graphene and beyond: a perspective

M. S. Dresselhaus, MITMay 30, 2012

Graphene and Beyond:A Perspective

Europe and Korea are launching large graphene programs

The European Union together with other European countries like the UK are investing 1 billion Euros in graphene research.Korea is heavily investing in graphene, with an application emphasis.

2

This conference is lookingbeyond graphene

• Research presentations from the research community

• Breakout sessions• 2D Layered Materials for Electronics Applications• 2D Layered Materials for Structural and Energy

Applications• 2D Layered Materials for Photonic and Sensing

Applications 3

Outline: Graphene and Beyond

• Background

• Introducing Isotopes

• Introducing Dopants

• hBN and Carbon BN Superlattices

• Other Graphene-Like Materials

• Layered Materials Unlike Graphene4

Graphene and the field of carbon research

Number of physics-related publications on carbon

Early history

Fullerenes

Nanotubes

Graphene

Graphiteintercalation compounds

c-c3a a P.R. Wallace, Phys. Rev. 71, 622 (1947)

In 1957-1960 McClure extended the 2D graphene electronic structure to 3D graphite and included the magnetic field dependence

Near the K point

is the overlap integral between nearest neighbor -orbitals (0 values are from 2.9 to 3.1eV).

0

( ) v | |FE linear relation

03v2F

a

and

and

EF

where

J.W. McClure, Phys. Rev., 108:612 (1957); 119:606 (1960)

The Electronic Structure of Graphene

Thickness determined by TEM

“This means that the thinnest films consist of few carbon layers, maybe even just one layer”

Graphene

monolayerbilayer

bilayer

trilayerFirst Brillouin zone

Graphene

Electronic structure

Anomalous Quantum Hall Effect in 1-LG Graphene

• Half integer quantum Hall effect, • Factor of 4 in 4e2/h • Berry’s phase of π

• This work attracted great attention and interest in grapheneNovoselov, Geim et al., Nature 438(197) 2005

Three anomalies:

Thinnest material sheet imaginable…yet the strongest! (5 times stronger than steel and much lighter!)

Graphene is a zero band gap semiconductor: it conducts as well as the best metals, yet its electrical properties can be modulated (it can be switched “ON” and “OFF”)

Very high current densities (equivalent to ~109 Å/cm2)

Superb heat conductor (~5·103 W/m·K)

High mobility (100000 cm2/Vs @RT) Ballistic conduction for hundreds of nm

Bipolar materials (electrons and holes)

Low energy behavior described by Dirac equation

Truly 2D: pure surface with no bulk!

Band structure can be modified by application of electromagnetic fields

Band structure of graphene structures depends on geometry (stacking, size, and atomic structure)

Interesting electron spin dynamics (weak spin orbit, nearly absent hyperfine interaction, etc…)

Mono-layer

Bi-layer

Raman Spectrum for Graphene

Ferrari et al., 2006

Outline: Graphene and Beyond

• Background

• Introducing Isotopes

• Introducing Dopants

• hBN and Carbon BN Superlattices

• Other Graphene-Like Materials

• Layered Materials Unlike Graphene14

M. Kalbac, H. Farhat, J. Kong, P. Janda, L. Kavan, and M. S. Dresselhaus. Nanoletters 11(5):1957-1963 (2011).

Ram

an in

tens

ity, a

. u.

2800260024002200200018001600Raman shift, cm -1

13C 1-LG

12C 1-LG

Ram

an in

tens

ity, a

. u.

2800260024002200200018001600Raman shift, cm -1

13C 1-LG

12C 1-LG

13C/12C 2-LG

Ram

an in

tens

ity, a

. u.

2800260024002200200018001600Raman shift, cm -1

13C 1-LG

12C 1-LG

13C/12C 2-LG

13C/12C 2-LG on BN

Top

Bottom

Isotope labeling in 2-LG

Isotopes allow us to study the behavior of individual layers in bilayer graphene

Costa et al., Carbon 49:4719-4723, 2011

Effect of 13C isotope dopingon the optical phonon modes:

Raman spectroscopy and localization

Raman spectra of SWCNT at different 13C concentrations G band linewidth G as a function

of 13C density

• Phonon lifetimes and localization length affected by the presence of13C isotope impurities.

• Measurable effects in Raman spectroscopy

Phonon Lifetime:

Phonon lifetime due to 13C scattering:

13C density dependence of the lifetime.

Plot of Iqn for the different phonon modes and wavectors.

Decoupling of density dependence and

wavevector

Phonon Scattering Mechanisms: E-PH, PH-PH (T-controlled), PH-IMP

J Rodriguez-Nieva, unpublished

Comparison Theory vs. Experiment:

Spectral width of Costa et al. vs. theory model.

Typical values of lifetimes at G-band:

Natural C:

50% dopedGraphene:

Estimated broadening:

Natural C:

50% doped Graphene:

Comparison with other processes (G-band):Negligible

Comparable

Outline: Graphene and Beyond

• Background

• Introducing Isotopes

• Introducing Dopants

• hBN and Carbon BN Superlattices

• Other Graphene-Like Materials

• Layered Materials Unlike Graphene19

Doped Nanoribbons

F. Lopez-Urias, E. Gracias-Espino, M. S. Dresselhaus, M. Terrones, et al. Unpublished (2012) 20

Similar general behavior for each dopant, but the magnitudes of the bonding interactions differ

275027002650260025502500

x0.9

Ram

an in

tens

ity, a

.u.

1650160015501500

Raman shift, cm-1

Doping of 2-LG

21Electrochemical doping of graphene as observed in Raman scattering

M. Kalbac et al.

Outline: Graphene and Beyond

• Background

• Introducing Isotopes

• Introducing Dopants

• hBN and Carbon BN Superlattices

• Other Graphene-Like Materials

• Layered Materials Unlike Graphene22

Property Graphite/Graphene h-BNDensity 2.1 g/cm3 2.1 g/cm3

Stacking AB AA′C-C/B-N distance 1.421 Å 1.446 ÅBand gap 0 5-6 eVElectrical semimetal insulatorDielectric constant - 3-4

- Ultra-flat- Chemically inert

hexagonal-BN sheetsAtomic force microscope topography images of boron nitride vs SiO2

Root mean squared roughness of BN = 50pm! (50-100pm typical)

boron nitride SiO2

SiO2 rms = 250pm (200-300pm typical)

Ram

an in

tens

ity, a

.u.

2800260024002200200018001600Raman frequency, cm-1

2-LG on BN substrate

Ram

an in

tens

ity, a

.u.

2800260024002200200018001600Raman frequency, cm-1

2-LG on BN substrate

Enhancement is similar for the top and bottom layers

M. Kalbac, O. Frank, et al. J. Phys. Chem. Lett. 2012, DOI: 10.1021/jz300176a

Enhancement of the G mode in Raman spectra of 2-LG

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Mobility= 110,000 cm2/Vs

Two orders of magnitude higher mobility than previous TLG on SiO2: Cracium et al. Nat. Nano. (2009); Zhu et al. PRB (2009)

ABA Trilayer Graphene

Koshino et al. PRB 81:115315 (2010)

BN substrates useful for studying layer stacking

Twisted Bilayer GrapheneVary twist angle Rich set of behaviors

θ

Low twist angles -low energy van Hove singularity-slowdown vF

Lopez et al. PRL 2007Li et al. Nature Physics 2010

Large twist anglesSingle-layer dispersion in both layers

Hass et al. PRL 2008

BN substrates useful for studying twisted layer stacking

Outline: Graphene and Beyond

• Background

• Introducing Isotopes

• Introducing Dopants

• hBN and Carbon BN Superlattices

• Other Graphene-Like Materials

• Layered Materials Unlike Graphene29

Graphene nanoribbons and flakes are special forms of graphene with edges

Single-layer graphene

Graphene flake

Graphene nanoribbon (GNR)

30

[Nakada, Phys. Rev. B (1996)]

Metallic

Metallic or SemiconductorArmchair ribbons

Zigzag ribbons

1 2 3 4 NN-1N-2

1

23 4 5 6 N-2 N-1

N

From tight binding calculations

Edges in graphene nanoribbonsSemiconductor

Spin-resolved band structure[Son, Nature (2006)]

16-zigzag GN

R

31

32

Dirac cones

Also: B. Lalmi et al. APL 97:223109 (2010)

Silicene

33

34

Nano Lett. 12, 1045 (2012)Also the Germanium-

based 2D-material

Outline: Graphene and Beyond

• Background

• Introducing Isotopes

• Introducing Dopants

• hBN and Carbon BN Superlattices

• Other Graphene-Like Materials

• Layered Materials Unlike Graphene35

36

Molybdenum Sulfide

Single-layer MoS2 is a direct gap semiconductor while multi-layer MoS2 is an indirect gap semiconductor

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Titanium OxideCalcium Niobium

OxideDouble

Hydroxide

Adv. Mater. 22:5082 (2010)

Oxides and HydroxidesTransition metal dichalcogenidesare semiconductors

More complex layered structures including transition metal dichalcogenides are in this class

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Topological Insulators: Bi2Se3, Bi2Te3 …

L. A. Wray et al. (2010)

SCIENCE 325, 278 (2009)

Nano Lett. 10:1209 (2010)

39

Nano Lett. 10, 5032 (2010)

Six varieties of Dirac cones in Bi1-xSbx

• Review of bulk bismuth, bulk Bi1-xSbx

• Construct various Dirac-cone-materials– Single-, bi-, and tri-Dirac-cone– Exact-, quasi-, and semi-Dirac-cone– Dirac cones with various anisotropies

• Different high-symmetry orientations of two-dimensional Bi1-xSbx

Crystal Structure of Bi1-xSbx

• Rhombohedral structure• 2 atoms in each unit cell (red

and green)• 2 FCC sub-lattices elongated

along the trigonal axis and inter-penetrating

• Trigonal axis has three-fold symmetry

• The bisectrix axis and the trigonal axis form a mirror plane.

Carrier-Pockets in the First Brillouin Zone of Bi1-xSbx

• The Brillouin Zone contains 1 T point, 3 three-fold symmetrical Lpoints and 6 H points with inversion symmetry and three-fold symmetry along the T axis

• The bottom of the conduction band is located at the L points• The top of the valence band is at the L point for bulk Bi and at the H

point for bulk Sb, and the exact location depends on x for Bi1-xSbx

Band Structure of Bi1-xSbx in 3D

x<0.07: Semimetalx=0.07~0.09: Indirect-Semiconductorx=0.09~0.15: Direct-Semiconductorx=0.15~0.22: Indirect-Semiconductorx>0.22: Semimetal

Band CrossingJPCS 57:89

• The L-point conduction band edge and valence band edge are close to each other and strongly coupled.

• The dispersion relation at the Lpoints is non-parabolic or linear

Different types of Dirac cones in Bi1-xSbx

• Dirac Point:• Dirac Cone: 2D projection of Dirac Point

– Single-Dirac-cone: Topological Insulator (Bi2Se3 surface states)

– Bi-Dirac-cone: Graphene– Tri-Dirac-cone—Bi1-xSbx

• Quasi-Dirac-cone• Semi-Dirac-cone: semi-classically dispersive

and semi-relativistically dispersive

( )E k v k

S. Tang & M. S. Dresselhaus, Nano Letters 12:2021(2012)

Anisotropic Single-Dirac-Cone in Bi1-xSbx Thin Film

Prediction only—no experiments

*Bisectrix-Oriented Growth—2D

Thermal smearing of ( )fE

, where f is the Fermi-Dirac Distribution. The effective range of smearing is ~kBT

Thermal shearing

3D Phase Diagram

Single-, Bi-, and Tri-Dirac-Cones in Bi1-xSbx

Single-Dirac-Cone Material:Bisectrix Oriented Growth

Bi-Dirac-Cone Material:Binary Oriented Growth

Tri-Dirac-Cone Material:Trigonal Oriented Growth

lz=100 nm

S. Tang & M. S. Dresselhaus, Constructing a Large Variety of Dirac-Cone Materials in the Bi1-xSbx Thin Film System, arXiv:1111.5525v1 (2011)

Group Velocity and Anisotropy

210Diracij lightv c

Bisectrix Growth Oriented lz=300nm

[6061] Growth Oriented lz=300nm

Anisotropy Coefficient

max

min

vv

velocity anisotropy for different in-film directions

Trigonal Growth

Bisectrix Growth

Binary Growth

Controlling the L-point Mini-Gap

Trigonal

Bisectrix

Binary

Eg vs. lz and growth orientation Eg vs. lz and x

Phase Diagrams forThin Film Bi1-xSx

SM: semi-metalISC: indirect-semiconductorDSC: direct-semiconductor

Antimony Composition x

S. Tang & M. S. Dresselhaus, Phase Diagrams of Bi1-xSbx Thin Films with Different Growth Orientations, to be submitted

Summary of Dirac Cone Types

• Predicted construction of different Dirac cones: – single-, bi-, and tri-Dirac-cone materials – exact-, quasi-, and semi-Dirac-cone materials– Dirac cones with different anisotropies

All are based on Bi1-xSbx thin films.

Europe and Korea are launching large graphene programs

The European Union together with other European countries like the UK are investing 1 billion Euros in graphene research.Korea is heavily investing in graphene, with an application emphasis.

52

This conference is lookingbeyond graphene

• Research presentations from the research community

• Breakout sessions• 2D Layered Materials for Electronics Applications• 2D Layered Materials for Structural and Energy

Applications• 2D Layered Materials for Photonic and Sensing

Applications 53