Electronic and optical properties of semiconductor and graphene quantum dots

Abstract

Our recent work on the electronic and optical properties of semiconductor and graphene quantum dots is reviewed. For strained self-assembled InAs quantum dots on GaAs or InP substrate atomic positions and strain distribution are described using valence-force field approach and continuous elasticity theory. The strain is coupled with the effective mass, k · p, effective bond-orbital and atomistic tight-binding models for the description of the conduction and valence band states. The single-particle states are used as input to the calculation of optical properties, with electronelectron interactions included via configuration interaction (CI) method. This methodology is used to describe multiexciton complexes in quantum dot lasers, and in particular the hidden symmetry as the underlying principle of multiexciton energy levels, manipulating emission from biexcitons for entangled photon pairs, and optical control and detection of electron spins using gates. The self-assembled quantum dots are compared with graphene quantum dots, one carbon atom-thick nanostructures. It is shown that the control of size, shape and character of the edge of graphene dots allows to manipulate simultaneously the electronic, optical, and magnetic properties in a single material system.

Keywords

quantum dots / electronic structure / multiexciton / graphene / magnetism

References

[1] L. Jacak, P. Hawrylak, and A. Wojs, Quantum Dots, Berlin: Springer, 1998

[2] D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures, Chichester: Wiley, 1999

[3] P. Hawrylak, and M. Korkusinski, Electronic Properties of Self-Assembled Quantum Dots, in: Single Quantum Dots — Fundamentals, Applications, and New Concepts, edited by P. Michler, Topics in Applied Physics, Berlin: Springer, 2003

[4] M. Korkusinski and P. Hawrylak, Coded qubit based on electron spin, in: Semiconductor Quantum Bits, edited by O. Benson and F. Henneberger, Singapore:Pan Stanford Pub-lishing, 2008

[5] P. Hawrylak, Magnetic ion-carrier interactions in quantum dots, pp 191-220, in: Introduction to the Physics of Diluted Magnetic Semiconductors, edited by Jacek Kossut and Jan Gaj, Springer Series in Materials Science144, 2011

[6] B. Trauzettel, D. V. Bulaev, D. Loss, and G. Burkard, Nat. Phys., 2007, 3(3): 192

[7] P. Hawrylak, Phys. Rev. Lett., 1993, 71(20): 3347

[8] P. Hawrylak, C. Gould, A. Sachrajda, Y. Feng, and Z. Wasilewski, Phys. Rev. B, 1999, 59(4): 2801

[9] M. Ciorga, A. S. Sachrajda, P. Hawrylak, C. Gould, P. Zawadzki, S. Jullian, Y. Feng, and Z. Wasilewski, Phys. Rev. B, 2000, 61(24): R16315

[10] M. Bayer, P. Hawrylak, K. Hinzer, S. Fafard, M. Korkusinski, Z. R. Wasilewski, O. Stern, and A. Forchel, Science, 2001, 291(5503): 451

[11] J. M. Elzerman, R. Hanson, J. S. Greidanus, L. H. Willems van Beveren, S. De Franceschi, L. M. K. Vandersypen, S. arucha, and L. P. Kouwenhoven, Phys. Rev. B, 2003, 67(16): 161308

[12] J. R. Petta, A. C. Johnson, C. M. Marcus, M. P. Hanson, and A. C. Gossard, Phys. Rev. Lett., 2004, 93(18): 186802

[13] M. Pioro-Ladri`ere, M. Ciorga, J. Lapointe, P. Zawadzki, M. Korkusinski, P. Hawrylak, and A. S. Sachrajda, Phys. Rev.Lett., 2003, 91(2): 026803

[14] P. Hawrylak and M. Korkusiński, Solid State Commun., 2005, 136(9-10): 508

[15] L. Gaudreau, S. A. Studenikin, A. S. Sachrajda, P. Zawadzki, A. Kam, J. Lapointe, M. Korkusinski, and P. Hawrylak, Phys. Rev. Lett., 2006, 97(3): 036807

[16] M. Korkusinski, I. P. Gimenez, P. Hawrylak, L. Gaudreau, S. A. Studenikin, and A. S. Sachrajda, Phys. Rev. B, 2007, 75(11): 115301

[17] G. Granger, L. Gaudreau, A. Kam, M. Pioro-Ladrière, S. A. Studenikin, Z. R. Wasilewski, P. Zawadzki, and A. S. Sachrajda, Phys. Rev. B, 2010, 82(7): 075304

[18] L. Goldstein, F. Glas, J. Y. Marzin, M. N. Charasse, and G. Le Roux, Appl. Phys. Lett., 1985, 47(10): 1099

[19] P. M. Petroff, Epitaxial Growth and Electronic Structure of Quantum Dots, in: Single Quantum Dots — Fundamentals, Applications, and New Concepts, edited by P. Michler, Topics in Applied Physics, Berlin: Springer, 2003

[20] Y. Arakawa and H. Sakaki, Appl. Phys. Lett., 1982, 40(11): 939

[21] N. N. Ledentsov, Semicond. Sci. Technol., 2011, 26(1): 014001

[22] S. Fafard, K. Hinzer, S. Raymond, M. Dion, J. McCaffrey, Y. Feng, and S. Charbonneau, Science, 1996, 274(5291): 1350

[23] M. V. Maximov, Yu. M. Shernyakov, A. F. Tsatsul’nikov, A. V. Lunev, A. V. Sakharov, V. M. Ustinov, A. Yu. Egorov, A. E. Zhukov, A. R. Kovsh, P. S. Kop’ev, L. V. Asryan, Zh. I. Alferov, N. N. Ledentsov, D. Bimberg, A. O. Kosogov, and P. Werner, J. Appl. Phys., 1998, 83(10): 5561

[24] S. Fafard, Z. R. Wasilewski, C. Ni Allen, K. Hinzer, J. P. McCaffrey, and Y. Feng, Appl. Phys. Lett., 1999, 75(7): 986

[25] G. Ortner, C. Ni Allen, C. Dion, P. Barrios, D. Poitras, D. Dalacu, G. Pakulski, J. Lapointe, P. J. Poole, W. Render, and S. Raymond, Appl. Phys. Lett., 2006, 88(12): 121119

[26] C. E. Valdivia, E. Desfonds, D. Masson, S. Fafard, A. Carlson, J. Cook, T. J. Hall, and K. Hinzer, Proc. SPIE, 2008, 7099: 709915

[27] A. Wojs and P. Hawrylak, Phys. Rev. B, 1997, 55(19): 13066

[28] A. Wojs and P. Hawrylak, Solid State Commun., 1996, 100(7): 487

[29] P. Hawrylak and A. Wojs, Semicond. Sci. Technol., 1996, 11(11S): 1516

[30] P. Hawrylak, Phys. Rev. B, 1999, 60(8): 5597

[31] M. Bayer, O. Stern, P. Hawrylak, S. Fafard, and A. Forchel, Nature, 2000, 405(6789): 923

[32] P. Hawrylak, Solid State Commun., 2003, 127(12): 793

[33] P. Hawrylak, G. A. Narvaez, M. Bayer, and A. Forchel, Phys. Rev. Lett., 2000, 85(2): 389

[34] J. Lefebvre, P. J. Poole, J. Fraser, G. C. Aers, D. Chithrani, and R. L. Williams, J. Cryst. Growth, 2002, 234(2-3): 391

[35] M. E. Reimer, M. Korkusinski, D. Dalacu, J. Lefebvre, J. Lapointe, P. J. Poole, G. C. Aers, W. R. McKinnon, P. Hawrylak, and R. L. Williams, Phys. Rev. B, 2008, 78(19): 195301

[36] D. Dalacu, K. Mnaymneh, V. Sazonova, P. J. Poole, G. C. Aers, J. Lapointe, and R. CheritonA. J. Spring Thorpe, and R.Williams, Phys. Rev. B, 2010,82(3): 033301

[37] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science, 2004, 306(5696): 666

[38] T. Ihn, S. Gustavsson, U. Gasser, B. Küng, T. Müller, R. Schleser, M. Sigrist, I. Shorubalko, R. Leturcq, and K. Ensslin, Solid State Commun., 2009, 149(35-36): 1419

[39] A. D. GüçlüP. Potasz, O. Voznyy, M. Korkusinski, and P. Hawrylak, Phys. Rev. Lett., 2009, 103(24): 246805

[40] O. Stier, M. Grundmann, and D. Bimberg, Phys. Rev. B, 1999, 59(8): 5688

[41] C. Pryor, J. Kim, L. W. Wang, A. J. Williamson, and A. Zunger, J. Appl. Phys., 1998, 83(5): 2548

[42] W. Sheng and P. Hawrylak, Phys. Rev. B, 2005, 72(3): 035326

[43] G. L. Bir and G. E. Pikus, Symmetry and Strain-Induced Effects in Semiconductors, New York: Wiley, 1974

[44] A. Zhou and W. Sheng, Eur. Phys. J. B, 2009, 68(2): 233

[45] L. R. C. Fonseca, J. L. Jimenez, and J. P. Leburton, Phys. Rev. B, 1998, 58(15): 9955

[46] A. Wojs, P. Hawrylak, S. Fafard, and L. Jacak, Phys. Rev. B, 1996, 54(8): 5604

[47] Z. R. Wasilewski, S. Fafard, and J. P. McCaffrey, J. Cryst. Growth, 1999, 201-202: 1131

[48] S. Raymond, S. Studenikin, A. Sachrajda, Z. Wasilewski, S. J. Cheng, W. Sheng, P. Hawrylak, A. Babinski, M. Potemski, G. Ortner, and M. Bayer, Phys. Rev. Lett., 2004, 92(18): 187402

[49] S. L. Chuang, Physics of Optoelectronic Devices, New York: Wiley, 1995

[50] T. B. Bahder, Phys. Rev. B, 1990, 41(17): 11992

[51] J. K. Cullum and R. A. Willoughby, Lanczos Algorithms for Large Symmetric Eigenvalue Computations, Philadelphia: SIAM, 2002

[52] W. Sheng and J.-P. Leburton, Phys. Stat. Sol. (b), 2003, 237: 394

[53] W. Sheng and J.-P. Leburton, Phys. Rev. B, 2001, 63: 161301(R)

[54] W. Sheng and J.-P. Leburton, Appl. Phys. Lett., 2002, 81(23): 4449

[55] J. I. Climente, M. Korkusinski, G. Goldoni, and P. Hawrylak, Phys. Rev. B, 2008, 78(11): 115323

[56] C. Y. Hsieh, R. Cheriton, M. Korkusinski, and P. Hawrylak, Phys. Rev. B, 2009, 80(23): 235320

[57] M. F. Doty, J. I. Climente, M. Korkusinski, M. Scheibner, A. S. Bracker, P. Hawrylak, and D. Gammon, Phys. Rev. Lett., 2009, 102(4): 047401

[58] Y. C. Chang, Phys. Rev. B, 1988, 37(14): 8215

[59] J. P. Loehr, Phys. Rev. B, 1994, 50(8): 5429

[60] S. J. Sun and Y. C. Chang, Phys. Rev. B, 2000, 62(20): 13631

[61] M. Zieli′nski, M. Korkusinski, and P. Hawrylak, Phys. Rev. B, 2010, 81(8): 085301

[62] E. S. Kadantsev, M. Zielinski, M. Korkusinski, and P. Hawrylak, J. Appl. Phys., 2010, 107(10): 104315

[63] E. S. Kadantsev and P. Hawrylak, Appl. Phys. Lett., 2011, 98(2): 023108

[64] L. He and A. Zunger, Phys. Rev. B, 2006, 73(11): 115324

[65] A. J. Williamson, L. W. Wang, and A. Zunger, Phys. Rev. B, 2000, 62(19): 12963

[66] A. Canning, L. W. Wang, A. Williamson, and A. Zunger, J. Comput. Phys., 2000, 160(1): 29

[67] G. Bester and A. Zunger, Phys. Rev. B, 2005, 71(4): 045318

[68] D. J. Chadi, Phys. Rev. B, 1977, 16(2): 790

[69] J. C. Slater and G. F. Koster, Phys. Rev., 1954, 94(6): 1498

[70] P. Vogl, H. P. Hjalamarson, and J. D. Dow, J. Phys. Chem. Solids, 1983, 44(5): 365

[71] J. M. Jancu, R. Scholz, F. Beltram, and F. Bassani, Phys. Rev. B, 1998, 57(11): 6493

[72] G. Klimeck, R. C. Bowen, T. B. Boykin, and T. A. Cwik, Superlattices Microstruct., 2000, 27(5-6): 519

[73] T. B. Boykin, G. Klimeck, R. C. Bowen, and F. Oyafuso, Phys. Rev. B, 2002, 66(12): 125207

[74] J. G. Díaz and G. W. Bryant, Phys. Rev. B, 2006, 73(7): 075329

[75] S. Lee, F. Oyafuso, P. von Allmen, and G. Klimeck, Phys. Rev. B, 2004, 69(4): 045316

[76] W. Sheng and J. P. Leburton, Appl. Phys. Lett., 2002, 80(15): 2755

[77] Y. Nabetani, T. Ishikawa, S. Noda, and A. Sasaki, J. Appl. Phys., 1994, 76(1): 347

[78] W. Sheng, Appl. Phys. Lett., 2006, 89(17): 173129

[79] W. Sheng, Appl. Phys. Lett., 2008, 92(4): 043113

[80] W. Sheng and S. J. Xu, Phys. Rev. B, 2008, 77(11): 113305

[81] M. Bayer, G. Ortner, O. Stern, A. Kuther, A. A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T. L. Reinecke, S. N. Walck, J. P. Reithmaier, F. Klopf, and F. Schäfer, Phys. Rev. B, 2002, 65(19): 195315

[82] O. Benson, C. Santori, M. Pelton, and Y. Yamamoto, Phys. Rev. Lett., 2000, 84(11): 2513

[83] N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, Phys. Rev. Lett., 2006, 96(13): 130501

[84] W. Sheng, S. J. Cheng, and P. Hawrylak, Phys. Rev. B, 2005, 71(3): 035316

[85] T. Kazimierczuk, M. Goryca, M. Koperski, A. Golnik, J. A. Gaj, M. Nawrocki, P. Wojnar, and P. Kossacki, Phys. Rev. B, 2010, 81(15): 155313

[86] T. Takagahara, Phys. Rev. B, 1993, 47(8): 4569

[87] T. Takagahara, Phys. Rev. B, 2000, 62(24): 16840

[88] S. V. Gupalov and E. L. Ivchenko, Phys. Solid State, 2000, 42(11): 2030

[89] E. Kadantsev and P. Hawrylak, Phys. Rev. B, 2010, 81(4): 045311

[90] G. Bester, S. Nair, and A. Zunger, Phys. Rev. B, 2003, 67: 161306(R)

[91] R. Seguin, A. Schliwa, S. Rodt, K. Pötschke, U. W. Pohl, and D. Bimberg, Phys. Rev. Lett., 2005, 95(25): 257402

[92] A. J. Shields, Nat. Photon., 2007, 1(4): 215

[93] K. Kowalik, O. Krebs, A. Golnik, J. Suffczynski, P. Wojnar, J. Kossut, J. A. Gaj, and P. Voisin, Phys. Rev. B, 2007, 75(19): 195340

[94] S. J. Cheng, W. Sheng, and P. Hawrylak, Phys. Rev. B, 2003, 68(23): 235330

[95] A. Babinski, M. Potemski, S. Raymond, J. Lapointe, and Z. R. Wasilewski, Phys. Rev. B, 2006, 74(15): 155301

[96] M. Bayer, A. Kuther, A. Forchel, A. Gorbunov, V. B. Timofeev, F. Schäfer, J. P. Reithmaier, T. L. Reinecke, and S. N. Walck,Phys. Rev. Lett., 1999, 82(8): 1748

[97] G. Medeiros-Ribeiroa, M. V. B. Pinheiro, V. L. Pimentel, and E. Marega, Appl. Phys. Lett., 2002, 80(22): 4229

[98] T. P. M. Alegre, F. G. G. Hernández, A. L. C. Pereira, and G. Medeiros-Ribeiro, Phys. Rev. Lett., 2006, 97(23): 236402

[99] W. Sheng, S. J. Xu, and P. Hawrylak, Phys. Rev. B, 2008, 77: 241307(R)

[100] W. Sheng, Appl. Phys. Lett., 2009, 94(12): 123113

[101] W. Sheng and A. Babinski, Phys. Rev. B, 2007, 75(3): 033316

[102] W. Sheng and P. Hawrylak, Phys. Rev. B, 2006, 73(12): 125331

[103] W. Sheng and J. Wang, Phys. Rev. B, 2010, 82(7): 073308

[104] K. Chang and J. B. Xia, Solid State Commun., 1997, 104(6): 351

[105] P. W. Fry, I. E. Itskevich, D. J. Mowbray, M. S. Skolnick, J. J. Finley, J. A. Barker, E. P. O’Reilly, L. R. Wilson, I. A. Larkin, P. A. Maksym, M. Hopkinson, M. Al-Khafaji, J. P. R. David, A. G. Cullis, G. Hill, and J. C. Clark, Phys. Rev. Lett., 2000, 84(4): 733

[106] K. Kowalik, O. Krebs, A. Lemâıtre, S. Laurent, P. Senellart, P. Voisin, and J. A. Gaj, Appl. Phys. Lett., 2005, 86(4): 041907

[107] M. M. Vogel, S. M. Ulrich, R. Hafenbrak, P. Michler, L. Wang, A. Rastelli, and O. G. Schmidt, Appl. Phys. Lett., 2007, 91(5): 051904

[108] T. Nakaoka, S. Tarucha, and Y. Arakawa, Phys. Rev. B, 2007, 76(4): 041301R

[109] M. F. Doty, M. Scheibner, I. V. Ponomarev, E. A. Stinaff, A. S. Bracker, V. L. Korenev, T. L. Reinecke, and D. Gammon, Phys. Rev. Lett., 2006, 97(19): 197202

[110] W. Sheng, Appl. Phys. Lett., 2010, 96(13): 133102

[111] W. Sheng, Appl. Phys. Lett., 2009, 95(11): 113105

[112] T. Andlauer and P. Vogl, Phys. Rev. B, 2009, 79(4): 045307

[113] K. Chang, J. B. Xia, and F. M. Peeters, Appl. Phys. Lett., 2003, 82(16): 2661

[114] M. Korkusinski, M. E. Reimer, R. L. Williams, and P. Hawrylak, Phys. Rev. B, 2009, 79(3): 035309

[115] R. L. Williams, G. C. Aers, J. Lefebvre, P. J. Poole, and D. Chithrani, Physica E, 2002, 13(2-4): 1200

[116] M. E. Reimer, D. Dalacu, J. Lapointe, P. J. Poole, D. Kim, G. C. Aers, W. R. McKinnon, and R. L. Williams, Appl. Phys. Lett., 2009, 94(1): 011108

[117] P. R. Wallace, Phys. Rev., 1947, 71(9): 622

[118] M. S. Dresselhaus and G. Dresselhaus, Adv. Phys., 1981, 30(2): 139

[119] J. Blinowski, N. H. Hau, C. Rigaux, J. P. Vieren, R. Le Toullec, G. Furdin, A. Hérold, and J. Melin, J. Physique, 1980, 41(1): 47

[120] D. M. Hoffman, P. C. Eklund, R. E. Heinz, P. Hawrylak, and K. R. Subbaswamy, Phys. Rev. B, 1985, 31(6): 3973

[121] P. Hawrylak, Solid State Commun., 1987, 63(3): 241

[122] A. H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys., 2009, 81(1): 109

[123] L. C. Campos, V. R. Manfrinato, J. D. Sanchez-Yamagishi, J. Kong, and P. Jarillo-Herrero, Nano Lett., 2009, 9(7): 2600

[124] J. S. Bunch, Y. Yaish, M. Brink, K. Bolotin, and P. L. McEuen, Nano Lett., 2005, 5(2): 287

[125] L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. W. Hill, K. S. Novoselov, and A. K. Geim, Science, 2008, 320(5874): 356

[126] B. Wunsch, T. Stauber, and F. Guinea, Phys. Rev. B, 2008, 77(3): 035316

[127] J. Wurm, A. Rycerz, I. Adagideli, M. Wimmer, K. Richter, and H. U. Baranger, Phys. Rev. Lett., 2009, 102(5): 056806

[128] F. Libisch, C. Stampfer, and J. Burgdorfer, Phys. Rev. B, 2009, 79(11): 115423

[129] J. Lu, P. S. Yeo, C. K. Gan, P. Wu, and K. P. Loh, Nat. Nanotechnol., 2011, 6(4): 247

[130] J. Akola, H. P. Heiskanen, and M. Manninen, Phys. Rev. B, 2008, 77(19): 193410

[131] M. Ezawa, Phys. Rev. B, 2010, 81(20): 201402

[132] P. Potasz, A. D. Güçlü and P. Hawrylak, Phys. Rev. B, 2010, 81(3): 033403

[133] A. D. GüçlüP. Potasz, and P. Hawrylak, Phys. Rev. B, 2010, 82(15): 155445

[134] M. Ezawa, Phys. Rev. B, 2007, 76(24): 245415

[135] J. Fern�ndez-Rossier and J. J. Palacios, Phys. Rev. Lett., 2007, 99(17): 177204

[136] W. L. Wang, S. Meng, and E. Kaxiras, Nano Lett., 2008, 8(1): 241

[137] J. Jung and A. H. MacDonald, Phys. Rev. B, 2009, 79(23): 235433

[138] T. Yamamoto, T. Noguchi, and K. Watanabe, Phys. Rev. B, 2006, 74: 121409(R)

[139] Z. Z. Zhang, K. Chang, and F. M. Peeters, Phys. Rev. B, 2008, 77(23): 235411

[140] X. Yan, X. Cui, B. S. Li, and L. S. Li, Nano Lett., 2010, 10(5): 1869

[141] M. L. Sadowski, G. Martinez, M. Potemski, C. Berger, and W. A. de Heer, Phys. Rev. Lett., 2006, 97(26): 266405

[142] M. Orlita, C. Faugeras, P. Plochocka, P. Neugebauer, G. Martinez, D. K. Maude, A. L. Barra, M. Sprinkle, C. Berger, W. A. de Heer, and M. Potemski, Phys. Rev. Lett., 2008, 101(26): 267601

[143] C. Stampfer, S. Fringes, J. Güttinger, F. Molitor, C. Volk, B. Terrés, J. Dauber, S. Engels, S. Schnez, and A. Jacobsen, Front. Phys., 2011, 6(3): 271

[144] K. Nakada, M. Fujita, G. Dresselhaus, and M. S. Dresselhaus, Phys. Rev. B, 1996, 54(24): 17954

[145] K. Wakabayashi, M. Fujita, H. Ajiki, and M. Sigrist, Phys. Rev. B, 1999, 59(12): 8271

[146] B. Wunsch, T. Stauber, F. Sols, and F. Guinea, Phys. Rev. Lett., 2008, 101(3): 036803

[147] L. Yang, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett., 2008, 101(18): 186401

[148] T. Ohta, A. Bostwick, T. Seyller, K. Horn, and E. Rotenberg, Science, 2006, 313(5789): 951

[149] E. V. Castro, K. S. Novoselov, S. V. Morozov, N. M. R. Peres, J. M. dos Santos, J. Nilsson, F. Guinea, A. K. Geim, and A. H. Neto, Phys. Rev. Lett., 2007, 99(21): 216802

[150] J. B. Oostinga, H. B. Heersche, X. Liu, A. F. Morpurgo, and L. M. K. Vandersypen, Nat. Mater., 2008, 7(2): 151

[151] K. F. Mak, C. H. Lui, J. Shan, and T. F. Heinz, Phys. Rev. Lett., 2009, 102(25): 256405

[152] Y. Zhang, T. T. Tang, C. Girit, Z. Hao, M. C. Martin, A. Zettl, M. F. Crommie, Y. R. Shen, and F. Wang, Nature, 2009, 459(7248): 820

[153] R. T. Weitz, M. T. Allen, B. E. Feldman, J. Martin, and A. Yacoby, Science, 2010, 330(6005): 812

[154] E. V. Castro, K. S. Novoselov, S. V. Morozov, N. M. R. Peres, J. M. B. Lopes dos Santos, J. Nilsson, F. Guinea, A. K. Geim, and A. H. Castro Neto, J. Phys.: Condens. Matter, 2010, 22(17): 175503

[155] L. M. Zhang, Z. Li, D. N. Basov, M. M. Fogler, Z. Hao, and M. C. Martin, Phys. Rev. B, 2008, 78(23): 235408

[156] T. Wassmann, A. P. Seitsonen, A. M. Saitta, M. Lazzeri, and F. Mauri, Phys. Rev. Lett., 2008, 101(9): 096402

[157] O. Voznyy, A. D. GüçlüP. Potasz, and P. Hawrylak, Phys. Rev. B, 2011, 83(16): 165417

[158] K. A. Ritter and J. W. Lyding, Nat. Mater., 2009, 8(3): 235

[159] D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Nature, 2003, 421(6926): 925

[160] E. H. Lieb, Phys. Rev. Lett., 1989, 62(10): 1201

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg