an experimental tour through some of the unique properties ... · graphene a.k. geim k.s. novoselov...
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An Experimental Tour Through Some of the Unique Properties of Graphene Alberto Morpurgo (University of Geneva)
What is Graphene? Conjugated structures of Carbon atoms
1D 0D 2D
Fullerenes Nanotubes Graphene
Carbon Electronics
Natural Graphite Exfoliation
Transfer Contact
Up to mm size exfoliated graphene
Seeing one-atom layers one at a time
Two inequivalent C atoms
† †
,i ii j iR RR R
i j
A AH Bt B
A simple tight-binding
† †| | 0i i
i j
ik R ik R
k k kR Ri i
e BAe
†
†| | 0
i
j
k R
k
i k R
iik R
B
Ae
OR pseudo spin
Solutions are plane waves
1
2 2
1( )Fv i E
2D Dirac Massless Electrons in Graphene
Linear dispersion relation Zero mass Semimetal Zero-gap semiconductor Two atoms in unit cell Pseudo-spin + Chiral electrons Two K-points New quantum numbers
0( )
0
x y k k
F
x y k k
k ikv E k
k ik
q K k
| ( ) |H E k
Graphene Transistors
Graphene First generation
~ 10.000 cm2/Vs
Carrier Mobility
Silicon Integrated circuits
~ 1.000 cm2/Vs
Novoselov/Geim 2004
Quantum Hall effect of Dirac fermions
Novoselov/Geim; Kim – November 2005
Quantum Dynamics of Electrons
2
( )2
V r Em
0mc
x
Schrödinger: Non-relativistic
Dirac: Relativistic
Ex.: Integrated Electronics
High-Energy Particle Physics
Large area graphene -CVD
Heat Methane at 1000 C
On Copper substrate: Methane decomposes Graphene grows
Polymer layer to support graphene
Remove Copper: wet etching
Final step: Transfer Graphene
Ruoff/Kong/Samsung 2009
Process is robust: after ~ 6 months of lab scale work
Samsung 2009
Produce by the meter – sell by the inch
Roll-to-roll synthesis of graphene
-100 0 100-100
-50
0
50
100
V (
V
)
I (nA)
Ease of access + Gate tuning Superconducting electronics
Spintronics
AM 2007
Van Wees 2007
Single Molecule Dectection
1 molecule donates/remove 1 electron
Detect change of resistivity
Novoselov/Geim 2007
1, 2, 3…More is different
Linear Parabolic Small Band overlap
Tunable band structure
Band structure of conventional Semiconductors
Fixed once you pick a material!
Ex.: Silicon band structure
Band structure of few-layer graphene can be tuned using gates
Double gating Top gate
Bottom gate
Single layer Double layer
Band-gap opening in nano-electronic devices
AM2008
AM2008
Turning bilayers into insulators
2
2
x y
x y
k ikH
k ik
Chiral particles with quadratic dispersion
Topological confinement Martin, Blanter, Morpurgo 2008
Bilayer graphene
Gate electrode
Gate insulator
+V
-V
+V
-V
+V
-V
-V
+V
Lateral confinement in
“Normal” confinement “Topological” confinement
Chiral zero modes
σg ).()(
)(2
2
kikk
ikkH
yx
yx
Topology in k-space
General expression for topological invariant
For 2 x 2 case
Hall conductance
With J. Li, M. Büttiker, I. Martin 2010
g(k) texture on one side of kink
Number of zero-modes is topologically protected
Ex.: Gate tunable light source
Frequency fixed by gap
= hn n
Gallium Arsenide
Graphene bilayer= Tunable gap
Tunable light sources from THz to far infrared
AM2009
Trilayer: the opposite effect
Trilayer graphene Bilayer graphene
Each « layer sequence » is a different material
Yacoby 2010
Cleaning graphene Observing the interactions between Dirac electrons
Exploring new substrates
Lau 2012
Kim 2010
Few atom thick crystals High-quality transistor action in metal dichalcogenides Kis 2011
2μm 2μm
Surface states in topological insulators AM 2011
Gate-induced superconductivity in ZrNCl Iwasa 2010
No
vose
lov
20
11
E. M. Purcell F.Bloch
1952: for their development of new methods for nuclear magnetic precision measurements and discoveries in connection therewith
1944: for his resonance method for recording the magnetic properties of atomic nuclei
Nuclear Magnetic Resonance Imaging
~ 1950
Today
I. Rabi
1977: First MRI scan on humans
Organic Conductors and Semiconductors
2000: for the discovery and development of conductive polymers
H.J. Heeger A.G. MacDiarmid H. Shirakawa
~1975
Today:
OLED TV
Flexible screens
1985: First semiconductor devices (OLEDs, Solar cells)
Graphene
A.K. Geim K.S. Novoselov
2010: for groundbreaking experiments regarding the two-dimensional material graphene
2005
2009
Tomorrow?
Transparent electrodes Molecular sensors High-frequency switches Optical sources Composite materials Photonic devices …
Already demonstrated today