Sub-Lattice Breaking Symmetry Effects On The Electronic...
Transcript of Sub-Lattice Breaking Symmetry Effects On The Electronic...
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Reza Asgari
Sub-Lattice Breaking Symmetry Effects On The Electronic Properties of
Graphene Sheets
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Rise of Graphene: 2004
K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, Science 306, 666 (2004)
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The Intense Interest in Graphene!!!
Statistics of searches on all nature.com websites
http://grapheneindustries.com
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Tight Binding Calculations for Graphene
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At low energiesthere are only twobands – the πbands that arisefrom the weakbonding betweenthe 2pz orbitals.
Low Energy Electronic Structure
⎟⎟⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
00
&0
0I
Iβ
σσ
α
mpH βα += .Weyl Representation of Dirac equation
Dirac equation
ARPES
S. Reich, J. Maultzsch, C. Thomsen, and P. Ordejon, Phys. Rev. B 66, 035412 (2002)
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Chirality
Helicity:
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1) Breaking of the sub-lattice symmetryDifferent density of particles on the A and B sub-latticesKekule distortion
2) Spin-orbit couplingRashba interactionIntrinsic spin-orbit interactions
3) Finite size effectArmchair Graphene nano-ribbons: Electron confinement Zigzag Graphene nano-ribbons: Edge states
4) …
Graphene, Mind the Gap
Gap/Mass Generation Mechanism:
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Alessandra Lanzara’s group, Nature Material
6, 770 (2007)
Graphene on SiCGap is 0.26 eV
Gap Generating By Sub-lattice Symmetry BreakingExperimental Observation
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Gap Generating By Sub-lattice Symmetry Breakingab initio LDA
S. Kim, J. Ihm, H. J. Choi, and Y. Son, Phys. Rev. Lett. 100, 176802 (2008)
Graphene on SiC substrateGap is 0.2 eV
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Graphene on Ni(111) substrateGap is 0.9 eV
Gap Generating By Sub-lattice Symmetry BreakingExperimental Observation
A. Gruneis and D. V. Vyalikh, Phys. Rev. B 77, 193401 (2008)
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Gap Generating By Sub-lattice Symmetry BreakingExperimental Observation
G. Li, A. Luican, and Y. Andrei, arXiv:0803.4016
Graphene suspended above graphite substrateGap is 10 meV
Guohong Li
Eva Y. Andrei
Adina Luican
Rutgers University
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Gap Generating By Sub-lattice Symmetry Breakingab initio LDA
G. Giovannetti, P. A. Khomyakov, G. Brocks, P. J. Kelly, and J. van den Brink, Phys. Rev B 76, 073103 (2007)
Since LDA generally underestimates the gap, the values that we obtain put a lower bound on the induced band gaps.
Graphene on Boron Nitride substrateGap is 53 meV
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Kekule Distortion
Is Similar to the Weyl Representation of Dirac’s equation
C. Hou, C. Chamon, and C. Mudry, Phys. Rev. Lett. 98, 186809 (2007)
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Different On-Site Energy on the A and B Sub-Lattices
A. Qaiumzadeh and R. Asgari, Phys Rev. B 79, 075414 (2009)
222 2||)(
vEgEE
Lg F
FFhπ
δρ =−= ∑k
k 22 hπρ m
F =
DOS. at Fermi level for 2DESDOS. at Fermi level for Graphene
A. Qaiumzadeh, F. K. Joibari, and R. Asgari, arXiv:0810:4681, Submitted to PRB
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Quasiparticle Renormalized Velocity
A. Qaiumzadeh, F. K. Joibari, and R. Asgari, arXiv:0810:4681, Submitted to PRB
S. Y. Zhou, D. A. Siegel, A. V. Fedorov, and A. Lanzara, Phys. Rev. Lett. 101, 086402 (2008)
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Inelastic Carrier Life Time
A. Qaiumzadeh, F. K. Joibari, and R. Asgari, arXiv: 0810.4681, Submitted to PRB
Is equal to the Fermi golden rule
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The Inelastic Mean Free Path
A. Qaiumzadeh, F. K. Joibari, and R. Asgari, arXiv: 0810.4681, Submitted to PRB
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The Band Gap Polarization
A. Qaiumzadeh, and R. Asgari, submitted to New J. Physics
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The Spectral Function
A. Qaiumzadeh, and R. Asgari, submitted to New J. Physics
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