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Francisco Guinea-Recent advances in graphene research

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Francisco Guinea-Recent advances in graphene research

Los días 22 y 23 de junio de 2016 organizamos en la Fundación Ramón Areces un simposio internacional sobre 'Materiales bidimensionales: explorando los límites de la física y la ingeniería'. En colaboración con el Massachusetts Institute of Technology (MIT), científicos de este prestigioso centro de investigación mostraron las propiedades únicas de materiales como el grafeno, de solo un átomo de espesor, y al mismo tiempo más resistente que el acero y mucho más ligero.

Los días 22 y 23 de junio de 2016 organizamos en la Fundación Ramón Areces un simposio internacional sobre 'Materiales bidimensionales: explorando los límites de la física y la ingeniería'. En colaboración con el Massachusetts Institute of Technology (MIT), científicos de este prestigioso centro de investigación mostraron las propiedades únicas de materiales como el grafeno, de solo un átomo de espesor, y al mismo tiempo más resistente que el acero y mucho más ligero.

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Francisco Guinea-Recent advances in graphene research

  1. 1. Recent advances in graphene research Outline l Graphene and Majorana particles l Graphene as an anharmonic membrane l Gauge fields in graphene P. San Jose, CSIC R. Aguado, CSIC, J. Lado,INL, Braga J. Frrnandez_Roissier, INL,Braga A. L. Vázquez de Parga, UAM R. Miranda, Imdea Nano F. Calleja; Imdea Nano H. Ochoa, CSIC M. Garnica, Imdea Nano S. Barja, Imdea Nano J. J. Navarrp, Imdea Nano A. Black, Imdea Nano M. M. Otrokov; DIPC E. V. Chulkov, DIPC A. Arnau, DIPC M. I. Katsnelson (Nijmegen) J. Gonzalez (CSIC) P. San-Jose (CSIC) V. Parente (Imdea) B. Amorim (Braga) R. Roldan (CSIC) L. Chirolli (Imdea) P. Le Doussal (Paris) B. Horowitz (Beersheva) K. Wiese (Paris) C. Gomez-Navarro (UAM) J. Gomez (UAM) G. Lopez-Polin (UAM) F. Perez-Murano (UAM) E. Khestanova (Manchester) I. V. Grigorieva (Manchester) A. K. Geim (Manchester) M. A. H. Vozmediano (CSIC) M. P. López Sancho (CSIC) Madrid, June 22nd, 2016 Materiales bidimensionales: explorando los límites de la ciencia y la ingeniería
  2. 2. Phys. Usp. 44, 131 (2001) 𝑡 𝑡 𝑡 𝑡 𝑡 −𝑡 −𝑡 −𝑡 −𝑡 −𝑡 +Δ +Δ +Δ +Δ −Δ −Δ −Δ −Δ −Δ +Δ electrons holes 𝐻 = 𝑡 𝑛=1 𝑛=𝑁−1 𝑐 𝑛+1 † 𝑐 𝑛 + 𝑐 𝑛 † 𝑐 𝑛+1 + Δ 𝑛=1 𝑛=𝑁−1 𝑐 𝑛+1 † 𝑐 𝑛 † + 𝑐 𝑛 𝑐 𝑛+1 The Kitaev model 𝐻± 𝜙 = 0 𝑡 ± Δ + 𝑡 ∓ Δ 𝑒 𝑖𝜙 𝑡 ± Δ + 𝑡 ∓ Δ 𝑒−𝑖𝜙 0 𝑡 + Δ 𝑡 − Δ 𝑡 + Δ 𝑡 − Δ 𝑡 + Δ 𝑡 − Δ 𝑡 + Δ 𝑡 − Δ 𝑡 + Δ 𝑡 − Δ 𝛾𝑛 = 𝑐 𝑛 † + 𝑐 𝑛 2 , 𝛾𝑛 = 𝑐 𝑛 † − 𝑐 𝑛 2𝑖 𝜖 𝜙 = ± 2 𝑡2 + Δ2 + 2 𝑡2 − Δ2 cos 𝜙 𝐻± = 2𝑖 𝑡 ± Δ 𝑛=1 𝑛= 𝑁−1 2 𝛾2𝑛−1 𝛾2𝑛 + 2𝑖 𝑡 ∓ Δ 𝑛=1 𝑛= 𝑁−1 2 𝛾2𝑛 𝛾2𝑛+1 One dimensional spinless superconductor
  3. 3. Phys. Rev. Lett. 105, 077001(2010) Phys. Rev. Lett. 105, 177002 (2010). Realization of the Kitaev model l One dimensional system l Strong spin-orbit coupling l Magnetic field l Superconductivity
  4. 4. Science 336, 1003 (2012) Science 346, 602 (2014) Phys. Rev. Lett. 109, 237003 (2012) Experiments
  5. 5. arXiv:1511.05161 Quantum link between QDev in Denmark and QuTech in Holland Research collaboration What do you do when you have two of the leading giants in the same research field? – compete with each other? – fight each other? – no, you start collaborating. The Center for Quantum Devices, QDev at the Niels Bohr Institute at the University of Copenhagen and QuTech at Delft University of Technology in Holland have therefore entered into an international partnership in the research of quantum technologies. The collaboration will be celebrated with an official ceremony with the attendence of ministers from both countries and the Dutch royal couple. Recent developments
  6. 6. arXiv:1603.04069
  7. 7. Edge states: the Integer Quantum Hall Regime Graphene l 2D metal l Excellent platform for QHE physics. l Very weak spin-orbit coupling l High degeneracy (spin and valley) l No superconductivity
  8. 8. Phys. Rev. Lett. 98, 157003 (2007) Phys. Rev. Lett. 110, 186805 (2013) Edge modes: theory Phys. Rev. Lett. 100, 096407 (2008)
  9. 9. Phase diagram of a Superconductor-graphene IQHE-Superconductor junction
  10. 10. Critical current, and Fraunhofer pattern for different phases Spectrum of the SNS junction, as measured by a normal point contact
  11. 11. Recent experiments Science 352, 966 (2016)
  12. 12. 0 50 100 150 200 0.1 0.2 0.3 0.4 0.5 0.6 Δ 𝑠𝑐 Δ 𝐴𝐹 E 𝑐 0 50 100 150 200 0.2 0.4 0.6 0.8 1.0 t t’ SC SCAF Generic SC-AF edge Flat band of midgap states Confirmed by analytical calculations. Also in 3D Square lattice Almost perfect nesting 3 2 1 1 2 3 k 0.4 0.2 0.2 0.4 E
  13. 13. 0 50 100 150 200 0.1 0.2 0.3 0.4 0.5 0.6 Δ 𝑠𝑐 Δ 𝐴𝐹 E 𝑐 0 50 100 150 200 0.2 0.4 0.6 0.8 1.0 t t’ SC SCAF Generic SC-AF edge Flat band of midgap states Confirmed by analytical calculations. Also in 3D Square lattice Almost perfect nesting 3 2 1 1 2 3 k 0.4 0.2 0.2 0.4 E
  14. 14. GRAPHENE’S SUPERLATIVES l Thinnest imaginable material l largest surface area (~2,700 m2 per gram) l strongest material ‘ever measured’ (theoretical limit) l stiffest known material (stiffer than diamond) l most stretchable crystal (up to 20% elastically) l record thermal conductivity (outperforming diamond) l highest current density at room T (106 times of copper) l completely impermeable (even He atoms cannot squeeze through) l highest intrinsic mobility (100 times more than in Si) l conducts electricity in the limit of no electrons l lightest charge carriers (zero rest mass) l longest mean free path at room T (micron range)
  15. 15. Bgraphene =22 eV Å-2 = 352 N/m Bdiamond x d=52.4 N/m T=300K L=1Km Why are there two dimensional crystals?            d L B Tk uLu B log0  Thermal fluctuations:
  16. 16. Elastic properties of graphene courtesy of M. M. Fogler
  17. 17. 𝐸𝑇 𝜅2 𝑞2 𝐸 ≃ 22 eVÅ−2 𝜅 ≃ 1 eV 𝑇 = 300K 𝑞−1 = 𝜅 𝐸𝑇 ≃ 1.3 Å
  18. 18.                                                                   22222 2 222 2222 2 2 2 22 1 22 22222 hh uu h u h urd hh uurdhrd t h rdH yx xyyx y yy x xx yx yyxx     Two dimensional membranes Out of plane displacements lead to changes in area h L L h L 2 2  Kinetic Bending Stretching Shear Two dimensional crystaline membranes are intrinsically anharmonic
  19. 19. Thermal expansion     2 24 22 1 2 qu quq q q q q              Flexural phonon Grüneisen parameter        22 3 log 8 Y kB     Thermal expansion In plane strains change the frequency of out of plane modes Negative thermal expansion coefficient Low T High T Lattice constant Bindingenergy Thermal expansion
  20. 20. Substrate effects Gapped flexural modes Thermal expansion
  21. 21. Out of plane fluctuations screen the in plane elastic constants 2 221 hcuYcE                        221 log   cuYc T TF 2 22 2 2 2 1     TY u F Y    
  22. 22. Load 2 Experiments
  23. 23. C D 1 2 N SiO2 Au A B 0.5 1.0 1.5 2.0 2.5 0 4 8 z(nm) x (µm) Si SiO2 Au A I Ar+F  Si SiO2 Au 2a Graphene Experiments 1500 2000 2500 3000 0 100 200 300 Counts Raman Shift (cm -1 ) <E2D>=33611 N/m <E2D>=53852 N/m C 0.9 1.2 1.5 1.8 300 400 500 600 0 10 20 30 Counts E2D (N/m) E3D (TPa) 0 25 50 75 0.0 0.2 0.4 0.6 F(N)  (nm) B A GD 0 2x10 13 4x10 13 6x10 13 200 300 400 500 600 0.0 0.3 0.6 0.9 1.2 1.5 1.8 0.6 0.9 1.2 1.5 1.8 E3D (TPa) E2D (N/m) Defects/cm 2 Defects (%) 0 2x10 12 4x10 12 6x10 12 3x10 13 4x10 13 0.6 1.2 1.8 0.00 0.05 0.10 0.15 1.0 FractureForce(N) Defects/cm 2 Defects (%) A B
  24. 24. The self consistent screening approximation J. Physique, 48, 1085 (1987) 4 2 q YT qd                                         qpGqGqpqqdpI qIb b qb pqGqpPqqbqdq qqGqG T      222 2 0 0 22 2 1 0 1 28 1 31 2 2   = = = + + +       358.0 821.0 ,      u u qqq qq       Power law divergences Self consistent theory, valid in high dimensions Agrees well with numerical simulaions
  25. 25. Vacancies and flexural modes      , 1 , 42 qq qG                       0 log 0 2 24 2 22 h a n hn V V      T-matrix approximation infinite mass vacancies 21 44            Vn    localization length l Vacancies localize flexural modes l Long wavelength flexural modes do not contribute to the screening of the elastic constants
  26. 26. 0 2x10 13 4x10 13 6x10 13 200 300 400 500 600 0.0 0.3 0.6 0.9 1.2 1.5 1.8 0.6 0.9 1.2 1.5 1.8 E3D (TPa) E2D (N/m) Defects/cm 2 Defects (%) 0 2x10 12 4x10 12 6x10 12 3x10 13 4x10 13 0.6 1.2 1.8 0.00 0.05 0.10 0.15 1.0 FractureForce(N) Defects/cm 2 Defects (%) A B                    VV ncn R KY u 2 0 2 2 0 2 1 1 11   geometric factor intrinsic localization length percolation 1 0 0 nm10020    Fk 
  27. 27. 20 30 40 50 60 70 80 0,00 0,05 0,10 0,15 Prestress(N/m) Temperature (ºC) Pristine Irradiated Thermal Expansion Coefficient: · Pristine: -9.4 x 10 -6 K-1 · Irradiated (LD ~ 5.5 nm): -1 x 10 -6 K- 1 Graphene thermal expansion coefficient 20 40 60 80 100 120 0,05 0,10 0,15 0,20 Prestress(N/m) Temperature (ºC) Thermal Expansion Coefficient: · Pristine: -6.2 x 10 -6 K-1 · Irradiated (LD ~ 5 nm): -1.1 x 10 -6 K-1 Membrane 1 Membrane 2 Pristine Irradiated LD : Mean distance between defects as measured by Raman
  28. 28. Young modulus and induced strains Young modulus measured by Raman is two times larger than the one measured by indentation arXiv:1504.05521
  29. 29. arXiv:1504.05521 Recent experiments
  30. 30. Ripples in graphene l Quenched (non thermal) ripples in suspended samples lLateral scale ~102 − 103 Å l Vertical scale ~10Å Instability due to the coupling to low energy electron-hole pairs? Also: wrinkles induced by absorbates, non trivial fixed point?
  31. 31. Strong and non uniform, spatially varying Spin-Orbit coupling in Pb-intercalated graphene leads to the observation of sharp pseudo-Landau levels without a external magnetic field C. L. Kane and E. J. Mele, Quantum Spin Hall in Graphene, Phys. Rev. Lett. 95, 226801 (2005). C. Weeks, J. Hu, J. Alicea, M. Franz, and R. Wu, Engineering a Robust Quantum Hall State in Graphene via Adatom Deposition, Phys. Rev. X 1, 021001 (2011). Experiments: B. Özyilmaz, et al., Nature Comm. 5, 4875 (2014).
  32. 32. Vs= 1 V , It= 0.9 nA 4.6 K Periodically Rippled Graphene on Ir(111) Wavelength ~ 25.2 ± 0.4 Å Corrug ~0.2 Å
  33. 33. Pb evaporated on gr/Ir(111) at 800K Partial Intercalation of Pb below graphene Intercalation of Pb /Graphene/Ir(111)
  34. 34. Atomic arrangement in Pb-intercalated Gr/Ir(111)
  35. 35. Graphene/Pb/Ir(111): Landau Levels without a magnetic field ED EF 4.6 K
  36. 36. Graphene/Pb/Ir(111) versus gr/Ir(111) Large Spin-Orbit coupling Small Spin-Orbit coupling δISO/δx pn
  37. 37. F. G., M. I. Katsnelson, A. K. Geim, Nature Phys. 6, 30 (2010) Scaling of resonances observed with STM Bubbles and strains in graphene Topography and spectroscopy of bubbles in graphene on Pt Comparison of theory and experiment
  38. 38. DFT calculations l Lead shows SO splittings of order 1 eV l Lead and graphene bands are strongly hybridized near the chemical potential
  39. 39. Effective Dirac-like Hamiltonian 𝐻 = 𝑣 𝐹Σ ∙ 𝑘 − 𝐴 ± 𝐴0 𝑠 𝑦 𝐴 = 𝐴 𝑥 𝑠 𝑦, 𝐴 𝑦 𝑠 𝑥 Non-abelian gauge potential Scalar potential Σ = ±𝜎 𝑥, 𝜎 𝑦 𝐴0 DFT (in blue) and tight-binding (in red) band structure calculation for a distance between graphene and the Pb adatoms of 2.7 Å, with spin-orbit coupling. The right panel zooms into the Dirac point region.
  40. 40. Inhomogeneous SO texture Smooth change of the SO coupling
  41. 41. The non-uniform spatial variation of the S-O coupling and related gauge fields leads to electronic confinement and pseudo-Landau levels…. … but associated to effective magnetic fields with opposite sign for each in plane spin polarization
  42. 42. Non trivial one dimensional channels at boundaries of 2D materials l Non trivial edge modes are possible at SC-graphene interfaces, when graphene is in the Integer Quantum Hall regime. l Generic states between superconductors and 2D antiferromagnets l Intercalated Pb induces resonances in the density of states of graphene l A large, inhomogeneous, spin-orbit coupling is induced l Spin-orbit coupling is a source of gauge fields Giant enhancement of spin-orbit coupling in graphene l Graphene is a highly anisotropic membrane. l The elastic properties of graphene are sample dependent Graphene and other 2D systems as elastic membranes
  43. 43. (interacting) Majoranas from way back:

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