sub-lattice breaking symmetry effects on the electronic...
TRANSCRIPT
Reza Asgari
Sub-Lattice Breaking Symmetry Effects On The Electronic Properties of
Graphene Sheets
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)
The Intense Interest in Graphene!!!
Statistics of searches on all nature.com websites
http://grapheneindustries.com
Tight Binding Calculations for Graphene
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)
Chirality
Helicity:
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:
Alessandra Lanzara’s group, Nature Material
6, 770 (2007)
Graphene on SiCGap is 0.26 eV
Gap Generating By Sub-lattice Symmetry BreakingExperimental Observation
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
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)
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
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
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)
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
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)
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
The Inelastic Mean Free Path
A. Qaiumzadeh, F. K. Joibari, and R. Asgari, arXiv: 0810.4681, Submitted to PRB
The Band Gap Polarization
A. Qaiumzadeh, and R. Asgari, submitted to New J. Physics
The Spectral Function
A. Qaiumzadeh, and R. Asgari, submitted to New J. Physics