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

… … (2011)

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

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

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

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

Motion and merging of Dirac points

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

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

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

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

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

Atoms are trapped in an optical lattice potential and form an artifical crystal Honeycomb « brickwall » 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)

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

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

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

Single Zener tunneling Double Zener tunneling Landau-Zener probability

Single Zener tunneling Double Zener tunneling Landau-Zener probability

Single Zener tunneling Double Zener tunneling Landau-Zener probability

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

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

Back to condensed matter : Black phosphorus

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

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

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… Merging of Dirac points in a 2D crystal G. M., F. Piéchon, J.N. Fuchs, M.O. Goerbig, Phys. Rev. B 80, (2009) It’s difficult to make predictions, especially about the future Bohr, Fermi, Einstein, Groucho Marx, Woody Allen, Confucius…

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… )      

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