Abstract
The Wannier equation for quasiparticles with a linear dispersion is investigated. It is shown that Coulomb bound compounds of mass less electron-hole pairs can only exist if the effective coupling strength exceeds the critical value of approximately 0.46. At the critical value, a second-order transition to a weak Coulomb regime is found. It is shown that the existence of bound excitons indicates an instability of the noninteracting ground state.
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K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438, 197 (2005)
Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature 438, 201 (2005)
R.S. Deacon, K.C. Chuang, R.J. Nicholas, K.S. Novoselov, A.K. Geim, Phys. Rev. B 76, 081406 (2007)
Z. Jiang, E.A. Henriksen, L.C. Tung, Y.J. Wang, M.E. Schwartz, M.Y. Han, P. Kim, H.L. Stormer, Phys. Rev. Lett. 98, 197403 (2007)
S.Y. Zhou, G.H. Gweon, A. Lanzara, Ann. Phys. 321, 1730 (2006)
A. Bostwick, T. Ohta, J.L. McChesney, T. Seyller, K. Horn, E. Rotenberg, Eur. Phys. J. 148, 5 (2007)
J. González, F. Guinea, M.A.H. Vozmediano, Phys. Rev. B 59, R2474 (1999)
D.E. Sheehy, J. Schmalian, Phys. Rev. Lett. 99, 226803 (2007)
L. Fritz, J. Schmalian, M. Müller, S. Sachdev, Phys. Rev. B 78, 085416 (2008)
A. Sinner, K. Ziegler, Phys. Rev. B 82, 165453 (2010)
D.V. Khveshchenko, Phys. Rev. Lett. 87, 246802 (2001)
D.V. Khveshchenko, W.F. Shively, Phys. Rev. B 73, 115104 (2006)
V. Juričić, I.F. Herbut, G.W. Semenoff, Phys. Rev. B 80, 081405 (2009)
J.E. Drut, T.A. Lähde, Phys. Rev. Lett. 102, 026802 (2009)
J.E. Drut, T.A. Lähde, Phys. Rev. B 79, 165425 (2009)
L. Yang, J. Deslippe, C.H. Park, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 103, 186802 (2009)
E. Malić, J. Maultzsch, S. Reich, A. Knorr, Phys. Rev. B 82, 035433 (2010)
A.D. Gçülü, P. Potasz, P. Hawrylak, Phys. Rev. B 82, 155445 (2010)
J.P. Reed, B. Uchoa, Y.I. Joe, Y. Gan, D. Casa, E. Fradkin, P. Abbamonte, Science 330, 805 (2010)
H. Min, R. Bistritzer, J.J. Su, A.H. MacDonald, Phys. Rev. B 78, 121401 (2008)
O.L. Berman, R.Y. Kezerashvili, Y.E. Lozovik, Phys. Rev. B 78, 035135 (2008)
O.L. Berman, Y.E. Lozovik, G. Gumbs, Phys. Rev. B 77, 155433 (2008)
L. Pauling, The Nature of the Chemical Bond and the Structure of Molecules and Crystals: An Introduction to Modern Structural Chemistry (Cornell University Press, Ithaca, New York, 1960)
A.H. Castro Neto, Physics 2, 30 (2009)
E.H. Hwang, S. Das Sarma, Phys. Rev. B 75, 205418 (2007)
F. Wang, D.J. Cho, B. Kessler, J. Deslippe, P.J. Schuck, S.G. Louie, A. Zettl, T.F. Heinz, Y.R. Shen, Phys. Rev. Lett. 99, 227401 (2007)
C.D. Spataru, S. Ismail-Beigi, L.X. Benedict, S.G. Louie, Phys. Rev. Lett. 92, 077402 (2004)
E. Malić, T. Winzer, E. Bobkin, A. Knorr, Phys. Rev. B 84, 205406 (2011)
K.F. Mak, J. Shan, T.F. Heinz, Phys. Rev. Lett. 106, 046401 (2011)
D.H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. von Klitzing, M. Lippitz, J. Smet, Nano Lett. 11, 1379 (2011)
H. Haug, S.W. Koch, Quantum theory of the optical and electronic properties of semiconductors (World Scientific, Singapore, 2009)
V.M. Pereira, J. Nilsson, A.H. Castro Neto, Phys. Rev. Lett. 99, 166802 (2007)
A.V. Shytov, M.I. Katsnelson, L.S. Levitov, Phys. Rev. Lett. 99, 236801 (2007)
J. Wang, H.A. Fertig, G. Murthy, Phys. Rev. Lett. 104, 186401 (2010)
J. Sabio, F. Sols, F. Guinea, Phys. Rev. B 81, 045428 (2010)
W. Li, G.Z. Liu, Phys. Lett. A 374, 2957 (2010)
I.S. Gradshteyn, I.M. Ryzhik, Tables of Integrals, Series, and Products, 6th edn. (Academic Press, San Diego, CA, 2000)
O.V. Gamayun, E.V. Gorbar, V.P. Gusynin, Phys. Rev. B 80, 165429 (2009)
J. Sabio, F. Sols, F. Guinea, Phys. Rev. B 82, 121413 (2010)
O.V. Gamayun, E.V. Gorbar, V.P. Gusynin, Phys. Rev. B 81, 075429 (2010)
T. Stroucken, J.H. Grönqvist, S.W. Koch, Phys. Rev. B 84, 205445 (2011)
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Grönqvist, J., Stroucken, T., Lindberg, M. et al. Wannier excitons signalling strong Coulomb coupling in graphene. Eur. Phys. J. B 85, 395 (2012). https://doi.org/10.1140/epjb/e2012-30593-0
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DOI: https://doi.org/10.1140/epjb/e2012-30593-0