Dominik Kreil, Michaela Haslhofer, and Helga M. Böhm
Received 7 June 2018; revised 6 July 2018; accepted 15 October
2018
References
/
Nuorodos
[1] N.D. Mermin, Crystalline order in two dimensions, Phys. Rev.
176, 250 (1968),
https://doi.org/10.1103/PhysRev.176.250
[2] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang,
S.V. Dubonos, I.V. Grigorieva, and A.A. Firsov, Electric field
effect in atomically thin carbon films, Science
306,
666–669 (2004),
https://doi.org/10.1126/science.1102896
[3]
Statistical Mechanics of Membranes and Surfaces,
eds. D.R. Nelson. T. Piran, and S. Weinberg (World Scientific,
2004),
https://doi.org/10.1142/5473
[4] P.L. Doussal and L. Radzihovsky, Self-consistent theory of
polymerized membranes, Phys. Rev. Lett.
69, 1209 (1992),
https://doi.org/10.1103/PhysRevLett.69.1209
[5] S.V. Morozov, K.S. Novoselov, M.I. Katsnelson, F. Schedin,
L.A. Ponomarenko, D. Jiang, and A.K. Geim, Strong suppression of
weak localization in graphene, Phys. Rev. Lett.
97,
016801 (2006),
https://doi.org/10.1103/PhysRevLett.97.016801
[6] A. Vakil and N. Engheta, Transformation optics using
graphene, Science
332, 1291–1294 (2011),
https://doi.org/10.1126/science.1202691
[7] B. Yao, Y. Liu, S.-W. Huang, C. Choi, Z. Xie, J.F. Flores,
Y. Wu, M. Yu, D.-L. Kwong, Y. Huang, et al., Broadband
gate-tunable terahertz plasmons in graphene heterostructures,
Nat. Photonics
12, 22 (2018),
https://doi.org/10.1038/s41566-017-0054-7
[8] F. J. Garcia de Abajo, Graphene plasmonics: challenges and
opportunities, ACS Photonics
1, 135–152 (2014),
https://doi.org/10.1021/ph400147y
[9] Z. Fei, G.O. Andreev, W. Bao, L.M. Zhang, A.S. McLeod, C.
Wang, M.K. Stewart, Z. Zhao, G. Dominguez, M. Thiemens, et al.,
Infrared nanoscopy of Dirac plasmons at the graphene-SiO
2
interface, Nano Lett.
11, 4701–4705 (2011),
https://doi.org/10.1021/nl202362d
[10] H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F.
Guinea, P. Avouris, and F. Xia, Damping pathways of mid-infrared
plasmons in graphene nanostructures, Nat. Photonics
7,
394 (2013),
https://doi.org/10.1038/nphoton.2013.57
[11] T. Low and P. Avouris, Graphene plasmonics for terahertz to
mid-infrared applications, ACS Nano
8, 1086–1101 (2014),
https://doi.org/10.1021/nn406627u
[12] A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov,
and A.K. Geim, The electronic properties of graphene, Rev. Mod.
Phys.
81, 109 (2009),
https://doi.org/10.1103/RevModPhys.81.109
[13] L.D. Landau, On the vibrations of the electronic plasma,
Zh. Eksp. Teor. Fiz.
10, 25 (1946)
[14] S.A. Wolf, D.D. Awschalom, R.A. Buhrman, J.M. Daughton, S.
von Molnar, M.L. Roukes, A.Y. Chtchelkanova, and D.M. Treger,
Spintronics: a spin-based electronics vision for the future,
Science
294, 1488–1495 (2001),
https://doi.org/10.1126/science.1065389
[15] A. Agarwal, M. Polini, G. Vignale, and M.E. Flatté,
Long-lived spin plasmons in a spin-polarized two-dimensional
electron gas, Phys. Rev. B
90, 155409 (2014),
https://doi.org/10.1103/PhysRevB.90.155409
[16] D. Kreil, R. Hobbiger, J.T. Drachta, and H.M. Böhm,
Excitations in a spin-polarized two-dimensional electron gas,
Phys. Rev. B
92, 205426 (2015),
https://doi.org/10.1103/PhysRevB.92.205426
[17] R. Hobbiger, J.T. Drachta, D. Kreil, and H.M. Böhm,
Phenomenological plasmon broadening and relation to the
dispersion, Solid State Commun.
252, 54–58 (2017),
https://doi.org/10.1016/j.ssc.2017.01.011
[18] D. Pines,
Elementary Excitations in Solids (Perseus
Books, Massachusetts, 1999),
https://www.crcpress.com/Elementary-Excitations-In-Solids/Pines/p/book/9780738201153
[19] C. Lee, J.Y. Kim, S. Bae, K.S. Kim, B.H. Hong, and E.J.
Choi, Optical response of large scale single layer graphene,
Appl. Phys. Lett.
98, 071905 (2011),
https://doi.org/10.1063/1.3555425
[20] M. Bonitz,
Quantum Kinetic Theory (Springer, 1998),
https://www.springer.com/gp/book/9783319241197
[21] C.F. Hirjibehedin, A. Pinczuk, B.S. Dennis, L.N. Pfeiffer,
and K.W. West, Evidence of electron correlations in plasmon
dispersions of ultralow density two-dimensional electron
systems, Phys. Rev. B
65, 161309 (2002),
https://doi.org/10.1103/PhysRevB.65.161309
[22] F. Perez, Spin-polarized two-dimensional electron gas
embedded in a semi-magnetic quantum well: Ground state, spin
responses, spin excitations, and Raman spectrum, Phys. Rev. B
79,
045306 (2009),
https://doi.org/10.1103/PhysRevB.79.045306
[23] S. Abdelouahed, A. Ernst, J. Henk, I.V. Maznichenko, and
I. Mertig, Spin-split electronic states in graphene: Effects due
to lattice deformation, Rashba effect, and adatoms by first
principles, Phys. Rev. B
82, 125424 (2010),
https://doi.org/10.1103/PhysRevB.82.125424
[24] D.V. Fedorov, M. Gradhand, S. Ostanin, I.V. Maznichenko,
A. Ernst, J. Fabian, and I. Mertig, Impact of electron-impurity
scattering on the spin relaxation time in graphene: A
first-principles study, Phys. Rev. Lett.
110, 156602
(2013),
https://doi.org/10.1103/PhysRevLett.110.156602
[25] M.W.C. Dharma-Wardana, Coulomb interactions of massless
Dirac fermions in graphene; pair-distribution functions and
exchange-driven spin-polarized phases, Solid State Comm.
140,
4–8 (2006),
https://doi.org/10.1016/j.ssc.2006.07.044
[26] D.R. Cooper, B. D'Anjou, N. Ghattamaneni, B. Harack, M.
Hilke, A. Horth, N. Majlis, M. Massicotte, L. Vandsburger, E.
Whiteway, et al., Experimental review of graphene, ISRN Cond.
Matt. Phys.
2012, Article ID 501686 (2012),
https://doi.org/10.5402/2012/501686
[27] B. Wunsch, T. Stauber, F. Sols, and F. Guine, Dynamical
polarization of graphene at finite doping, New J. Phys.
8,
318 (2006),
https://doi.org/10.1088/1367-2630/8/12/318
[28] N. Iwamoto, Static local-field corrections of
two-dimensional electron liquids, Phys. Rev. B
43,
2174–2182 (1991),
https://doi.org/10.1103/PhysRevB.43.2174
[29] G. Giuliani and G. Vignale,
Quantum Theory of the
Electron Liquid (Cambridge University Press, 2005),
https://doi.org/10.1017/CBO9780511619915
[30] R. Asgari, A.L. Subaşı, A.A. Sabouri-Dodaran, and B.
Tanatar, Static local-field factors in a two-dimensional
electron liquid, Phys. Rev. B
74, 155319 (2006),
https://doi.org/10.1103/PhysRevB.74.155319
[31] J. Moreno and D.C. Marinescu, Local-field factors in a
polarized two-dimensional electron gas, Phys. Rev. B
68(19),
195210 (2003),
https://doi.org/10.1103/PhysRevB.68.195210
[32] H.M. Böhm, R. Holler, E. Krotscheck, and M. Panholzer,
Dynamic many-body theory: Dynamics of strongly correlated Fermi
fluids, Phys. Rev. B
82(22), 224505 (2010),
https://doi.org/10.1103/PhysRevB.82.224505
[33] M. Panholzer, M. Gatti, and L. Reining, Nonlocal and
nonadiabatic effects in the charge-density response of solids: A
time-dependent density-functional approach, Phys. Rev. Lett.
120(16),
166402 (2018),
https://doi.org/10.1103/PhysRevLett.120.166402
[34] M. Gibertini, A. Singha, V. Pellegrini, M. Polini, G.
Vignale, A. Pinczuk, L.N. Pfeiffer, and K.W. West, Engineering
artificial graphene in a two-dimensional electron gas, Phys.
Rev. B
79, 241406 (2009),
https://doi.org/10.1103/PhysRevB.79.241406
[35] M. Polini, F. Guinea, M. Lewenstein, H.C. Manoharan, and
V. Pellegrini, Artificial honeycomb lattices for electrons,
atoms and photons, Nat. Nanotechnol.
8, 625 (2013),
https://doi.org/10.1038/nnano.2013.161
[36] S. Wang, D. Scarabelli, L. Du, Y.Y. Kuznetsova, L.N.
Pfeiffer, K.W. West, G.C. Gardner, M.J. Manfra, V. Pellegrini,
S.J. Wind, et al., Observation of Dirac bands in artificial
graphene in small-period nanopatterned GaAs quantum wells, Nat.
Nanotechnol.
13, 29 (2018),
https://doi.org/10.1038/s41565-017-0006-x
[37] Note 1. The parameter
rS , termed
α
in graphene, has the constant value of approx. 2.2
[38] Y. Liu, R.F. Willis, K.V. Emtsev, and T. Seyller, Plasmon
dispersion and damping in electrically isolated two-dimensional
charge sheets, Phys. Rev. B
78, 201403 (2008),
https://doi.org/10.1103/PhysRevB.78.201403
[39] D. Kreil, C. Staudinger, K. Astleithner, and H.M. Böhm,
Resonant and anti-resonant modes of the dilute, spin-inbalanced,
two-dimensional electron liquid including correlations, Contrib.
Plasm. Phys.
58, 179–188 (2018),
https://doi.org/10.1002/ctpp.201700147
[40] U. Fano, Sullo spettro di assorbimento dei gas nobili
presso il limite dello spettro d'arco, Nuovo Cimento
12,
154–161 (1935),
https://doi.org/10.1007/BF02958288
[41] F.J. Garcia de Abajo, Colloquium: Light scattering by
particle and hole arrays, Rev. Mod. Phys.
79, 1267
(2007),
https://doi.org/10.1103/RevModPhys.79.1267
[42] J. Aizpurua, T. Taubner, F.J. García de Abajo, M. Brehm,
and R. Hillenbrand, Substrate-enhanced infrared near-field
spectroscopy, Opt. Expr.
16, 1529–1545 (2008),
https://doi.org/10.1364/OE.16.001529
[43] Z. Fei, private communication