bloch oscillations = uniform motion in reciprocal space

  18. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice l l l l Bloch oscillations = uniform motion in reciprocal space

  19. Landau-Zener probability Single Zener tunneling Double Zener tunneling

  20. Landau-Zener probability Single Zener tunneling Double Zener tunneling

  21. Landau-Zener probability Single Zener tunneling Double Zener tunneling

  22. Laser intensities tune the anisotropy of the optical potential Experiment Laser intensities TB couplings Universal hamiltonian L.-K. Lim, J.-N. Fuchs, G.M., PRL,PRA (2013) Theory

  23. Coherent double Dirac cone  Interferences in reciprocal space Combining probability amplitudes gives Dynamical phase coherent Geometrical phase E. Shimshoni, Y. Gefen, Ann. Phys. (1991) S. Gasparinetti et al. PRL (2011) L.-K. Lim, J.-N. Fuchs, G. M., PRL 112, 155302 (2014)

  24. Back to condensed matter : Black phosphorus

  25. Back to condensed matter : Black phosphorus

  26. Back to condensed matter : Black phosphorus

  27. Back to condensed matter : Black phosphorus Emergence of Dirac points under vertical strain !

  28. Black phosphorus J. Kim et al. , Science 2015 Emergence of Dirac points under vertical strain !

  29. Merging of Dirac points in a 2D crystal G. M., F. Piéchon, J.N. Fuchs, M.O. Goerbig, Phys. Rev. B 80, 153412 (2009) Referee B The authors propose that merging of Dirac points might be possible with cold atoms in optical lattices. I think that it is a very long shot, given that the systems are yet to be realized experimentally. Referee C  While the physical system is certainly interesting, its relevance to current experiments is rather tenuous… It’s difficult to make predictions, especially about the future Bohr, Fermi, Einstein, Groucho Marx, Woody Allen, Confucius…

  30. Conclusions and perspectives Universal description of motion and merging of Dirac points in 2D crystals Condensed matter : New thermodynamic and transport properties Interaction effects : from Dirac to Schrödinger Cold atoms : Landau-Zener probe of the Dirac points Interference effects, Berry phase effects New direction : coupled bands effects, orbital magnetism Photonic crystals (Segev et al., Technion) Polaritons in honeycomb semiconducting structures (J. Bloch, Marcoussis) Condensed matter (organic conductors, black phosphorus… ) 2 -1 1 0 1 1

  31. Many thanks to Jean-Noël Fuchs Mark Goerbig Frédéric Piéchon Petra Dietl Pierre Delplace Lih-King Lim Raphael De Gail Arnaud Raoux

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