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.
Modern Roaming for Notes and Nomad – Cheaper Faster Better Stronger
Francisco Guinea-Recent advances in graphene research
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
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
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
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. Phys. Rev. Lett. 98, 157003 (2007)
Phys. Rev. Lett. 110, 186805 (2013)
Edge modes: theory
Phys. Rev. Lett. 100, 096407 (2008)
9.
10. Phase diagram of a Superconductor-graphene IQHE-Superconductor junction
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. 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
15. 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)
16. 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:
31. 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?
32. 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).
33.
34. 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
39. 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
40. DFT calculations
l Lead shows SO
splittings of order 1 eV
l Lead and graphene
bands are strongly
hybridized near the
chemical potential
41. 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.
43. 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
44. 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