Strain effects on the spin-orbit-induced band structure splittings in monolayer MoS2 and graphene

Cheiwchanchamnangij, Tawinan; Lambrecht, Walter R.  L.; Song, Yang; Dery, Hanan

doi:10.1103/PhysRevB.88.155404

Title: Strain effects on the spin-orbit-induced band structure splittings in monolayer MoS $_{2}$ and graphene

Journal Article · Mon Oct 07 00:00:00 EDT 2013 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PhysRevB.88.155404· OSTI ID:1593465

Cheiwchanchamnangij, Tawinan ^[1];

^[1]; Song, Yang ^[2]; Dery, Hanan ^[2]

Case Western Reserve Univ., Cleveland, OH (United States)
Univ. of Rochester, NY (United States)

The strain effects on the spin-orbit-induced splitting of the valence-band maximum and conduction-band minimum in monolayer MoS₂ and the gap in graphene are calculated using first-principles calculations. The dependence of these splittings on the various symmetry types of the strain is described by means of an effective Hamiltonian based on the method of invariants, and the parameters in the model are extracted by fitting to the theory. These splittings are related to acoustic-phonon deformation potentials or electron-phonon-coupling matrix elements which enter the spin-dependent scattering theory of conduction in these materials.

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Research Organization:: Case Western Reserve Univ., Cleveland, OH (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)

Grant/Contract Number:: SC0008933; DMR-1104595; DMR-1124601; ECCS-1231570; HDTRA1-13-1-0013

OSTI ID:: 1593465

Journal Information:: Physical Review. B, Condensed Matter and Materials Physics, Vol. 88, Issue 15; ISSN 1098-0121

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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References (54)

Band-structure topologies of graphene: Spin-orbit coupling effects from first principles Gmitra, M.; Konschuh, S.; Ertler, C. Physical Review B, Vol. 80, Issue 23 https://doi.org/10.1103/PhysRevB.80.235431	journal	December 2009
Intrinsic spin lifetime of conduction electrons in germanium Li, Pengke; Song, Yang; Dery, Hanan Physical Review B, Vol. 86, Issue 8 https://doi.org/10.1103/PhysRevB.86.085202	journal	August 2012
Unconventional Quantum Hall Effect and Tunable Spin Hall Effect in Dirac Materials: Application to an Isolated ${MoS}_{2}$ Trilayer Li, Xiao; Zhang, Fan; Niu, Qian Physical Review Letters, Vol. 110, Issue 6 https://doi.org/10.1103/PhysRevLett.110.066803	journal	February 2013
Analysis of phonon-induced spin relaxation processes in silicon Song, Yang; Dery, Hanan Physical Review B, Vol. 86, Issue 8 https://doi.org/10.1103/PhysRevB.86.085201	journal	August 2012
Strain effect on the optical conductivity of graphene Pellegrino, F. M. D.; Angilella, G. G. N.; Pucci, R. Physical Review B, Vol. 81, Issue 3 https://doi.org/10.1103/PhysRevB.81.035411	journal	January 2010
Strain-dependent electronic and magnetic properties of MoS2 monolayer, bilayer, nanoribbons and nanotubes Lu, Peng; Wu, Xiaojun; Guo, Wanlin Physical Chemistry Chemical Physics, Vol. 14, Issue 37 https://doi.org/10.1039/c2cp42181j	journal	January 2012
Nonsingular Hankel functions as a new basis for electronic structure calculations Bott, E.; Methfessel, M.; Krabs, W. Journal of Mathematical Physics, Vol. 39, Issue 6 https://doi.org/10.1063/1.532437	journal	June 1998
Invariant expansion for the trigonal band structure of graphene Winkler, R.; Zülicke, U. Physical Review B, Vol. 82, Issue 24 https://doi.org/10.1103/PhysRevB.82.245313	journal	December 2010
First-principles theory of nonlocal screening in graphene van Schilfgaarde, M.; Katsnelson, M. I. Physical Review B, Vol. 83, Issue 8 https://doi.org/10.1103/PhysRevB.83.081409	journal	February 2011
Quantum Theory of Cyclotron Resonance in Semiconductors: General Theory Luttinger, J. M. Physical Review, Vol. 102, Issue 4 https://doi.org/10.1103/PhysRev.102.1030	journal	May 1956
Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors Zhu, Z. Y.; Cheng, Y. C.; Schwingenschlögl, U. Physical Review B, Vol. 84, Issue 15 https://doi.org/10.1103/PhysRevB.84.153402	journal	October 2011
Strain-induced semiconductor to metal transition in the two-dimensional honeycomb structure of MoS2 Scalise, Emilio; Houssa, Michel; Pourtois, Geoffrey Nano Research, Vol. 5, Issue 1 https://doi.org/10.1007/s12274-011-0183-0	journal	November 2011
The electronic properties of graphene Castro Neto, A. H.; Guinea, F.; Peres, N. M. R. Reviews of Modern Physics, Vol. 81, Issue 1, p. 109-162 https://doi.org/10.1103/RevModPhys.81.109	journal	January 2009
Bandgap Engineering of Strained Monolayer and Bilayer MoS₂ Conley, Hiram J.; Wang, Bin; Ziegler, Jed I. Nano Letters, Vol. 13, Issue 8, p. 3626-3630 https://doi.org/10.1021/nl4014748	journal	July 2013
Thickness and strain effects on electronic structures of transition metal dichalcogenides: 2H- $M X_{2}$ semiconductors ( $M$ $=$ Mo, W; $X$ $=$ S, Se, Te) Yun, Won Seok; Han, S. W.; Hong, Soon Cheol Physical Review B, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevB.85.033305	journal	January 2012
Intrinsic spin Hall effect in monolayers of group-VI dichalcogenides: A first-principles study Feng, Wanxiang; Yao, Yugui; Zhu, Wenguang Physical Review B, Vol. 86, Issue 16 https://doi.org/10.1103/PhysRevB.86.165108	journal	October 2012
Monolayer MoS $_{2}$ : Trigonal warping, the $Γ$ valley, and spin-orbit coupling effects Kormányos, Andor; Zólyomi, Viktor; Drummond, Neil D. Physical Review B, Vol. 88, Issue 4 https://doi.org/10.1103/PhysRevB.88.045416	journal	July 2013
Nanospintronics Based on Magnetologic Gates Dery, Hanan; Wu, Hui; Ciftcioglu, Berkehan IEEE Transactions on Electron Devices, Vol. 59, Issue 1 https://doi.org/10.1109/TED.2011.2173498	journal	January 2012
Comment on the average potential of a Wigner solid Kleinman, Leonard Physical Review B, Vol. 24, Issue 12 https://doi.org/10.1103/PhysRevB.24.7412	journal	December 1981
Effects of strain on band structure and effective masses in MoS $_{2}$ Peelaers, H.; Van de Walle, C. G. Physical Review B, Vol. 86, Issue 24 https://doi.org/10.1103/PhysRevB.86.241401	journal	December 2012
Two-dimensional crystals-based heterostructures: materials with tailored properties Novoselov, K. S.; Castro Neto, A. H. Physica Scripta, Vol. T146 https://doi.org/10.1088/0031-8949/2012/T146/014006	journal	January 2012
Robust optical emission polarization in MoS $_{2}$ monolayers through selective valley excitation Sallen, G.; Bouet, L.; Marie, X. Physical Review B, Vol. 86, Issue 8 https://doi.org/10.1103/PhysRevB.86.081301	journal	August 2012
Valley polarization and intervalley scattering in monolayer MoS ₂ Kioseoglou, G.; Hanbicki, A. T.; Currie, M. Applied Physics Letters, Vol. 101, Issue 22 https://doi.org/10.1063/1.4768299	journal	November 2012
Transport Theory of Monolayer Transition-Metal Dichalcogenides through Symmetry Song, Yang; Dery, Hanan Physical Review Letters, Vol. 111, Issue 2 https://doi.org/10.1103/PhysRevLett.111.026601	journal	July 2013
Quantum Spin Hall Effect in Graphene Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 95, Issue 22 https://doi.org/10.1103/PhysRevLett.95.226801	journal	November 2005
Tuning the Electronic and Magnetic Properties of MoS 2 Nanoribbons by Strain Engineering Pan, Hui; Zhang, Yong-Wei The Journal of Physical Chemistry C, Vol. 116, Issue 21 https://doi.org/10.1021/jp3015782	journal	May 2012
Tight-binding theory of the spin-orbit coupling in graphene Konschuh, Sergej; Gmitra, Martin; Fabian, Jaroslav Physical Review B, Vol. 82, Issue 24 https://doi.org/10.1103/PhysRevB.82.245412	journal	December 2010
Magnetoelectric effects and valley-controlled spin quantum gates in transition metal dichalcogenide bilayers Gong, Zhirui; Liu, Gui-Bin; Yu, Hongyi Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms3053	journal	June 2013
Intrinsic and Rashba spin-orbit interactions in graphene sheets Min, Hongki; Hill, J. E.; Sinitsyn, N. A. Physical Review B, Vol. 74, Issue 16 https://doi.org/10.1103/PhysRevB.74.165310	journal	October 2006
‘‘Absolute’’ deformation potentials: Formulation and ab initio calculations for semiconductors Van de Walle, Chris G.; Martin, Richard M. Physical Review Letters, Vol. 62, Issue 17 https://doi.org/10.1103/PhysRevLett.62.2028	journal	April 1989
Phonon-limited mobility in $n$ -type single-layer MoS $_{2}$ from first principles Kaasbjerg, Kristen; Thygesen, Kristian S.; Jacobsen, Karsten W. Physical Review B, Vol. 85, Issue 11 https://doi.org/10.1103/PhysRevB.85.115317	journal	March 2012
Mechanical and electronic properties of monolayer MoS2 under elastic strain Yue, Qu; Kang, Jun; Shao, Zhengzheng Physics Letters A, Vol. 376, Issue 12-13 https://doi.org/10.1016/j.physleta.2012.02.029	journal	February 2012
Spin--Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems Winkler, Roland; Höhler, Gerhard; Kühn, Johann H. Springer Tracts in Modern Physics, Vol. 191 https://doi.org/10.1007/b13586	book	January 2003
Strain Engineering of Graphene’s Electronic Structure Pereira, Vitor M.; Castro Neto, A. H. Physical Review Letters, Vol. 103, Issue 4 https://doi.org/10.1103/PhysRevLett.103.046801	journal	July 2009
Fusion of the LAPW and LMTO methods: The augmented plane wave plus muffin-tin orbital method Kotani, Takao; van Schilfgaarde, Mark Physical Review B, Vol. 81, Issue 12 https://doi.org/10.1103/PhysRevB.81.125117	journal	March 2010
Quasiparticle self-consistent $G W$ method: A basis for the independent-particle approximation Kotani, Takao; van Schilfgaarde, Mark; Faleev, Sergey V. Physical Review B, Vol. 76, Issue 16 https://doi.org/10.1103/PhysRevB.76.165106	journal	October 2007
Acoustic deformation potentials and heterostructure band offsets in semiconductors Cardona, Manuel; Christensen, Niels E. Physical Review B, Vol. 35, Issue 12 https://doi.org/10.1103/PhysRevB.35.6182	journal	April 1987
Fundamentals of Semiconductors Yu, Peter Y.; Cardona, Manuel Springer https://doi.org/10.1007/978-3-662-03848-2	book	January 1999
Control of valley polarization in monolayer MoS2 by optical helicity Mak, Kin Fai; He, Keliang; Shan, Jie Nature Nanotechnology, Vol. 7, Issue 8 https://doi.org/10.1038/nnano.2012.96	journal	June 2012
Quasiparticle band structure calculation of monolayer, bilayer, and bulk MoS $_{2}$ Cheiwchanchamnangij, Tawinan; Lambrecht, Walter R. L. Physical Review B, Vol. 85, Issue 20 https://doi.org/10.1103/PhysRevB.85.205302	journal	May 2012
Phonons and electron-phonon scattering in carbon nanotubes Suzuura, Hidekatsu; Ando, Tsuneya Physical Review B, Vol. 65, Issue 23 https://doi.org/10.1103/PhysRevB.65.235412	journal	May 2002
Valley polarization in MoS2 monolayers by optical pumping Zeng, Hualing; Dai, Junfeng; Yao, Wang Nature Nanotechnology, Vol. 7, Issue 8 https://doi.org/10.1038/nnano.2012.95	journal	June 2012
Size, Shape, and Low Energy Electronic Structure of Carbon Nanotubes Kane, C. L.; Mele, E. J. Physical Review Letters, Vol. 78, Issue 10 https://doi.org/10.1103/PhysRevLett.78.1932	journal	March 1997
Fundamentals of Semiconductors Yu, Peter Y.; Cardona, Manuel Graduate Texts in Physics https://doi.org/10.1007/978-3-642-00710-1	book	January 2010
An Information Theory-Inspired Strategy for Design of Re-programmable Encrypted Graphene-based Coding Metasurfaces at Terahertz Frequencies Momeni, Ali; Rouhi, Kasra; Rajabalipanah, Hamid Scientific Reports, Vol. 8, Issue 1 https://doi.org/10.1038/s41598-018-24553-2	journal	April 2018
Tight-binding theory of the spin-orbit coupling in graphene Konschuh, Sergej; Gmitra, Martin; Fabian, Jaroslav Universität Regensburg https://doi.org/10.5283/epub.22864	text	January 2010
Fundamentals of Semiconductors: Physics and Materials Properties Yu, Peter Y.; Cardona, Manuel Graduate Texts in Physics https://doi.org/10.1007/b137661	book	January 2005
The electronic properties of graphene Neto, A. H. Castro; Guinea, F.; Peres, N. M. R. arXiv https://doi.org/10.48550/arxiv.0709.1163	text	January 2007
Invariant expansion for the trigonal band structure of graphene Winkler, R.; Zülicke, U. arXiv https://doi.org/10.48550/arxiv.0807.4204	text	January 2008
Band-structure topologies of graphene: spin-orbit coupling effects from first principles Gmitra, M.; Konschuh, S.; Ertler, C. arXiv https://doi.org/10.48550/arxiv.0904.3315	text	January 2009
Analysis of phonon-induced spin relaxation processes in silicon Song, Yang; Dery, Hanan arXiv https://doi.org/10.48550/arxiv.1201.6660	text	January 2012
Intrinsic Spin Lifetime of Conduction Electrons in Germanium Li, Pengke; Song, Yang; Dery, Hanan arXiv https://doi.org/10.48550/arxiv.1205.1829	text	January 2012
Intrinsic spin Hall effect in monolayers of group-VI dichalcogenides: A first-principles study Feng, Wanxiang; Yao, Yugui; Zhu, Wenguang arXiv https://doi.org/10.48550/arxiv.1209.1964	text	January 2012
Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation Kotani, Takao; van Schilfgaarde, Mark; Faleev, Sergey V. arXiv https://doi.org/10.48550/arxiv.cond-mat/0611002	text	January 2006

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Title: Strain effects on the spin-orbit-induced band structure splittings in monolayer MoS $_{2}$ and graphene