1 Introduction ................................................. 1
1.1 "Crystals" one atom thick: a new paradigm ............... 1
1.2 Roles of symmetry and topology .......................... 7
1.2.1 Linear bands, "massless Dirac" particles ......... 7
1.2.2 "Pseudo-spins" from dual sublattices and
helicity ........................................ 11
1.3 Analogies to relativistic physics backed by
experiment ............................................. 14
1.4 Possibility of carbon ring electronics ................. 17
1.5 Nobel Prize in Physics in 2010 to Andre K. Geim and
Konstantin S. Novoselov ................................ 17
2 Physics in two dimensions (2D) .............................. 20
2.1 Introduction ........................................... 20
2.2 2D electrons on liquid helium and in semiconductors .... 21
2.3 The quantum Hall effect, unique to 2D .................. 24
2.3.1 Hall effect at low magnetic field ............... 25
2.3.2 High field effects .............................. 27
2.3.3 von Klitzing's discovery of the quantized Hall
effect .......................................... 28
2.4 Formal theorems on 2D long-range order ................. 32
2.4.1 Absolute vs. relative thermal motions in 2D ..... 32
2.4.2 The Hohenberg-Landau-Mermin-Peierls-Wagner
Theorem ......................................... 38
2.4.3 2D vs. 2D embedded in 3D ........................ 39
2.4.4 Soft membrane, crumpling instability ............ 40
2.5 Predictions against growth of 2D crystals .............. 44
2.6 "Artificial" methods for creating 2D crystals .......... 45
2.7 Elastic behavior of thin plates and ribbons ............ 45
2.7.1 Strain Nomenclature and Energies ................ 47
2.7.2 Curvature and Gaussian curvature ................ 49
2.7.3 Isometric distortions of a soft inextensible
membrane ........................................ 50
2.7.4 Vibrations and waves on elastic sheets and
ribbons of graphene ............................. 51
2.7.5 An excursion into one dimension ................. 55
3 Carbon in atomic, molecular and crystalline (3D and 2D)
forms ....................................................... 57
3.1 Atomic carbon C: (ls)2(2s)2(2p)2 ....................... 57
3.1.1 Wavefunctions for principal quantum numbers
n = 1 and n = 2 ................................. 58
3.1.2 Linear combinations of n = 2 wavefunctions ...... 60
3.1.3 Two-electron states as relevant to covalent
bonding ......................................... 61
3.1.4 Pauli principle and filled states of the
carbon atom ..................................... 61
3.2 Molecular carbon: CH4, C6H6, С60 ....................... 63
3.2.1 Covalent bonding in simple molecules ............ 63
3.2.2 Methane CH4: tetrahedral bonding ................ 67
3.2.3 Benzene С6Н6: sp2 and π bonding ................. 68
3.2.4 Fullerene C60 ................................... 81
3.2.5 Graphane and Fluorographene ..................... 82
3.3 Crystals: diamond and graphite ......................... 83
3.3.1 Mined graphite .................................. 83
3.3.2 Synthetic "Kish" graphite ....................... 83
3.3.3 Synthetic HOPG: Highly Oriented Pyrolytic
Graphite ........................................ 84
4 Electron bands of graphene .................................. 86
4.1 Semimetal vs. conductor of relativistic electrons ...... 86
4.2 Linear bands of Wallace and the anomalous neutral
point .................................................. 90
4.2.1 Pseudo-spin wavefunction ......................... 90
4.3 L. Pauling: graphene lattice with "1/3 double-bond
character" ............................................. 92
4.4 McClure: diamagnetism and zero-energy Landau level ..... 92
4.5 Fermi level manipulation by chemical doping ............ 93
4.6 Bilayer graphene ....................................... 93
5 Sources and forms of graphene ............................... 98
5.1 Graphene single-crystals, flakes and cloths ............ 98
5.1.1 Micro-mechanically cleaved graphite ............. 98
5.1.2 Chemically and liquid-exfoliated graphite
flakes ......................................... 101
5.2 Epitaxially and catalytically grown crystal layers .... 108
5.2.1 Epitaxial growth on SiC: Si face vs. С face .... 109
5.2.2 Catalytic growth on Ni or Cu, with transfer .... 112
5.2.3 Large area roll-to-roll production of
graphene ....................................... 114
5.2.4 Grain structure of CVD graphene films .......... 115
5.2.5 Hybrid boron-carbon-nitrogen BCN films ......... 118
5.2.6 Atomic layer deposition ........................ 120
5.3 Graphene nanoribbons .................................. 121
5.3.1 Zigzag and armchair terminations ............... 122
5.3.2 Energy gap at small ribbon width, transistor
dynamic range .................................. 123
5.3.3 Chemical synthesis of perfect armchair
nanoribbons .................................... 125
6 Experimental probes of graphene ............................ 128
6.1 Transport, angle-resolved photoemission
spectroscopy .......................................... 128
6.2 Optical, Raman effect, thermal conductivity ........... 129
6.3 Scanning tunneling spectroscopy and potentiometry ..... 132
6.4 Capacitance spectroscopy .............................. 133
6.5 Inverse compressibility with scanning single
electron transistor (SSET) ............................ 136
7 Mechanical and physical properties of graphene ............. 139
7.1 Experimental aspects of 2D graphene crystals .......... 139
7.1.1 Classical (extrinsic) origin of ripples and
wrinkles in monolayer graphene ................. 141
7.1.2 Stability of graphene in supported samples up
to 30 inches ................................... 146
7.1.3 Phonon dispersion in graphene .................. 150
7.1.4 Experimental evidence of nanoscale roughness ... 158
7.1.5 Electrical conductivity of graphene in
experiment ..................................... 164
7.2 Theoretical approaches to "intrinsic corrugations" .... 169
7.3 Impermeable even to helium ............................ 176
7.4 Nanoelectromechanical resonators ...................... 178
7.5 Metal-insulator Mott-Anderson transition in
ultrapure screened graphene ........................... 179
7.6 Absence of "intrinsic ripples" and "minimum
conductivity" in graphene ............................. 183
8 Anomalous properties of graphene ........................... 185
8.1 Sublimation of graphite and "melting" of graphene ..... 185
8.2 Electron and hole puddles, electrostatic doping and
the "minimum conductivity" ............................ 191
8.3 Giant non-locality in transport ....................... 193
8.4 Anomalous integer and fractional quantum Hall
effects ............................................... 197
8.5 Absence of backscattering, carrier mobility ........... 199
8.6 Proposed nematic phase transition in bilayer
graphene .............................................. 202
8.7 Klein tunneling, Dirac equation ....................... 204
8.8 Superconducting proximity effect, graphene Josephson
junction .............................................. 213
8.9 Quasi-Rydberg impurity states; Zitterbewegung ......... 219
9 Applications of graphene ................................... 223
9.1 Transistor-like devices ............................... 224
9.1.1 High-frequency FET transistors ................. 225
9.1.2 Vertically configured graphene tunneling FET
devices ........................................ 231
9.1.3 The graphene Barristor, a solid state triode
device ......................................... 237
9.2 Phototransistors, optical detectors and modulators .... 237
9.3 Wide area conductors, interconnects, solar cells,
Li-ion batteries and hydrogen storage ................. 244
9.3.1 Interconnects .................................. 248
9.3.2 Hydrogen storage, supercapacitors .............. 249
9.4 Spintronic applications of graphene ................... 251
9.5 Sensors of single molecules, "electronic nose" ........ 254
9.6 Metrology, resistance standard ........................ 255
9.7 Memory elements ....................................... 255
9.8 Prospects for graphene in new digital electronics
beyond CMOS ........................................... 257
9.8.1 Optimizing silicon FET switches ................. 257
9.8.2 Potentially manufacturable graphene FET
devices ........................................ 263
9.8.3 Tunneling FET devices .......................... 264
9.8.4 Manufacturable graphene tunneling FET
devices ........................................ 266
10 Summary and assessment ..................................... 270
References .................................................... 275
Author Index .................................................. 296
Subject Index ................................................. 301
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