Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations
Abstract
The quasiparticle band structure can be properly described by Hedin's GW approximation (GW), at a high computational cost. For band gaps, semilocal density functionals up to the generalized gradient approximation (GGA) level cannot compete with the accuracy of hybrid-based approximations or GW. Meta-GGA density functionals with a strong dependence on the kinetic energy density ingredient can potentially give wider band gaps compared with GGAs. The recent TASK meta-GGA density functional from Aschebrock and Kümmel [Phys. Rev. Research 1, 033082 (2019)], is constructed with an enhanced nonlocality in the generalized Kohn-Sham scheme and therefore harbors great opportunities for band gap prediction. Although this approximation was found to yield excellent band gaps of bulk solids, this accuracy cannot be straightforwardly transferred to low-dimensional materials. Additionally, the reduced screening of these materials results in larger band gaps compared with their bulk counterparts, as an additional barrier to overcome. In this paper we demonstrate how the alteration of this functional affects the band gaps of monolayers and nanoribbons and present accurate band gaps competing with the revised Heyd-Scuseria-Ernzerhof (HSE06) approximation. In order to achieve this goal, we have modified the TASK functional (a) by changing the tight upper bound for one- or two-electron systems ( ) from 1.174 to 1.29 and (b) by changing the limit of the interpolation function ) of the TASK functional that interpolates the exchange enhancement factor from to 1. The resulting modified TASK (mTASK) was tested for various materials from three dimensions to two dimensions to one dimension (nanoribbons) and was compared with the results of the higher-level hybrid functional HSE06 or with the approximation within many-body perturbation theory. We find that mTASK systematically improves the band gaps and band structures of two-dimensional (2D) and 1D systems, without significantly affecting the accuracy of the original TASK for the bulk 3D materials, when compared with the Perdew-Burke-Ernzerhof (PBE) GGA and the strongly constrained and appropriately normed (SCAN) meta-GGA. We further demonstrate the applicability of mTASK by assessing the band structures of transition metal dichalcogenide nanoribbons with respect to various bending curvatures.
- Publication Date:
- Research Org.:
- Temple Univ., Philadelphia, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); US Army Research Office (ARO); National Science Foundation (NSF)
- OSTI Identifier:
- 1853746
- Grant/Contract Number:
- SC0021263; W911NF-16-2-0189; 1625061
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Materials
- Additional Journal Information:
- Journal Volume: 5; Journal Issue: 6; Journal ID: ISSN 2475-9953
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; Band gap; Density functional theory
Citation Formats
Neupane, Bimal, Tang, Hong, Nepal, Niraj K., Adhikari, Santosh, and Ruzsinszky, Adrienn. Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations. United States: N. p., 2021.
Web. doi:10.1103/physrevmaterials.5.063803.
Neupane, Bimal, Tang, Hong, Nepal, Niraj K., Adhikari, Santosh, & Ruzsinszky, Adrienn. Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations. United States. https://doi.org/10.1103/physrevmaterials.5.063803
Neupane, Bimal, Tang, Hong, Nepal, Niraj K., Adhikari, Santosh, and Ruzsinszky, Adrienn. Mon .
"Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations". United States. https://doi.org/10.1103/physrevmaterials.5.063803. https://www.osti.gov/servlets/purl/1853746.
@article{osti_1853746,
title = {Opening band gaps of low-dimensional materials at the meta-GGA level of density functional approximations},
author = {Neupane, Bimal and Tang, Hong and Nepal, Niraj K. and Adhikari, Santosh and Ruzsinszky, Adrienn},
abstractNote = {The quasiparticle band structure can be properly described by Hedin's GW approximation (GW), at a high computational cost. For band gaps, semilocal density functionals up to the generalized gradient approximation (GGA) level cannot compete with the accuracy of hybrid-based approximations or GW. Meta-GGA density functionals with a strong dependence on the kinetic energy density ingredient can potentially give wider band gaps compared with GGAs. The recent TASK meta-GGA density functional from Aschebrock and Kümmel [Phys. Rev. Research 1, 033082 (2019)], is constructed with an enhanced nonlocality in the generalized Kohn-Sham scheme and therefore harbors great opportunities for band gap prediction. Although this approximation was found to yield excellent band gaps of bulk solids, this accuracy cannot be straightforwardly transferred to low-dimensional materials. Additionally, the reduced screening of these materials results in larger band gaps compared with their bulk counterparts, as an additional barrier to overcome. In this paper we demonstrate how the alteration of this functional affects the band gaps of monolayers and nanoribbons and present accurate band gaps competing with the revised Heyd-Scuseria-Ernzerhof (HSE06) approximation. In order to achieve this goal, we have modified the TASK functional (a) by changing the tight upper bound for one- or two-electron systems (hX0) from 1.174 to 1.29 and (b) by changing the limit of the interpolation function fX(α→∞) of the TASK functional that interpolates the exchange enhancement factor FX(s,α) from α=0 to 1. The resulting modified TASK (mTASK) was tested for various materials from three dimensions to two dimensions to one dimension (nanoribbons) and was compared with the results of the higher-level hybrid functional HSE06 or with the G0W0 approximation within many-body perturbation theory. We find that mTASK systematically improves the band gaps and band structures of two-dimensional (2D) and 1D systems, without significantly affecting the accuracy of the original TASK for the bulk 3D materials, when compared with the Perdew-Burke-Ernzerhof (PBE) GGA and the strongly constrained and appropriately normed (SCAN) meta-GGA. We further demonstrate the applicability of mTASK by assessing the band structures of transition metal dichalcogenide nanoribbons with respect to various bending curvatures.},
doi = {10.1103/physrevmaterials.5.063803},
journal = {Physical Review Materials},
number = 6,
volume = 5,
place = {United States},
year = {Mon Jun 21 00:00:00 EDT 2021},
month = {Mon Jun 21 00:00:00 EDT 2021}
}
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Works referenced in this record:
Strain and screening: Optical properties of a small-diameter carbon nanotube from first principles
journal, February 2019
- Wagner, Christian; Schuster, Jörg; Schleife, André
- Physical Review B, Vol. 99, Issue 7
HLE16: A Local Kohn–Sham Gradient Approximation with Good Performance for Semiconductor Band Gaps and Molecular Excitation Energies
journal, January 2017
- Verma, Pragya; Truhlar, Donald G.
- The Journal of Physical Chemistry Letters, Vol. 8, Issue 2
Optical properties of semiconductors within the independent-quasiparticle approximation
journal, October 1993
- Del Sole, R.; Girlanda, Raffaello
- Physical Review B, Vol. 48, Issue 16
Deorbitalized meta-GGA exchange-correlation functionals in solids
journal, September 2018
- Mejia-Rodriguez, Daniel; Trickey, S. B.
- Physical Review B, Vol. 98, Issue 11
More realistic band gaps from meta-generalized gradient approximations: Only in a generalized Kohn-Sham scheme
journal, May 2016
- Yang, Zeng-hui; Peng, Haowei; Sun, Jianwei
- Physical Review B, Vol. 93, Issue 20
Projector augmented-wave method
journal, December 1994
- Blöchl, P. E.
- Physical Review B, Vol. 50, Issue 24, p. 17953-17979
Optical Properties and Band Gap of Single- and Few-Layer MoTe 2 Crystals
journal, October 2014
- Ruppert, Claudia; Aslan, Ozgur Burak; Heinz, Tony F.
- Nano Letters, Vol. 14, Issue 11
Hybrid functionals based on a screened Coulomb potential
journal, May 2003
- Heyd, Jochen; Scuseria, Gustavo E.; Ernzerhof, Matthias
- The Journal of Chemical Physics, Vol. 118, Issue 18
Computational Search for Single-Layer Transition-Metal Dichalcogenide Photocatalysts
journal, September 2013
- Zhuang, Houlong L.; Hennig, Richard G.
- The Journal of Physical Chemistry C, Vol. 117, Issue 40
Erratum: Accurate and simple analytic representation of the electron-gas correlation energy [Phys. Rev. B 45, 13244 (1992)]
journal, August 2018
- Perdew, John P.; Wang, Yue
- Physical Review B, Vol. 98, Issue 7
Modeling with Hybrid Density Functional Theory the Electronic Band Alignment at the Zinc Oxide–Anatase Interface
journal, August 2012
- Conesa, José C.
- The Journal of Physical Chemistry C, Vol. 116, Issue 35
Density-functional exchange correlation through coordinate scaling in adiabatic connection and correlation hole
journal, May 1991
- Levy, Mel
- Physical Review A, Vol. 43, Issue 9
Charge Transfer Equilibria Between Diamond and an Aqueous Oxygen Electrochemical Redox Couple
journal, November 2007
- Chakrapani, V.; Angus, J. C.; Anderson, A. B.
- Science, Vol. 318, Issue 5855
Communication: Effect of the orbital-overlap dependence in the meta generalized gradient approximation
journal, August 2012
- Sun, Jianwei; Xiao, Bing; Ruzsinszky, Adrienn
- The Journal of Chemical Physics, Vol. 137, Issue 5
Tuning Interlayer Coupling in Large-Area Heterostructures with CVD-Grown MoS 2 and WS 2 Monolayers
journal, May 2014
- Tongay, Sefaattin; Fan, Wen; Kang, Jun
- Nano Letters, Vol. 14, Issue 6
From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999
- Kresse, G.; Joubert, D.
- Physical Review B, Vol. 59, Issue 3, p. 1758-1775
Band Offsets at Semiconductor-Oxide Interfaces from Hybrid Density-Functional Calculations
journal, September 2008
- Alkauskas, Audrius; Broqvist, Peter; Devynck, Fabien
- Physical Review Letters, Vol. 101, Issue 10
The Computational 2D Materials Database: high-throughput modeling and discovery of atomically thin crystals
journal, September 2018
- Haastrup, Sten; Strange, Mikkel; Pandey, Mohnish
- 2D Materials, Vol. 5, Issue 4
Hybrid density functional theory band structure engineering in hematite
journal, June 2011
- Pozun, Zachary D.; Henkelman, Graeme
- The Journal of Chemical Physics, Vol. 134, Issue 22
Density functional theory and the band gap problem
journal, March 1985
- Perdew, John P.
- International Journal of Quantum Chemistry, Vol. 28, Issue S19
Understanding band gaps of solids in generalized Kohn–Sham theory
journal, March 2017
- Perdew, John P.; Yang, Weitao; Burke, Kieron
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 11
Optical Spectrum of : Many-Body Effects and Diversity of Exciton States
journal, November 2013
- Qiu, Diana Y.; da Jornada, Felipe H.; Louie, Steven G.
- Physical Review Letters, Vol. 111, Issue 21
New generalized gradient approximation functionals
journal, January 2000
- Boese, A. Daniel; Doltsinis, Nikos L.; Handy, Nicholas C.
- The Journal of Chemical Physics, Vol. 112, Issue 4
Evaluating density functional performance for the quasi-two-dimensional electron gas
journal, February 2000
- Pollack, L.; Perdew, J. P.
- Journal of Physics: Condensed Matter, Vol. 12, Issue 7, p. 1239-1252
Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)]
journal, June 2006
- Heyd, Jochen; Scuseria, Gustavo E.; Ernzerhof, Matthias
- The Journal of Chemical Physics, Vol. 124, Issue 21
Direct and indirect transitions in the region of the band gap using electron-energy-loss spectroscopy
journal, October 1998
- Rafferty, B.; Brown, L. M.
- Physical Review B, Vol. 58, Issue 16
Atomically Thin A New Direct-Gap Semiconductor
journal, September 2010
- Mak, Kin Fai; Lee, Changgu; Hone, James
- Physical Review Letters, Vol. 105, Issue 13, Article No.136805
Local Strain Engineering in Atomically Thin MoS 2
journal, October 2013
- Castellanos-Gomez, Andres; Roldán, Rafael; Cappelluti, Emmanuele
- Nano Letters, Vol. 13, Issue 11
Accurate Band Gaps of Semiconductors and Insulators with a Semilocal Exchange-Correlation Potential
journal, June 2009
- Tran, Fabien; Blaha, Peter
- Physical Review Letters, Vol. 102, Issue 22
Bending Two-Dimensional Materials To Control Charge Localization and Fermi-Level Shift
journal, March 2016
- Yu, Liping; Ruzsinszky, Adrienn; Perdew, John P.
- Nano Letters, Vol. 16, Issue 4
First-principles study of mechanical and electronic properties of bent monolayer transition metal dichalcogenides
journal, July 2019
- Nepal, Niraj K.; Yu, Liping; Yan, Qimin
- Physical Review Materials, Vol. 3, Issue 7
Large excitonic effects in monolayers of molybdenum and tungsten dichalcogenides
journal, September 2012
- Ramasubramaniam, Ashwin
- Physical Review B, Vol. 86, Issue 11
Orbital Localization, Charge Transfer, and Band Gaps in Semilocal Density-Functional Theory
journal, July 2013
- Armiento, R.; Kümmel, S.
- Physical Review Letters, Vol. 111, Issue 3
A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)
journal, July 2004
- Yanai, Takeshi; Tew, David P.; Handy, Nicholas C.
- Chemical Physics Letters, Vol. 393, Issue 1-3, p. 51-57
Fourth-order gradient expansion of the fermion kinetic energy: Extra terms for nonanalytic densities
journal, July 1986
- Perdew, John P.; Sahni, Viraht; Harbola, Manoj K.
- Physical Review B, Vol. 34, Issue 2
Compact Representations of Kohn-Sham Invariant Subspaces
journal, April 2009
- Gygi, François
- Physical Review Letters, Vol. 102, Issue 16
Giant bandgap renormalization and excitonic effects in a monolayer transition metal dichalcogenide semiconductor
journal, August 2014
- Ugeda, Miguel M.; Bradley, Aaron J.; Shi, Su-Fei
- Nature Materials, Vol. 13, Issue 12
Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities
journal, November 1983
- Perdew, John P.; Levy, Mel
- Physical Review Letters, Vol. 51, Issue 20
Strongly Constrained and Appropriately Normed Semilocal Density Functional
journal, July 2015
- Sun, Jianwei; Ruzsinszky, Adrienn; Perdew, John P.
- Physical Review Letters, Vol. 115, Issue 3
Elastic, electronic, and dielectric properties of bulk and monolayer ZrS 2 , ZrSe 2 , HfS 2 , HfSe 2 from van der Waals density-functional theory: Bulk and monolayer ZrS 2 , ZrSe 2 , HfS 2 , HfSe 2 from van der Waals DFT
journal, May 2017
- Zhao, Qiyi; Guo, Yaohui; Si, Keyu
- physica status solidi (b), Vol. 254, Issue 9
Large-Area Synthesis of Monolayer and Few-Layer MoSe 2 Films on SiO 2 Substrates
journal, April 2014
- Lu, Xin; Utama, M. Iqbal Bakti; Lin, Junhao
- Nano Letters, Vol. 14, Issue 5
Generalized Kohn-Sham schemes and the band-gap problem
journal, February 1996
- Seidl, A.; Görling, A.; Vogl, P.
- Physical Review B, Vol. 53, Issue 7
Band offsets and heterostructures of two-dimensional semiconductors
journal, January 2013
- Kang, Jun; Tongay, Sefaattin; Zhou, Jian
- Applied Physics Letters, Vol. 102, Issue 1
Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits
journal, August 2005
- Perdew, John P.; Ruzsinszky, Adrienn; Tao, Jianmin
- The Journal of Chemical Physics, Vol. 123, Issue 6
Self-consistent hybrid functional for condensed systems
journal, May 2014
- Skone, Jonathan H.; Govoni, Marco; Galli, Giulia
- Physical Review B, Vol. 89, Issue 19
Why does the B3LYP hybrid functional fail for metals?
journal, July 2007
- Paier, Joachim; Marsman, Martijn; Kresse, Georg
- The Journal of Chemical Physics, Vol. 127, Issue 2
A simple measure of electron localization in atomic and molecular systems
journal, May 1990
- Becke, A. D.; Edgecombe, K. E.
- The Journal of Chemical Physics, Vol. 92, Issue 9
Tightly Bound Excitons in Monolayer
journal, July 2014
- He, Keliang; Kumar, Nardeep; Zhao, Liang
- Physical Review Letters, Vol. 113, Issue 2
Photoluminescence emission and Raman response of monolayer MoS_2, MoSe_2, and WSe_2
journal, January 2013
- Tonndorf, Philipp; Schmidt, Robert; Böttger, Philipp
- Optics Express, Vol. 21, Issue 4
Accurate electronic band gaps of two-dimensional materials from the local modified Becke-Johnson potential
journal, June 2020
- Rauch, Tomáš; Marques, Miguel A. L.; Botti, Silvana
- Physical Review B, Vol. 101, Issue 24
Solid-state optical absorption from optimally tuned time-dependent range-separated hybrid density functional theory
journal, August 2015
- Refaely-Abramson, Sivan; Jain, Manish; Sharifzadeh, Sahar
- Physical Review B, Vol. 92, Issue 8
Density-based mixing parameter for hybrid functionals
journal, January 2011
- Marques, Miguel A. L.; Vidal, Julien; Oliveira, Micael J. T.
- Physical Review B, Vol. 83, Issue 3
On the extended Thomas-Fermi approximation to the kinetic energy density
journal, October 1976
- Brack, M.; Jennings, B. K.; Chu, Y. H.
- Physics Letters B, Vol. 65, Issue 1
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem
journal, August 1965
- Hedin, Lars
- Physical Review, Vol. 139, Issue 3A
A new parametrization of exchange–correlation generalized gradient approximation functionals
journal, April 2001
- Boese, A. Daniel; Handy, Nicholas C.
- The Journal of Chemical Physics, Vol. 114, Issue 13
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996
- Kresse, G.; Furthmüller, J.
- Physical Review B, Vol. 54, Issue 16, p. 11169-11186
Many-body effects on the electronic and optical properties of strained semiconducting carbon nanotubes
journal, July 2013
- Spataru, Catalin D.; Léonard, François
- Physical Review B, Vol. 88, Issue 4
Toward reliable density functional methods without adjustable parameters: The PBE0 model
journal, April 1999
- Adamo, Carlo; Barone, Vincenzo
- The Journal of Chemical Physics, Vol. 110, Issue 13
Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory
journal, December 2014
- Eich, F. G.; Hellgren, Maria
- The Journal of Chemical Physics, Vol. 141, Issue 22
Density Functionals that Recognize Covalent, Metallic, and Weak Bonds
journal, September 2013
- Sun, Jianwei; Xiao, Bing; Fang, Yuan
- Physical Review Letters, Vol. 111, Issue 10
Self-consistent approximation to the Kohn-Sham exchange potential
journal, March 1995
- Gritsenko, Oleg; van Leeuwen, Robert; van Lenthe, Erik
- Physical Review A, Vol. 51, Issue 3
Defect levels through hybrid density functionals: Insights and applications
journal, March 2011
- Alkauskas, Audrius; Broqvist, Peter; Pasquarello, Alfredo
- physica status solidi (b), Vol. 248, Issue 4
Electron Localization in Solid-State Structures of the Elements: the Diamond Structure
journal, February 1992
- Savin, Andreas; Jepsen, Ove; Flad, Jürgen
- Angewandte Chemie International Edition in English, Vol. 31, Issue 2
Accurate and simple analytic representation of the electron-gas correlation energy
journal, June 1992
- Perdew, John P.; Wang, Yue
- Physical Review B, Vol. 45, Issue 23, p. 13244-13249
A hybrid functional scheme for defect levels and band alignments at semiconductor-oxide interfaces: Hybrid functional scheme for defect levels and band alignments
journal, January 2010
- Broqvist, Peter; Alkauskas, Audrius; Pasquarello, Alfredo
- physica status solidi (a), Vol. 207, Issue 2
Ultranonlocality and accurate band gaps from a meta-generalized gradient approximation
journal, November 2019
- Aschebrock, Thilo; Kümmel, Stephan
- Physical Review Research, Vol. 1, Issue 3
Benchmarking the AK13 Exchange Functional: Ionization Potentials and Electron Affinities
journal, November 2014
- Cerqueira, Tiago F. T.; Oliveira, Micael J. T.; Marques, Miguel A. L.
- Journal of Chemical Theory and Computation, Vol. 10, Issue 12
The self-consistent implementation of exchange-correlation functionals depending on the local kinetic energy density
journal, November 2003
- Arbuznikov, Alexei V.; Kaupp, Martin
- Chemical Physics Letters, Vol. 381, Issue 3-4
Orthogonal rational functions on a semi-infinite interval
journal, May 1987
- Boyd, John P.
- Journal of Computational Physics, Vol. 70, Issue 1
DFT study of structural and electronic properties of MoS 2(1−x) Se 2x alloy (x = 0.25)
journal, April 2018
- Gusakova, Julia; Gusakov, Vasilii; Tay, Beng Kang
- Journal of Applied Physics, Vol. 123, Issue 16
Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems
journal, October 2016
- Brawand, Nicholas P.; Vörös, Márton; Govoni, Marco
- Physical Review X, Vol. 6, Issue 4
Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space
journal, May 2012
- Moussa, Jonathan E.; Schultz, Peter A.; Chelikowsky, James R.
- The Journal of Chemical Physics, Vol. 136, Issue 20
Deorbitalization strategies for meta-generalized-gradient-approximation exchange-correlation functionals
journal, November 2017
- Mejia-Rodriguez, Daniel; Trickey, S. B.
- Physical Review A, Vol. 96, Issue 5
Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals
journal, November 1997
- Becke, Axel D.
- The Journal of Chemical Physics, Vol. 107, Issue 20
Gedanken densities and exact constraints in density functional theory
journal, May 2014
- Perdew, John P.; Ruzsinszky, Adrienn; Sun, Jianwei
- The Journal of Chemical Physics, Vol. 140, Issue 18
Long-Range-Corrected Hybrids Based on a New Model Exchange Hole
journal, March 2009
- Weintraub, Elon; Henderson, Thomas M.; Scuseria, Gustavo E.
- Journal of Chemical Theory and Computation, Vol. 5, Issue 4
Linear optical response in silicon and germanium including self-energy effects
journal, October 1989
- Levine, Zachary H.; Allan, Douglas C.
- Physical Review Letters, Vol. 63, Issue 16
Development and assessment of new exchange-correlation functionals
journal, October 1998
- Hamprecht, Fred A.; Cohen, Aron J.; Tozer, David J.
- The Journal of Chemical Physics, Vol. 109, Issue 15
Kohn-Sham potential with discontinuity for band gap materials
journal, September 2010
- Kuisma, M.; Ojanen, J.; Enkovaara, J.
- Physical Review B, Vol. 82, Issue 11
Optics of Semiconductors from Meta-Generalized-Gradient-Approximation-Based Time-Dependent Density-Functional Theory
journal, November 2011
- Nazarov, V. U.; Vignale, G.
- Physical Review Letters, Vol. 107, Issue 21
ELF: The Electron Localization Function
journal, September 1997
- Savin, Andreas; Nesper, Reinhard; Wengert, Steffen
- Angewandte Chemie International Edition in English, Vol. 36, Issue 17