Abstract
By applying the full π-band Holstein model, we analytically have calculated the electronic density of states (DOS) and optical conductivity of doped gapped graphene-like structures including silicon carbide (SiC), boron nitride (BN), and beryllium monoxide (BeO) beyond the Dirac cone approximation. We have implemented the Kubo linear response formalism which is established to get the retarded self-energy here. For strong electron-phonon (e-ph) coupling strengths, an addition peak in the optical conductivity has been found, associated with transitions between the midgap states and the Van Hove singularities of the main π-bands. Optical conductivity (optical absorption) decreases (increases) with the gap which is useful in the fabrication of low-dimensional-based solar cells. At large gaps, a clean sheet of doped graphene has a zero optical conductivity at low energies because of the optically interband excitations through the Dirac points. Also, the Drude weight remains unchanged for all cases at low energy regimes. Consequently, DOS and optical conductivity remain constant with temperature at low e-ph interaction strengths.
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Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V., Firsov, A.A.: Science 306, 666 (2004)
Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., Firsov, A.A.: Nature 438, 197 (2005)
Novoselov, K.S., Jiang, D., Schedin, F., Booth, T.J., Khotkevich, V.V., Morozov, S.V., Geim, A.K.: Proc Natl Acad Sci. 102, 10451 (2005)
Yarmohammadi, M., Zareyan, M.: Chin. Phys. B 25, 068105 (2016)
Geim, A.K.: Science 324, 1530 (2009)
Avouris, P.: Nano Lett. 10, 4285 (2010)
Bonaccorso, F., Sun, Z., Hasan, T., Ferrari, A.C.: Nature Phot. 4, 611 (2010)
Xiaoguang, W., Peeters, F.M., Devreese, J.T.: Phys. Rev. B 31, 3420 (1985)
Das Sarma, S., Mason, B.A.: Ann. Phys. (NY) 163, 78 (1985)
Sood, A.K., Menendez, J., Cardona, M., Ploog, K.: Phys. Rev. Lett. 54, 2111 (1985)
TralleroGiner, C., Garca-Moliner, F., Velasco, V.R., Cardona, M.: Phys. Rev. B 45, 11944 (1992)
Shields, A.J., Cardona, M., Eberl, K.: Phys. Rev. Lett. 72, 412 (1994)
Su, W.P., Schrieffer, J.R., Heeger, A.J.: Phys. Rev. Lett. 42, 1698 (1979)
Goodvin, G.L., Berciu, M., Sawatzky, G.A.: Phys. Rev. B 74, 245104 (2006)
Holstein, T.: Ann. Phys. 8, 325 (1959)
Holstein, T.: Ann. Phys. 8, 343 (1959)
Piscanec, S., et al.: Phys. Rev. Lett. 93, 185503 (2004)
Piscanec, S., et al.: Phys. Rev. B 75, 035427 (2007)
Pisana, S., et al.: Nature Mater. 6, 198 (2007)
Nair, R.R., Blake, P., Grigorenko, A.N., Novoselov, K.S., Booth, T.J., Stauber, T., Peres, N.M.R., Geim, A.K.: Science 320, 1308 (2008)
Li, Z.Q., Henriksen, E.A., Jiang, Z., Hao, Z., Martin, M.C., Kim, P., Stormer, H.L., Basov, D.N.: Nat. Phys. 4, 532 (2008)
Yarmohammadi, M.: AIP Adv. 6, 085008 (2016)
Horng, J., Chen, C.-F., Geng, B., Girit, C., Zhang, Y., Hao, Z., Bechtel, H.A., Martin, M., Zettl, A., Crommie, M.F., et al.: Phys. Rev. B, 165113 (2011)
Peres, N.M.R., Guinea, F., Castro Neto, A.H.: Phys. Rev. B 73, 125411 (2006)
Gusynin, V.P., Sharapov, S.G.: Phys. Rev. B 73, 245411 (2006)
Stauber, T., Peres, N.M.R., Castro Neto, A.H.: Phys. Rev. B 78, 085418 (2008)
Stauber, T., Peres, N.M.R., Geim, A.K.: Phys. Rev. B 78, 085432 (2008)
Carbotte, J.P., Nicol, E.J., Sharapov, S.G.: Phys. Rev. B 81, 045419 (2010)
Peres, N.M.R., Ribeiro, R.M., Castro Neto, A.H.: Phys. Rev. Lett. 105, 055501 (2010)
Vasko, F.T., Mitin, V.V., Ryzhii, V., Otsuji, T.: Phys. Rev. B 86, 235424 (2012)
Orlita, M., Potemski, M.: Semicond. Sci. Technol. 25, 063001 (2010)
Li, G., Luican, A., Andrei, E.Y.: Phys. Rev. Lett 102, 176804 (2009)
Sasaki, K., Sato, K., Jiang, J., Saito, R., Onari, S., Tanaka, Y.: Phys. Rev. B 75, 235430 (2007)
Peres, N.M.R., Stauber, T.: Int. J. Mod. Phys. B 16, 2529 (2008)
Gusynin, V.P., Sharapov, S.G., Carbotte, J.P.: Phys. Rev. Lett. 96, 256802 (2006)
Stauber, T., Peres, N.M.R.: J. Phys: Condens. Matter 20, 055002 (2008)
Calandra, M., Mauri, F.: Phys. Rev. B 76, 205411 (2007)
Peres, N.M.R., Stauber, T., Castro Neto, A.H.: EPL 84, 38002 (2008)
Kuzmenko, A.B., van Heumen, E., Carbone, F., van der Marel, D.: Phys. Rev. Lett. 100, 117401 (2008)
Horng, J., Chen, C.-F., Geng, B., Girit, C., Zhang, Y., Hao, Z., Bechtel, H.A., Martin, M., Zettl, A., Crommie, M.F., Shen, Y.R., Wang, F.: Phys. Rev. B 83, 165113 (2011)
Fei, Z., Shi, Y., Pu, L., Gao, F., Liu, Y., Sheng, L., Wang, B., Zhang, R., Zheng, Y.: Phys. Rev. B 78, 201402 (2008)
Mak, K.F., Shan, J., Heinz, T.F.: Phys. Rev. Lett. 106, 046401 (2011)
Santoso, I., Gogoi, P.K., Su, H.B., Huang, H., Lu, Y., Qi, D., Chen, W., Majidi, M.A., Feng, Y.P., Wee, A.T.S., Loh, K.P., Venkatesan, T., Saichu, R.P., Goos, A., Kotlov, A., Rubhausen, M., Rusydi, A.: Phys. Rev. B 84, 081403 (2011)
Semenoff, G.W.: Phys. Rev. Lett. 53, 2449 (1984)
Katsnelson, M.I., Novoselov, K.S., Geim, A.K.: Nature Phys. 2, 620 (2006)
Lin, Y., Jenkins, K.A., Valdes-Garcia, A., Small, J.P., Farmer, D.B., Avouris, P.: Nano Lett. 9, 422 (2009)
Kedzierski, J., Hsu, P., Healey, P., Wyatt, P.W., Keast, C.L., Sprinkle, M., Berger, C., De Heer, W.A.: IEEE Trans Electron Devices 55, 2078 (2008)
Haisma, J., Hattu, N., Pulles, J.T.C.M., Steding, E., Vervest, J.C.G.: Appl Opt 46, 6793 (2007)
Haisma, J., Spierings, G.A.C.M.: Philips J Res 49, 47 (1995)
Haisma, J., Spierings, G.A.C.M.: Mater. Sci. Eng. R 37, 1 (2002)
Wyckoff, R.W.G.: Crystal Structures. Wiley, New York (1963)
Persson, C., Lindefelt, U.: Phys. Rev. B 54, 10257 (1996)
Morkoç, H., Strite, S., Gao, G.B., Lin, M.E., Sverdlov, B., Burns, M.: J. Appl. Phys. 76, 1363 (1994)
Ettisserry, D., Goldsman, N., Lelis, A.: J. Appl. Phys. 115, 103706 (2014)
Sun, X.-H., Li, C.-P., Wong, W.-K., Wong, N.-B., Lee, C.-S., Lee, S.-T., Teo, B.-K.: J. Am. Chem. Soc. 124, 14464 (2002)
Pei, L.Z., Tang, Y.H., Chen, Y.W., Guo, C., Li, X.X., Yuan, Y., Zhang, Y.: J. Appl. Phys. 99, 114306 (2006)
Pei, L.Z., Tang, Y.H., Chen, Y.W., Guo, C.: J. Appl. Phys. 100, 046105 (2006)
Wu, R., Chen, J., Yang, G., Wu, L., Zhou, S., Wang, J., Pan, Y.: J. Cryst. Growth 310, 3573 (2008)
Baierle, R.J., Piquini, P., Neves, L.P., Miwa, R.H.: Phys. Rev. B 74, 155425 (2006)
Baierle, R.J., Miwa, R.H.: Phys. Rev. B 76, 205410 (2007)
Gali, A.: Phys. Rev. B 75, 085416 (2007)
Wang, Q.H., Kalantar-Zadeh, K., Kis, A., Coleman, J.N., Strano, M.S.: Nat. Nanotechnol. 7, 699 (2012)
Eichler, J., Lesniak, C.: J. Eur. Ceram. Soc. 28, 1105 (2008)
Alem, N., et al.: Phys. Rev. B 80, 155425 (2009)
Kijko, V.S., Makurin, Y.N., Ivanovskii, A.L.: Beryllium Oxide Based Ceramic, Preparation, Physical, Chemical Properties and Applications. Ural Division of the RAS, Ekaterinburg (2006)
Vidal-Valet, G., Vidal, J.P., Kurki-Suonic, K., Kurki-Suonic, R.: Acta Crystalloger. 43, 340 (1987)
Sorokin, P.B., Fedorov, A.S., Chernozatonskii, L.A.: Phys. Solid State 48, 398 (2006)
Stauber, T., Peres, N.M.R.: J. Phys. Condens. Matter 20, 055002 (2008)
Wirtz, L., Rubio, A.: Solid State Commun. 131, 141 (2004)
Mahan, G.D.: Many Particle Physics. Plenum Press, New York (1993)
Economou, E.N.: Green’s Functions in Quantum Physics, 3rd edn. Springer, Heidelberg (2006)
Grosso, G., Parravicini, G.P.: Solid State Physics, 2nd edn. Academic Press, New York (2014)
Yuan, S., Roldan, R., Raedt, H., Katsnelson, M.I.: Phys. Rev. B 84, 195418 (2011)
Yuan, S., De Raedt, H., Katsnelson, M.I.: Phys. Rev. B 82, 115448 (2010)
Pereira, V.M., Lopes dos Santos, J.M.B., Castro Neto, A.H.: Phys. Rev. B 77, 115109 (2008)
Yuan, S., Roldan, R., Katsnelson, M.I.: Phys. Rev. B 84, 035439 (2011)
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Hoi, B.D., Mirabbaszadeh, K., Habibiyan, H. et al. Optical Absorption of SiC, BN, and BeO Nanosheets in Holstein Model. J Supercond Nov Magn 30, 2435–2444 (2017). https://doi.org/10.1007/s10948-017-4076-7
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DOI: https://doi.org/10.1007/s10948-017-4076-7