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(1)

Electronic Properties

of Nano-Carbon Systems

Carbon Nanotubes Graphene

Intercalated Graphite Networks

Individual Wires Siegmar Roth

s.roth@fkf.mpg.de

(2)

Lecture 2:

10th March 2009

“Electronic Properties of

Graphitic Materials”

(3)

This lecture has 77 viewgraphs, I plan questions and a break

at viewgraphs #22 and #43 Please interrupt at any time

to ask questions

In science questions are more important than the answers

Practice to ask questions!!

(4)

This lecture is given from the

Kirchberg Winterschool IWEPNM

While we are following this lecture, the following talks are scheduled in the main auditory:

J. Hone: “Graphene Mechanics, …, NEMS”

K. Kern: “Doping Effects in Graphene”

J.C. Meyer: “Microscopic Studies of Graphene”

T.F. Heinze: “Optical Spectroscopy of Graphene”

E. Andrei: “Scanning Tunneling in Graphene”

A.C. Ferrari: “Raman Spectroscopy on Graphene”

(5)

“nano”

APS: objects of which at least one of the three dimensions < 100 nm

Better: at least one of the dimensions must be smaller than a characteristic lenth governing the physics of the sample

2DEGs, Quantum Wires and Quantum Dots certainly are “nano”

(6)

Surfaces are “nano”

(7)

Graphitic momolayers are “nano”

(8)

What is graphite?

What are graphitic materials?

What are their electronic properties?

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γραφειν

Photography program

Kalligraphy 1g = 1 gram Pornography grammer

Geography

Graphite

(11)

Etymology tells us:

Graphite is black - otherwise we would not see what we write absorbs light

probally is metallic

Graphite is easy to cleave into chiplets

probably is a layered structure mono-atomic layers?

(12)

The Crysatl Structure of Graphite

(13)

Digression: Crystals

(cryos = cold)

Crystals: faces (regular outside) Æregular inside

periodic arrangement of atoms or molecules

Solid state physics is physics inside a crystal Ideal: crystals should be infinite

If low-dimensional, they should be

alone in the universe

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Questions?

(24)

Ringberg Digression:

Special effects in surfaces and layers:

Hall Effect

Quantum Hall Effect (infinite 2-dim systems,

finite 2-dim systems, edge-effects …)

(25)

Sample Current

Voltage ~ Resistance Hall Voltage Magnetic Field perpendicular to plaine

Hall Effect … Lorentz Force Coriolis Force

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Sweeping Magnetic Field

In practice often: sweep the gate

The gate voltage controls the electron density in the surface layer

(29)

Sample Current

Voltage ~ Resistance Hall Voltage Magnetic Field perpendicular to plaine

Hall Effect … Lorentz Force Coriolis Force

gate changes

electron density in surface layer

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2126 2126

Vg(V) Rxy(h/e2 )

Vg(V) Rxx(k)

T = 1.5 K B = 10 T

sample B:

HOPG

4b. Transport and Raman spectroscopy

on mono- and bilayers of graphite

(32)

Electronic properties of graphitic carbons Graphite is a well-known electric conductor in industry

Contacts in electromotors Galvanic contacts:

Contacts in batteries Contacts for fuel cells Electro steel

Graphitic contact sprays

Graphitized beard hair of Edison’s

servant for filaments in light bulbs

(33)

Why is graphite a metal?

two-dimenssional lattice

1 spare electron per lattice site (like alkali metals)

half-filled electron energy band

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What is special about the hexagonal graphite lattice?

Hexagonal Symmetry

Bi-atomic elementary cell (not a primitive lattice) Note: gaps in the electronic density of states

come from the interaction of the electrons with the crystalline lattice. A non-primitive lattice can create gaps, like in silicon or diamond

(38)

Zero-Gap Semiconductor Linear Dispersion Relation Massless Dirac Equation

Effective Speed of Light ~c/300

“Pocket-QED”

(Quantum Electrodynamics):

Zitterbewegung

Klein Oscillations

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Non-primitive lattice

Two atoms in elementary cell

Superposition of two primitive triagonal lattices Triangular lattice in STM

Excitations on Lattice A only or on Lattice B only Symmetry breaking be edge effects

or by stacking (double and multi-layers, graphite crystals)

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Paso doble

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Questions?

(45)

Graphene

Remember: “ ~ene” is for

conjugated double bonds

Graphene: graphitic monolayers

A theoretical model system since

many decades

(46)

Graphene

Graphitic Monolayers Double-layer Graphene

Oligotichotic Graphene (Oligographene)

Thin graphitic flakes

(47)

Graphene

Graphane

(Alkenes, Alkanes Graphene Ribbons Dangling Bonds

Dangling Bonds saturated by Hydrogen

(48)

How do we make graphene?

Scotch Tape (“Nanomechanical Cleaving”) Defoliation of Graphite

“Epitaxy” on SiC

Epitaxy on Nickel Films

(49)

Hye Jin Park’s Device:

Transparent Conductive Film

of Oligographene Transparency: ~90%, 1kΩ/sq

ITO

Graphene, Oligographene CNT Networks

Chicken Wire

Nano-holes in Copper Sheets (Ebbesen)

(50)

“Fossils”, found by Viera

B. Noyes: Phys. Rev. 24, 190 (1924)

“The Variation of the Resistance of Carbon and Graphite with Temperature”

P.R. Wallace: Phys. Rev. 71, 622 (1947)

“Band Theory of Graphite”

D. Bowen : Phys. Rev. 76, 1878 (1949)

“Theory of Electrical Resistivity of Polycrystalline Graphite”

A.K. Dutta: Phys. Rev. 90, 187 (1953)

“Electrical Conductivity of Single Crystals of Graphite”

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“There is nothing new on earth”

Waves of fashion:

1940’s: Conjugated bonds (benzene, poly-enes, graphene)

1980’s: Layers structures: graphite

chalcogenides intercalation compounds 2000’s: Graphene

(Geim, Kim, …)

Science is a social endeavour, there are waves of fashion …

(52)

Known from the period

of intercalation compounds

Anisotropic conductivity in graphite:

undoped: 104 p-doped: 106 n-doped: 102

(53)

Chen-Wei’s question at the last group meeting:

Why bother to peel-off single layers?

Can’t we simply take the top layer of a single crystal or even

of a HOPG sample?

(54)

What is HOPG?

Highly Oriented Pyrolytic Graphite

Poycrystalline, but the c-axes are parallel Grain size up to several micrometers

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Linear Dispersion Relation

What is the dispersion relation?

Originally the relation between

velocity and wavelenght for a wave package If the velocity depends on the wavelength

(which is true for most waves in most media) the wave package disperses

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Dispersion relation for a free particle:

parabolic!

E = mv

2

E = p

2

/2m

in wave language

E = hν p = 2πhk k =1/ λ

ν = const. k

2

(57)

Parabolic Dispersion Relation

DOS Dispersion Rel.

holes

electrons

(58)

Linear Dispersion Relation:

Light in vacuum

Electrons in graphene

( influence of honeycomb lattice on electrons)

λ ν = c ν = c/λ 1/λ = k

ν = c k

c(electrons in graphene) = c(light in vacuum)/300

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Zero-Gap Semiconductor Dirac Point

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k lin.disp. rel. ν

Dirac Point

Charge Neutrality Pt

“Midgap”

Gating

Bipolar Transport

(62)

Questions?

(63)

Carbon Nanotubes:

Like graphene, but:

curvature

no edge (cylinders)

(detrimental edge effects in graphene

~ 10 nm on each side!)

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Nanotubes:

Rolling (Diameter) Srew-like rolling

helicity

structural indices (n, m)

Chirality (= handedness)

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Semiconducting Nanotubes Metallic Nanotubes

Single-Walled Nanotubes

Multi-Walled Nanotubes

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TEM of Multi-Walled Carbon Nanotube

Electrical conductance mainly in outer wall

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…. Graphene ___ Nanotube Nanotube:

lateral (axial) confinement

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Fullerene

Curved in two directions, Semiconductors

Bandgap ~ 1 eV

C

60

C

70

C

80

higher Fullerenes

carbon nanotubes

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Fullerene Crystals

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Fulleren Molecules:

C

60

has 60 molecular orbitals They spread over about 10 eV (average spacing ~ 160 meV,

but there is a larger gap (~1eV) in the middle

In crystal the molecular orbitals

develop into bands of ~ 0.5 eV width The gap in the middle does not close

Æ Semiconductors

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Fulleren crystals can be doped

(“intercalated”) to become degenerate semiconductors (metal-like),

they even become superconductors

with transition temperatures up to 40 K?

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Endohedral Metallofullerene

Charge transfer from metal to carbon cage

“Doping from inside”

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Dy@C82

(Dy@C82)n@nanotube Dy atom

Metallofullerene Peapod

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Next lecture

Tuesday, 17th March

from Korea University, Seoul Perhaps:

“Carbon Nanotubes:

Synthetic Routs”

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Questions?

참조

관련 문서

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철근에 해당하는 것은 교원 섬유로 짜여진 바구니이며, 그 그물눈을 채우고 있는 시멘트에 해당하는 것이 골질이다.. 골질은 탄산 칼슘·인산 칼슘