Ground State Properties of Monolayer Doped Graphene


We performed theoretical investigations on self-energy, screening charge density, screened potential and pair distribu- tion function for a doped single layer graphene. Random phase approximation density-density response function and graphene’s massless Diracfermions concept have been used in our calculations. Local field effects have been included using Hubbard approximation to go beyond random phase approximation. Ultraviolet wave vector cutoff has been used to exclude the effect of vacuum states. Our computed self energy of graphene though displays a behavour similar to that of 2DEG, its magnitude differs drastically from that of 2DEG. Freidel oscillations are seen in computed screened potential and density of screening charge of graphene, which can be seen as a signature of Fermi liquid state in doped graphene. In agreement with experimental results, our computed pair distribution function, as a function of carrier density, suggests that exchange and correlation terms make negligible contribution to compressibility of graphene. Incorporation of LFC reduces the magnitude of self energy, screening charge density and screened potential.

Share and Cite:

K. Mishra, S. Ashraf and A. Sharma, "Ground State Properties of Monolayer Doped Graphene," World Journal of Condensed Matter Physics, Vol. 2 No. 1, 2012, pp. 36-41. doi: 10.4236/wjcmp.2012.21006.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] E. H. Hwang, B. Y.-K. Hu and S. Das Sarma, “Many- Body Exchange-Correlation Effects in Graphene,” Phy- sica E, Vol. 40, No. 5, 2008, pp. 1653-1655. doi:10.1016/j.physe.2007.10.043
[2] S. Das Sarma, E. H. Hwang and W.-K. Tse, “Many-Body Interaction Effects in Doped and Undoped Graphene: Fermi Liquid Versus Non-Fermi Liquid,” Physical Re- view B, Vol. 75, No. 12, 2007, pp. 121406-121409. doi:10.1103/PhysRevB.75.121406
[3] M. Calandra and F. Mauri, “Electron-Phonon Coupling and Electron Self-Energy in Electron-Doped Graphene: Calculation of Angular-Resolved Photoemission Spectra, ” Physical Review B, Vol. 76, No. 20, 2007, pp. 205411-205419. doi:10.1103/PhysRevB.76.205411
[4] C. H. Park, F. Giustino, M. L. Cohen and S. G. Louie, “Velocity Renormalization and Carrier Lifetime in Graphene from the Electron-Phonon Interaction,” Physical Review Letters, Vol. 99, No. 8, 2007, pp. 086804-086807. doi:10.1103/PhysRevLett.99.086804
[5] W. K. Tse and S. Das Sarma, “Phonon-Induced Many- Body Renormalization of the Electronic Properties of Graphene,” Physical Review Letters, Vol. 99, No. 23, 2007, pp. 236802-236805. doi:10.1103/PhysRevLett.99.236802.
[6] N. W. Ashcroft and N. D. Mermin, “Solid State Physics,” Saunders College, Philadelphia, 1976.
[7] I. S. Terekov, A. I. Milstein, V. N. Kotov and O. P. Sushkov, “Screening of Coulomb Impurities in Graphene,” Physical Review Letters, Vol. 100, No. 7, 2008, pp. 076803-076806. doi:10.1103/PhysRevLett.100.076803;
[8] A. V. Shytov, M. I. Katsnelson, and L. S. Levitov, “Va- cuum Polarization and Screening of Supercritical Impurities in Graphene,” Physical Review Letters, Vol. 99, No. 23, 2007, pp. 236801-236804. doi:10.1103/PhysRevLett.99.236801
[9] T. Ando, “Screening Effect and Impurity Scattering in Monolayer Graphene,” Journal of the Physical Society of Japan, Vol. 75, No. 7, 2006, pp. 074716-074722. doi:10.1143/JPSJ.75.074716
[10] E. Hwang and S. D. Sarma, “Dielectric Function, Screen- ing, and Plasmons in Two-Dimensional Graphene,” Physical Review B, Vol. 75, No. 6, 2007, pp. 205418-205423. doi:10.1103/PhysRevB.75.205418
[11] B. Wunsch, T. Stauber, F. Sols and F. Guinea, “Dyna- mical Polarization of Graphene at Finite Doping,” New Journal of Physics, Vol. 8, No. 12, 2006, p. 318. doi:10.1088/1367-2630/8/12/318
[12] P. K. Pyatkovskiy, “Dynamical Polarization, Screening, and Plasmons in Gapped Graphene,” Journal of Physics: Condensed Matter, Vol. 21, No. 2, 2009, p. 025506. doi:10.1088/0953-8984/21/2/025506
[13] A. H. C. Neto, F. Guinea, N. M. Peres, K. S. Novoselov and A. K. Geim, “The Electronic Properties of Gra- phene,” Reviews of Modern Physics, Vol. 81, No. 1, 2009, pp. 109-162. doi:10.1103/RevModPhys.81.109
[14] J. Martin, N. Akerman, G. Ulbricht, T. Lohmann, J. H. Smet, K. von Klitzing and A. Yacoby, “Observation of Electron-Hole Puddles in Graphene Using a Scanning Single-Electron Transistor,” Nature Physics, Vol. 4, No. 2, 2008, pp. 144-148. doi:10.1038/nphys781
[15] D. S. L. Abergel, P. Pietilainen and T. Chakraborty, “Electronic Compressibility of Graphene: The Case of Vanishing Electron Correlations and the Role of Chirality,” Physical Review B, Vol. 80, No. 8, 2009, pp. 081408- 081411. doi:10.1103/PhysRevB.80.081408
[16] S. S. Z. Ashraf, K. N Mishra and A. C. Sharma, “Static Structure Factor and Pair Correlation Function of Gra- phene,” Journal of Physics: Condensed Matter, Vol. 22, No. 35, 2010, p. 355303. doi:10.1088/0953-8984/22/35/355303
[17] S. S. Z. Ashraf and A. C. Sharma, “Many Particle Aspects of a Semiconductor Quantum Wire within an Im- proved Random Phase Approximation,” Journal of Physics: Condensed Matter, Vol. 17, No. 19, 2005, p. 3043. doi:10.1088/0953-8984/17/19/018
[18] Y. Barlas, T. Pereg-Barnea, M. Polini, R. Asgari and A. H. M. Donald, “Chirality and Correlations in Graphene,” Physical Review Letters, Vol. 98, No. 23, 2007, pp. 236601-236604. doi:10.1103/PhysRevLett.98.236601
[19] D. S. L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler and T. Chakraborty, “Properties of Graphene: A Theoretical Perspective,” Advances in Physics, Vol. 59, No. 4, 2010, pp. 261-482. doi:10.1080/00018732.2010.487978
[20] V. V. Cheianov and V. I. Fal’ko, “Friedel Oscillations, Impurity Scattering, and Temperature Dependence of Re- sistivity in Graphene,” Physical Review Letters, Vol. 97, No. 22, 2006, pp. 226801-226804. doi:10.1103/PhysRevLett.97.226801
[21] M. Ono, et al., “Observation of the Screened Potential and the Friedel Oscillation by Low-Temperature Scan- ning Tunneling Microscopy/Spectroscopy,” Applied Surface Science, Vol. 256, No. 2, 2009, pp. 469-474. doi:10.1016/j.apsusc.2009.07.023
[22] G. E. Simion and G. F. Giuliani, “Friedel Oscillations in a Fermi Liquid,” Physical Review B, Vol. 72, No. 4, 2005, pp. 045127-045134. doi:10.1103/PhysRevB.72.045127
[23] G. D. Mahan, “Many Particle Physics,” 2nd Edition, Plenum, New York, 1990.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.