Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T08:41:02.682Z Has data issue: false hasContentIssue false
  • English
  • Français

Perturbation theory for weakly coupled two-dimensional layers

Published online by Cambridge University Press:  28 March 2016

Georgios A. Tritsaris ,
Sharmila N. Shirodkar ,
Efthimios Kaxiras ,
Paul Cazeaux ,
Mitchell Luskin ,
Petr Plecháč  and
Eric Cancès
Georgios A. Tritsaris
Affiliation:
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Sharmila N. Shirodkar
Affiliation:
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Efthimios Kaxiras*
Affiliation:
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
Paul Cazeaux
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
Mitchell Luskin
Affiliation:
School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
Petr Plecháč
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, USA
Eric Cancès
Affiliation:
Université Paris Est, Ecole des Ponts and INRIA, 77455 Marne-la-Vallée, France
*
a) Address all correspondence to this author. e-mail: [email protected]
Get access

Abstract

A key issue in two-dimensional structures composed of atom-thick sheets of electronic materials is the dependence of the properties of the combined system on the features of its parts. Here, we introduce a simple framework for the study of the electronic structure of layered assemblies based on perturbation theory. Within this framework, we calculate the band structure of commensurate and twisted bilayers of graphene (Gr) and hexagonal boron nitride (h-BN), and of a Gr/h-BN heterostructure, which we compare with reference full-scale density functional theory calculations. This study presents a general methodology for computationally efficient calculations of two-dimensional materials and also demonstrates that for relatively large twist in the graphene bilayer, the perturbation of electronic states near the Fermi level is negligible.

Keywords

electronic structurenanostructuresimulation
Type
Invited Articles
Information
Journal of Materials Research , Volume 31 , Issue 7: Focus Issue: Two-Dimensional Heterostructure Materials , 14 April 2016 , pp. 959 - 966
Copyright
Copyright © Materials Research Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Geim, A.K. and Grigorieva, I.V.: van der Waals heterostructures. Nature 499(7459), 419–425 (2013).CrossRefGoogle ScholarPubMed
Britnell, L., Ribeiro, R.M., Eckmann, A., Jalil, R., Belle, B.D., Mishchenko, A., Kim, Y-J., Gorbachev, R.V., Georgiou, T., Morozov, S.V., Grigorenko, A.N., Geim, A.K., Casiraghi, C., Castro Neto, A.H., and Novoselov, K.S.: Strong light-matter interactions in heterostructures of atomically thin films. Science 340(6138), 1311–1314 (2013).Google Scholar
Xu, M., Liang, T., Shi, M., and Chen, H.: Graphene-like two-dimensional materials. Chem. Rev. 113(5), 3766–3798 (2013).Google Scholar
Warner, J.H., Rümmeli, M.H., Gemming, T., Büchner, B., Andrew, G., and Briggs, D.: Direct imaging of rotational stacking faults in few layer graphene. Nano Lett. 9(1), 102–106 (2009).Google Scholar
Yan, W., Liu, M., Dou, R-F., Meng, L., Feng, L., Chu, Z-D., Zhang, Y., Liu, Z., Nie, J-C., and He, L.: Angle-dependent van Hove singularities in a slightly twisted graphene bilayer. Phys. Rev. Lett. 109, 126801 (2012).Google Scholar
Yin, L-J., Qiao, J-B., Xu, R., Dou, R-F., Nie, J-C., and He, L.: Electronic structures and their Landau quantizations in twisted graphene bilayer and trilayer. arXiv e-print:1410.1621 (2014).Google Scholar
Wang, Y., Su, Z., Wu, W., Nie, S., Lu, X., Wang, H., McCarty, K., Pei, S-S., Robles-Hernandez, F., Hadjiev, V.G., and Bao, J.: Four-fold Raman enhancement of 2D band in twisted bilayer graphene: Evidence for a doubly degenerate dirac band and quantum interference. Nanotechnology 25(33), 335201 (2014).Google Scholar
Brihuega, I., Mallet, P., González-Herrero, H., Trambly de Laissardière, G., Ugeda, M.M., Magaud, L., Gómez-Rodríguez, J.M., Ynduráin, F., and Veuillen, J-Y.: Unraveling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene by scanning tunneling microscopy and theoretical analysis. Phys. Rev. Lett. 109, 196802 (2012).CrossRefGoogle Scholar
Coh, S., Tan, L.Z., Louie, S.G., and Cohen, M.L.: Theory of the Raman spectrum of rotated double-layer graphene. Phys. Rev. B 88(16), 165431 (2013).CrossRefGoogle Scholar
Koshino, M.: Interlayer interaction in general incommensurate atomic layers. New J. Phys. 17(1), 015014 (2015).Google Scholar
Ghader, D., Szczȩśniak, D., and Khater, A.: Theory for the electronic structure of incommensurate twisted bilayer graphene. arXiv e-print:1501.06334 (2015).Google Scholar
Pal, H.K., Carter, S., and Kindermann, M.: Theory of twisted bilayer graphene near commensuration. arXiv e-print:1409.1971 (2014).Google Scholar
Cao, B. and Li, T.: Interlayer electronic coupling in arbitrarily stacked MoS2 bilayers controlled by interlayer S–S interaction. J. Phys. Chem. C 119(2), 1247–1252 (2014).CrossRefGoogle Scholar
Bokdam, M., Amlaki, T., Brocks, G., and Kelly, P.J.: Band gaps in incommensurable graphene on hexagonal boron nitride. Phys. Rev. B 89(20), 201404 (2014).Google Scholar
Hohenberg, P. and Kohn, W.: Inhomogeneous electron gas. Phys. Rev. 136(3B), B864–B871 (1964).CrossRefGoogle Scholar
Kohn, W. and Sham, L.J.: Self-consistent equations including exchange and correlation effects. Phys. Rev. 140(4A), A1133–A1138 (1965).Google Scholar
Ribeiro, R.M. and Peres, N.M.R.: Stability of boron nitride bilayers: Ground-state energies, interlayer distances, and tight-binding description. Phys. Rev. B 83(23), 235312 (2011).Google Scholar
Cappelluti, E., Roldán, R., Silva-Guillén, J.A., Ordejón, P., and Guinea, F.: Tight-binding model and direct-gap/indirect-gap transition in single-layer and multilayer MoS2 . Phys. Rev. B 88(7), 075409 (2013).CrossRefGoogle Scholar
Fang, S., Kuate Defo, R., Shirodkar, S.N., Lieu, S., Tritsaris, G.A., and Kaxiras, E.: Ab initio tight-binding hamiltonian for transition metal dichalcogenides. Phys. Rev. B 92, 205108 (2015).CrossRefGoogle Scholar
Enkovaara, J., Rostgaard, C., Mortensen, J.J., Chen, J., Dulak, M., Ferrighi, L., Gavnholt, J., Glinsvad, C., Haikola, V., Hansen, H.A., Kristoffersen, H.H., Kuisma, M., Larsen, A.H., Lehtovaara, L., Ljungberg, M., Lopez-Acevedo, O., Moses, P.G., Ojanen, J., Olsen, T., Petzold, V., Romero, N.A., Stausholm-Møller, J., Strange, M., Tritsaris, G.A., Vanin, M., Walter, M., Hammer, B., Häkkinen, H., Madsen, G.K.H., Nieminen, R.M., Nørskov, J.K., Puska, M., Rantala, T.T., Schiøtz, J., Thygesen, K.S., and Jacobsen, K.W.: Electronic structure calculations with GPAW: A real-space implementation of the projector augmented-wave method. J. Phys.: Condens. Matter 22(25), 253202 (2010).Google ScholarPubMed
Blöchl, P.E.: Projector augmented-wave method. Phys. Rev. B 50(24), 17953–17979 (1994).Google Scholar
Tritsaris, G.A., Malone, B.D., and Kaxiras, E.: Optoelectronic properties of single-layer, double-layer, and bulk tin sulfide: A theoretical study. J. Appl. Phys. 113(23), 233507 (2013).Google Scholar
Lebedeva, I.V., Knizhnik, A.A., Popov, A.M., Lozovik, Y.E., and Potapkin, B.V.: Interlayer interaction and relative vibrations of bilayer graphene. Phys. Chem. Chem. Phys. 13(13), 5687–5695 (2011).Google Scholar
Lin, X., Xu, Y., Hakro, A.A., Hasan, T., Hao, R., Zhang, B., and Chen, H.: Ab initio optical study of graphene on hexagonal boron nitride and fluorographene substrates. J. Mater. Chem. C 1(8), 1618–1627 (2013).Google Scholar
Fan, Y., Zhao, M., Wang, Z., Zhang, X., and Zhang, H.: Tunable electronic structures of graphene/boron nitride heterobilayers. Appl. Phys. Lett. 98(8), 083103 (2011).Google Scholar
Tritsaris, G.A., Vinichenko, D., Kolesov, G., Friend, C.M., and Kaxiras, E.: Dynamics of the photogenerated hole at the rutile TiO2(110)/water interface: A nonadiabatic simulation study. J. Phys. Chem. C 118, 27393–27401 (2014).CrossRefGoogle Scholar
Kolesov, G., Vinichenko, D., Tritsaris, G.A., Friend, C.M., and Kaxiras, E.: Anatomy of the photochemical reaction: Excited-state dynamics reveals the C–H acidity mechanism of methoxy photo-oxidation on titania. J. Phys. Chem. Lett. 6(9), 1624–1627 (2015).CrossRefGoogle Scholar