an experimental tour through some of the unique properties ... · graphene a.k. geim k.s. novoselov...

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