Graphene Nanoribbons
and the Experimentalist who used Mathematica

Peter H. Jacobse	Department of Physics, University of California, Berkeley

Peter Herman Jacobse

Physicist: Working on graphene nanoribbons

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Dynamic[Show[Switch[choice,"Rijksuniversiteit Groningen",rug,"Universiteit Utrecht",uu,"University of California, Berkeley",ucb,"Crommie group",crommiegroup,_,mathemaTBlogo],ImageSize->Large]]}]

Creator of MathemaTB

mathemaTBlogo

Get["C:\\MathemaTB\\MathemaTB.m"]

Graphene

* 2004 Manchester, UK

PrintTemporary[Show[graphenepaper]];Pause[4];

Carbon in two dimensions (flattest material possible)

{R,latvec}=BuildLattice["Honeycomb",Size->1.42]/@{"Geometry","LatticeVectors"};
MoleculePlot[R,LatticeVectors->latvec,Copies->{20,20,1},PlotRange->{{-10,10},{-10,10},{-1,1}}]

Graphene

Electrons behave as massless particles

Almost like photons

Replacement for silicon?

a1={-Sqrt[3]/2,1/2};a2={0,1};
Plot3D[Table[sgn Abs[1+Exp[I k.a1]+Exp[I k.a2]]/.{k->{kx,ky}},{sgn,{-1,1}}],{kx,-6,6},{ky,-6,6},AspectRatio->1,PlotPoints->50]

NO: no band gap

Required for transistors and diodes

Graphene Nanoribbons (GNRs)

* 2010 Zurich, Switzerland

PrintTemporary[Show[gnrpaper]];Pause[5];

On-surface synthesis: atomically precise GNR

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PrintTemporary[Table[Show[talirzpaper[[i]],ImageSize->Large],{i,Length[talirzpaper]}]//Column];Pause[8];

Quantum confinement opens band gap

Graphene Nanoribbons (GNRs)

Quantum confinement opens band gap

Row[Show[#,ImageSize->Large]&/@quantized]

Graphene Nanoribbons (GNRs)

Different molecules -> different ribbons -> different properties

Row[Show[#,ImageSize->Large]&/@{zigzaggnr,bananagnr}]

Column[Show[#,ImageSize->Large]&/@topognrpaper]

(spintronic) wires, resistors, ,,,

Heterostructures can be engineered inside single nanoribbons

Single nanoribbon diodes, transistors, ...

MathemaTB: A tool to crunch the QM (of a nanoribbon/molecule/crystal)

Column[Show[#,ImageSize->Large]&/@mappingpaper]

Show[conductance,ImageSize->Large]

Column[Show[#,ImageSize->Large]&/@liebpaper]

Row[Show[#,ImageSize->Large]&/@chevronresults]

MathemaTB

MathemaTB

MathemaTB

moleculeresults

ribbonresults

latticeresults

MathemaTB: implications

mathemaTBlogo

MathemaTB allows me to explore the electronic structure of graphene nanoribbons

MathemaTB is a tool for

Quick and dirty tight-binding calculations just to get a qualitative taste of the underlying physics

But equivalently, a neat tool that allows me to perform quantitative and publication-worthy figures

MathemaTB’s tight-binding: more general than graphene nanoribbons

Made available to the general public

For you, to have as much fun playing around with tight-binding as I have

Acknowledgments

PrintTemporary[Show[crommiegroup,ImageSize->Large]];Pause[8];

Financial support

Dutch Research Council (formerly: Netherlands Organization for Scientific Research)

Utrecht University

Condensed Matter and Interfaces: 		Ingmar Swart, Mark J. J. Mangnus, Stephan J. M. Zevenhuizen, Marlou R. Slot, ...

Theoretical Physics: 				Cristiane Morais Smith, Guido C. P. van Miert, Sander N. Kempkes

Organic Chemistry and Catalysis:		Robertus J. M. Klein Gebbink, Marc-Etienne Moret, Adri van den Hoogenband, ...

University of California, Berkeley

Crommie Group (STM):				Michael F. Crommie, Daniel J. Rizzo, Paul Butler, Ziqin Yue, Gregg Hauser, Yi Chen, Wei Ruan, ...

Fischer Group (chemistry):			Felix R. Fischer, Ryan D. McCurdy, Gregory Veber

Louie Group (theoretical physics):		Steven G. Louie, Jingwei Jiang

My amazing audience!

Easy ways to get MathemaTB: Google MathemaTB or go to peterjacobse.com
(Extensive manual with plenty of examples online)

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conductance=;
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latticeresults=ImageCollage[{,,,,,,}];
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