Flatland:Physics in 2-dimensional world

Hyeonsik Cheong

Department of Physics

Sogang University

Edwin Abbott Abbott

(1884)

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Flatland: THE FILM (2007)

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Dimensionality

• Our world is 3 dimensional.

• Einstein says, “No! There are 4 dimensions!”

• Superstring Theory: No, the world is in 10-

dimensional space!

High-dimensional Physics?

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Low Dimensional Physics

• Thin film, Quantum Well (2D)

2~10 nm

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Low Dimensional Physics

• Quantum Wire, Nanowire, Carbon

Nanotube (1D)

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Low Dimensional Physics

• Quantum Dot, Nanoparticle (0D)

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Physics in ‘real’ 2 dimension?

Ultimate 2D material.

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Graphene

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graphene

Diamond Graphite

Graphene

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Graphene – The Beginning

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Nobel Prize in Physics - 2010

Andre K. Geim Konstantin S. Novoselov

“for groundbreaking experiments regarding the two-dimensional material graphene”

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Nobel Prize in Physics - 2010

Scotch Tape!

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Peculiar Band Structure

Dirac pointkx

ky

E( ) FE vk k

2 22 21

2 2 2

pE mv k

m m ‘Nomal’ particles:

2 4 2 2 2 2 2 2E m c p c c m c k Relativistic particle:

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“Massless Dirac Fermion”

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Dirac Equation

Klein Tunneling

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Zeitschrift fur Physik 53, 157 (1929)

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Half-integer quantum Hall effect

2 21 1

4( ) , 0, 1, 2,2

xy

e eR n n

h h

K. S. Novoselov et al., Nature 438, 197 (2005)

Y. Zhang et al., Nature 438, 201 (2005)

B = 14 T, T = 4 K

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Graphene’s Superlatives• Thinnest imaginable material

• Largest surface-to-weight ratio (~2700m2 per gram)

• Strongest material ‘ever measured’ (theoretical limit)

• Stiffest known material (stiffer than diamond)

• Most stretchable material (up to 20% elastically)

• Record thermal conductivity (outperforming diamond)

• Highest current density at room T (106 times of copper)

• Highest intrinsic mobility (100 more times than in Si)

• Conducts electricity in the limit of no electrons

• Lightest charge carriers (zero rest mass)

• Longest mean free path at room T (micron range)

• Completely impermeable (even He atoms cannot squeeze through)

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(from Geim’s talk)

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But

Such small pieces of graphene

Are not very useful!

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PDMS

Ni deposition heating carbon deposition cooling graphene formation

Removal of Ni Etching Floating Transfer

Chemical Vapor Deposition (CVD)

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Keun Soo Kim et al.

Nature 457, 706 (2009)

Large area graphene

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Roll-to-Roll Process

Graphene on Cu foil

Polymer support

Cu etchant

Graphene on

polymer support

Target substrateGraphene on target

Released

polymer support

S. Bae et al. Nature Nanotech. 5, 574 (2010)

Large area graphene

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b

Fig. 2

c

1st

2nd

Before

heating

After

heating

a

8 inch

f

d

e

Stencil mask

Screen

printer

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Graphene touch screen

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Applications of graphene

• Replacement for silicon: electronic

devices

• Transparent electrode: display, touch

screen

• Anode material for lithium ion batteries

• Replacement for copper wires

• …

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Limitations of Si devices

• High-capacity, high-speed memories and

CPU’s more, smaller transitors

Heat problem

Typical Si MOSFET Cooling device for CPU

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Graphene’s Superlatives• Thinnest imaginable material

• Largest surface-to-weight ratio (~2700m2 per gram)

• Strongest material ‘ever measured’ (theoretical limit)

• Stiffest known material (stiffer than diamond)

• Most stretchable material (up to 20% elastically)

• Record thermal conductivity (outperforming diamond)

• Highest current density at room T (106 times of copper)

• Highest intrinsic mobility (100 more times than in Si)

• Conducts electricity in the limit of no electrons

• Lightest charge carriers (zero rest mass)

• Longest mean free path at room T (micron range)

• Completely impermeable (even He atoms cannot squeeze through)

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(from Geim’s talk)

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Transparent electrodes• Current technology ITO (Indium Tin Oxide)

on glass

– Scarcity of In

– Durability of glass

– Inflexible

• Advantages of graphene

– Flexible (1-atom thick)

– Good conductivity

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TV Commercial

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Courtesy BH Hong

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The Hype!

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Future Devices

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Other Applications

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ACS Nano, 2011, 5, 1321.

Graphene Application Materials PDP LED Low

Resistivity Graphene Heat Sink

Alibaba.com

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Importance in physics community

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Beyond Graphene

• Limitations of Graphene

– No band gap (Low on/off)

– Made of single element (Carbon)

• New class of 2-dimensional materials

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Beyond Graphene

• Limitations of Graphene

– No band gap (Low on/off)

– Made of single element (Carbon)

• New class of 2-dimensional materials

– Transition metal chalcogenides: MoS2, WSe2, MoTe2, GaSe

– Black Phosphorus, Hexagonal Boron Nitride

– Semiconductor, Superconductor, Magnetic, etc.

– Can complement graphene in future electronics

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Beyond Graphene

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MoS2

Nature Nanotechnology 6, 147 (2011).

On/off ratio > 108

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Black phosphorus

Liu et al., ACS Nano 8(4), 4033 (2014)

Li et al., Nat. Nanotech. 9(5), 372 (2014)

• Least reactive allotrope of phosphorus

• High carrier mobility ~ 1,000 V∙cm2/s & on/off ratio ~105

promising candidate for FET devices

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2D Heterostructures

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2D Heterostructures

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Major Research Centers

Research Centers of 2D Materials

Harvard/Columbia(Philip Kim)

U. Manchester(Geim & Novoselov)

Korea

Singapore

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EU Graphene Flagship

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€1 billion for 10 years

Manchester

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Singapore

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Korea

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Korea

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세계 그래핀 연구의 주요 중심지

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IF 9.611

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EU-Korea Workshop

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Summary

• Graphene and 2D materials show various

novel physical phenomena, many of

which are not understood yet.

• It is the task of the physicists to discover

useful properties among many 2D

materials.

• More research (and more people) is

needed…

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Terima kasih!

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