An efficient computational framework for charge density estimation in twisted bilayer graphene

Rakib, Tawfiqur; Ertekin, Elif; Pochet, Pascal; Johnson, Harley T.

doi:10.1016/j.commatsci.2021.110746

Title: An efficient computational framework for charge density estimation in twisted bilayer graphene

Authors:: Rakib, Tawfiqur; Ertekin, Elif; Pochet, Pascal; Johnson, Harley T.

Publication Date:: 2021-11-01

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:: 1812978

Grant/Contract Number:: SC0020177

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Computational Materials Science

Additional Journal Information:: Journal Name: Computational Materials Science Journal Volume: 199 Journal Issue: C; Journal ID: ISSN 0927-0256

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Citation Formats


                    Rakib, Tawfiqur, Ertekin, Elif, Pochet, Pascal, and Johnson, Harley T. An efficient computational framework for charge density estimation in twisted bilayer graphene.  Netherlands: N. p., 2021. 
Web.  doi:10.1016/j.commatsci.2021.110746.

Copy to clipboard


                    Rakib, Tawfiqur, Ertekin, Elif, Pochet, Pascal, & Johnson, Harley T. An efficient computational framework for charge density estimation in twisted bilayer graphene.  Netherlands.  https://doi.org/10.1016/j.commatsci.2021.110746

Copy to clipboard


                    Rakib, Tawfiqur, Ertekin, Elif, Pochet, Pascal, and Johnson, Harley T. Mon .  
"An efficient computational framework for charge density estimation in twisted bilayer graphene".  Netherlands.  https://doi.org/10.1016/j.commatsci.2021.110746.

Copy to clipboard


                    
@article{osti_1812978,

  title        = {An efficient computational framework for charge density estimation in twisted bilayer graphene},

  author       = {Rakib, Tawfiqur and Ertekin, Elif and Pochet, Pascal and Johnson, Harley T.},

  abstractNote = {},

  doi          = {10.1016/j.commatsci.2021.110746},

  journal      = {Computational Materials Science},

  number       = C,

  volume       = 199,

  place        = {Netherlands},

  year         = {2021},

  month        = {11}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (Publisher)

Publisher's Version of Record
https://doi.org/10.1016/j.commatsci.2021.110746

Other availability

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle $θ \sim 1 . 08^{\circ}$
journal, May 2019

Lucignano, Procolo; Alfè, Dario; Cataudella, Vittorio
Physical Review B, Vol. 99, Issue 19
DOI: 10.1103/PhysRevB.99.195419

Generalized Gradient Approximation Made Simple
journal, October 1996

Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
DOI: 10.1103/PhysRevLett.77.3865

Optical absorption in twisted bilayer graphene
journal, May 2013

Moon, Pilkyung; Koshino, Mikito
Physical Review B, Vol. 87, Issue 20
DOI: 10.1103/PhysRevB.87.205404

Graphene Bilayer with a Twist: Electronic Structure
journal, December 2007

Lopes dos Santos, J. M. B.; Peres, N. M. R.; Castro Neto, A. H.
Physical Review Letters, Vol. 99, Issue 25
DOI: 10.1103/PhysRevLett.99.256802

Publisher’s Note: 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)]
journal, November 2012

Brihuega, I.; Mallet, P.; González-Herrero, H.
Physical Review Letters, Vol. 109, Issue 20
DOI: 10.1103/PhysRevLett.109.209905

Multiscale modelling of charged impurities in two-dimensional materials
journal, April 2019

Lischner, Johannes
Computational Materials Science, Vol. 160
DOI: 10.1016/j.commatsci.2019.01.012

Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018

Cao, Yuan; Fatemi, Valla; Fang, Shiang
Nature, Vol. 556, Issue 7699
DOI: 10.1038/nature26160

Strain solitons and topological defects in bilayer graphene
journal, June 2013

Alden, J. S.; Tsen, A. W.; Huang, P. Y.
Proceedings of the National Academy of Sciences, Vol. 110, Issue 28
DOI: 10.1073/pnas.1309394110

Structural and electronic transformation in low-angle twisted bilayer graphene
journal, November 2017

Gargiulo, Fernando; Yazyev, Oleg V.
2D Materials, Vol. 5, Issue 1
DOI: 10.1088/2053-1583/aa9640

Origin of the vortex displacement field in twisted bilayer graphene
journal, August 2020

Gornostyrev, Yu. N.; Katsnelson, M. I.
Physical Review B, Vol. 102, Issue 8
DOI: 10.1103/PhysRevB.102.085428

Helical network model for twisted bilayer graphene
journal, July 2018

Efimkin, Dmitry K.; MacDonald, Allan H.
Physical Review B, Vol. 98, Issue 3
DOI: 10.1103/PhysRevB.98.035404

Buckling of 2D nano hetero-structures with moire patterns
journal, May 2020

Chandra, Y.; Saavedra Flores, E. I.; Adhikari, S.
Computational Materials Science, Vol. 177
DOI: 10.1016/j.commatsci.2019.109507

Comparison of performance of van der Waals-corrected exchange-correlation functionals for interlayer interaction in graphene and hexagonal boron nitride
journal, February 2017

Lebedeva, Irina V.; Lebedev, Alexander V.; Popov, Andrey M.
Computational Materials Science, Vol. 128
DOI: 10.1016/j.commatsci.2016.11.011

Flat bands in slightly twisted bilayer graphene: Tight-binding calculations
journal, September 2010

Suárez Morell, E.; Correa, J. D.; Vargas, P.
Physical Review B, Vol. 82, Issue 12
DOI: 10.1103/PhysRevB.82.121407

Coupling-constant dependence of atomization energies
journal, January 1997

Ernzerhof, Matthias; Perdew, John P.; Burke, Kieron
International Journal of Quantum Chemistry, Vol. 64, Issue 3
DOI: 10.1002/(SICI)1097-461X(1997)64:3<285::AID-QUA2>3.0.CO;2-S

Twisted Bilayer Graphene: Moiré with a Twist
journal, August 2016

Dai, Shuyang; Xiang, Yang; Srolovitz, David J.
Nano Letters, Vol. 16, Issue 9
DOI: 10.1021/acs.nanolett.6b02870

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
DOI: 10.1103/PhysRevB.59.1758

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995

Plimpton, Steve
Journal of Computational Physics, Vol. 117, Issue 1
DOI: 10.1006/jcph.1995.1039

Origin of van Hove singularities in twisted bilayer graphene
journal, August 2015

Ribeiro, H. B.; Sato, K.; Eliel, G. S. N.
Carbon, Vol. 90
DOI: 10.1016/j.carbon.2015.04.005

Exact continuum model for low-energy electronic states of twisted bilayer graphene
journal, August 2019

Carr, Stephen; Fang, Shiang; Zhu, Ziyan
Physical Review Research, Vol. 1, Issue 1
DOI: 10.1103/PhysRevResearch.1.013001

Moiré structures in twisted bilayer graphene studied by transmission electron microscopy
journal, February 2019

Latychevskaia, Tatiana; Escher, Conrad; Fink, Hans-Werner
Ultramicroscopy, Vol. 197
DOI: 10.1016/j.ultramic.2018.11.009

Maximized electron interactions at the magic angle in twisted bilayer graphene
journal, July 2019

Kerelsky, Alexander; McGilly, Leo J.; Kennes, Dante M.
Nature, Vol. 572, Issue 7767
DOI: 10.1038/s41586-019-1431-9

Moire bands in twisted double-layer graphene
journal, July 2011

Bistritzer, R.; MacDonald, A. H.
Proceedings of the National Academy of Sciences, Vol. 108, Issue 30
DOI: 10.1073/pnas.1108174108

Structural and electron diffraction scaling of twisted graphene bilayers
journal, March 2018

Zhang, Kuan; Tadmor, Ellad B.
Journal of the Mechanics and Physics of Solids, Vol. 112
DOI: 10.1016/j.jmps.2017.12.005

Theory of the scanning tunneling microscope
journal, January 1985

Tersoff, J.; Hamann, D. R.
Physical Review B, Vol. 31, Issue 2
DOI: 10.1103/PhysRevB.31.805

Fourier transform analysis of STM images of multilayer graphene moiré patterns
journal, March 2015

Joucken, Frédéric; Frising, Fernande; Sporken, Robert
Carbon, Vol. 83
DOI: 10.1016/j.carbon.2014.11.030

Local spectroscopy of moiré-induced electronic structure in gate-tunable twisted bilayer graphene
journal, October 2015

Wong, Dillon; Wang, Yang; Jung, Jeil
Physical Review B, Vol. 92, Issue 15
DOI: 10.1103/PhysRevB.92.155409

Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions
journal, August 2018

Zou, Liujun; Po, Hoi Chun; Vishwanath, Ashvin
Physical Review B, Vol. 98, Issue 8
DOI: 10.1103/PhysRevB.98.085435

Atomic simulations of the formation of twist grain boundary and mechanical properties of graphene/aluminum nanolaminated composites
journal, February 2020

Zhou, Xiaohuan; Liu, Xia; Lei, Jun
Computational Materials Science, Vol. 172
DOI: 10.1016/j.commatsci.2019.109342

Strongly correlated Chern insulators in magic-angle twisted bilayer graphene
journal, December 2020

Nuckolls, Kevin P.; Oh, Myungchul; Wong, Dillon
Nature, Vol. 588, Issue 7839
DOI: 10.1038/s41586-020-3028-8

Localization of lattice dynamics in low-angle twisted bilayer graphene
journal, February 2021

Gadelha, Andreij C.; Ohlberg, Douglas A. A.; Rabelo, Cassiano
Nature, Vol. 590, Issue 7846
DOI: 10.1038/s41586-021-03252-5

Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene
journal, April 2019

Yoo, Hyobin; Engelke, Rebecca; Carr, Stephen
Nature Materials, Vol. 18, Issue 5
DOI: 10.1038/s41563-019-0346-z

The electronic properties of bilayer graphene
journal, April 2013

McCann, Edward; Koshino, Mikito
Reports on Progress in Physics, Vol. 76, Issue 5
DOI: 10.1088/0034-4885/76/5/056503

Semiempirical GGA-type density functional constructed with a long-range dispersion correction
journal, January 2006

Grimme, Stefan
Journal of Computational Chemistry, Vol. 27, Issue 15, p. 1787-1799
DOI: 10.1002/jcc.20495

Higher-Order Topological Insulator in Twisted Bilayer Graphene
journal, November 2019

Park, Moon Jip; Kim, Youngkuk; Cho, Gil Young
Physical Review Letters, Vol. 123, Issue 21
DOI: 10.1103/PhysRevLett.123.216803

Tkatchenko-Scheffler van der Waals correction method with and without self-consistent screening applied to solids
journal, February 2013

Bučko, Tomáš; Lebègue, S.; Hafner, Jürgen
Physical Review B, Vol. 87, Issue 6
DOI: 10.1103/PhysRevB.87.064110

$G$ -band Raman double resonance in twisted bilayer graphene: Evidence of band splitting and folding
journal, September 2009

Ni, Zhenhua; Liu, Lei; Wang, Yingying
Physical Review B, Vol. 80, Issue 12
DOI: 10.1103/PhysRevB.80.125404

Raman Spectrum of Graphene and Graphene Layers
journal, October 2006

Ferrari, A. C.; Meyer, J. C.; Scardaci, V.
Physical Review Letters, Vol. 97, Issue 18, Article No. 187401
DOI: 10.1103/PhysRevLett.97.187401

Energy and moiré patterns in 2D bilayers in translation and rotation: A study using an efficient discrete–continuum interlayer potential
journal, July 2017

Zhang, Kuan; Tadmor, Ellad B.
Extreme Mechanics Letters, Vol. 14
DOI: 10.1016/j.eml.2016.10.010

Electronic localization in small-angle twisted bilayer graphene
journal, June 2021

Hung Nguyen, V.; Paszko, D.; Lamparski, M.
2D Materials, Vol. 8, Issue 3
DOI: 10.1088/2053-1583/ac044f

Atomic Structure and Mechanical Properties of Twisted Bilayer Graphene
journal, December 2018

Zheng, Shaolong; Cao, Qiang; Liu, Sheng
Journal of Composites Science, Vol. 3, Issue 1
DOI: 10.3390/jcs3010002

Periodic overlayers and moiré patterns: theoretical studies of geometric properties
journal, July 2012

Hermann, Klaus
Journal of Physics: Condensed Matter, Vol. 24, Issue 31
DOI: 10.1088/0953-8984/24/31/314210

Toward Moiré engineering in 2D materials via dislocation theory
journal, December 2017

Pochet, Pascal; McGuigan, Brian C.; Coraux, Johann
Applied Materials Today, Vol. 9
DOI: 10.1016/j.apmt.2017.07.007

Raman spectra of twisted CVD bilayer graphene
journal, October 2017

Ramnani, Pankaj; Neupane, Mahesh R.; Ge, Supeng
Carbon, Vol. 123
DOI: 10.1016/j.carbon.2017.07.064

Abnormal conductivity in low-angle twisted bilayer graphene
journal, November 2020

Zhang, Shuai; Song, Aisheng; Chen, Lingxiu
Science Advances, Vol. 6, Issue 47
DOI: 10.1126/sciadv.abc5555

Angle-Dependent van Hove Singularities in a Slightly Twisted Graphene Bilayer
journal, September 2012

Yan, Wei; Liu, Mengxi; Dou, Rui-Fen
Physical Review Letters, Vol. 109, Issue 12
DOI: 10.1103/PhysRevLett.109.126801

Similar Records in DOE PAGES and OSTI.GOV collections:

Corrugation-driven symmetry breaking in magic-angle twisted bilayer graphene

Journal Article Rakib, Tawfiqur ; Pochet, Pascal ; Ertekin, Elif ; ... - Communications Physics

Abstract The discovery of unconventional superconductivity in magic-angle twisted bilayer graphene (tBLG) supported the twist-angle-induced flat band structure predictions made a decade earlier. Numerous physical properties have since been linked to the interlayer twist angle using the flat band prediction as a guideline. However, some key observations like the nematic phase and striped charge order behind the superconductivity are missing in this initial model. Here we show that a thermodynamically stable large out-of-plane displacement, or corrugation of the bilayer, induced by the interlayer twist, demonstrates partially filled states of the flat band structure, accompanied by a broken symmetry, in themore »« less
https://doi.org/10.1038/s42005-022-01013-y
Accurate tight-binding model for twisted bilayer graphene describes topological flat bands without geometric relaxation

Journal Article Pathak, Shivesh ; Rakib, Tawfiqur ; Hou, Run ; ... - Physical Review B
https://doi.org/10.1103/PhysRevB.105.115141
Topologically derived dislocation theory for twist and stretch moiré superlattices in bilayer graphene

Journal Article Annevelink, Emil ; Johnson, Harley T. ; Ertekin, Elif - Physical Review B

In this work, we develop a continuum dislocation description of twist and stretch moiré superlattices in two-dimensional material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moiré structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints and that minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer and a Peierls-Nabarro-like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result ofmore »« less
https://doi.org/10.1103/physrevb.102.184107

Full Text Available
WKB Estimate of Bilayer Graphene’s Magic Twist Angles

Journal Article Ren, Yafei ; Gao, Qiang ; MacDonald, A. H. ; ... - Physical Review Letters

We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which wemore »« less
https://doi.org/10.1103/physrevlett.126.016404

Full Text Available
Unconventional Superconductivity and Density Waves in Twisted Bilayer Graphene

Journal Article Isobe, Hiroki ; Yuan, Noah F. Q. ; Fu, Liang - Physical Review. X

We smore »« less
Cited by 52
https://doi.org/10.1103/PhysRevX.8.041041

Similar Records

Title: An efficient computational framework for charge density estimation in twisted bilayer graphene

Citation Formats

Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle θ ∼ 1 . 08 ∘ journal, May 2019

Generalized Gradient Approximation Made Simple journal, October 1996

Optical absorption in twisted bilayer graphene journal, May 2013

Graphene Bilayer with a Twist: Electronic Structure journal, December 2007

Publisher’s Note: 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)] journal, November 2012

Multiscale modelling of charged impurities in two-dimensional materials journal, April 2019

Unconventional superconductivity in magic-angle graphene superlattices journal, March 2018

Strain solitons and topological defects in bilayer graphene journal, June 2013

Structural and electronic transformation in low-angle twisted bilayer graphene journal, November 2017

Origin of the vortex displacement field in twisted bilayer graphene journal, August 2020

Helical network model for twisted bilayer graphene journal, July 2018

Buckling of 2D nano hetero-structures with moire patterns journal, May 2020

Comparison of performance of van der Waals-corrected exchange-correlation functionals for interlayer interaction in graphene and hexagonal boron nitride journal, February 2017

Flat bands in slightly twisted bilayer graphene: Tight-binding calculations journal, September 2010

Coupling-constant dependence of atomization energies journal, January 1997

Twisted Bilayer Graphene: Moiré with a Twist journal, August 2016

From ultrasoft pseudopotentials to the projector augmented-wave method journal, January 1999

Fast Parallel Algorithms for Short-Range Molecular Dynamics journal, March 1995

Origin of van Hove singularities in twisted bilayer graphene journal, August 2015

Exact continuum model for low-energy electronic states of twisted bilayer graphene journal, August 2019

Moiré structures in twisted bilayer graphene studied by transmission electron microscopy journal, February 2019

Maximized electron interactions at the magic angle in twisted bilayer graphene journal, July 2019

Moire bands in twisted double-layer graphene journal, July 2011

Structural and electron diffraction scaling of twisted graphene bilayers journal, March 2018

Theory of the scanning tunneling microscope journal, January 1985

Fourier transform analysis of STM images of multilayer graphene moiré patterns journal, March 2015

Local spectroscopy of moiré-induced electronic structure in gate-tunable twisted bilayer graphene journal, October 2015

Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions journal, August 2018

Atomic simulations of the formation of twist grain boundary and mechanical properties of graphene/aluminum nanolaminated composites journal, February 2020

Strongly correlated Chern insulators in magic-angle twisted bilayer graphene journal, December 2020

Localization of lattice dynamics in low-angle twisted bilayer graphene journal, February 2021

Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene journal, April 2019

The electronic properties of bilayer graphene journal, April 2013

Semiempirical GGA-type density functional constructed with a long-range dispersion correction journal, January 2006

Higher-Order Topological Insulator in Twisted Bilayer Graphene journal, November 2019

Tkatchenko-Scheffler van der Waals correction method with and without self-consistent screening applied to solids journal, February 2013

G -band Raman double resonance in twisted bilayer graphene: Evidence of band splitting and folding journal, September 2009

Raman Spectrum of Graphene and Graphene Layers journal, October 2006

Energy and moiré patterns in 2D bilayers in translation and rotation: A study using an efficient discrete–continuum interlayer potential journal, July 2017

Electronic localization in small-angle twisted bilayer graphene journal, June 2021

Atomic Structure and Mechanical Properties of Twisted Bilayer Graphene journal, December 2018

Periodic overlayers and moiré patterns: theoretical studies of geometric properties journal, July 2012

Toward Moiré engineering in 2D materials via dislocation theory journal, December 2017

Raman spectra of twisted CVD bilayer graphene journal, October 2017

Abnormal conductivity in low-angle twisted bilayer graphene journal, November 2020

Angle-Dependent van Hove Singularities in a Slightly Twisted Graphene Bilayer journal, September 2012

Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle $θ \sim 1 . 08^{\circ}$
journal, May 2019

Generalized Gradient Approximation Made Simple
journal, October 1996

Optical absorption in twisted bilayer graphene
journal, May 2013

Graphene Bilayer with a Twist: Electronic Structure
journal, December 2007

Publisher’s Note: 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)]
journal, November 2012

Multiscale modelling of charged impurities in two-dimensional materials
journal, April 2019

Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018

Strain solitons and topological defects in bilayer graphene
journal, June 2013

Structural and electronic transformation in low-angle twisted bilayer graphene
journal, November 2017

Origin of the vortex displacement field in twisted bilayer graphene
journal, August 2020

Helical network model for twisted bilayer graphene
journal, July 2018

Buckling of 2D nano hetero-structures with moire patterns
journal, May 2020

Comparison of performance of van der Waals-corrected exchange-correlation functionals for interlayer interaction in graphene and hexagonal boron nitride
journal, February 2017

Flat bands in slightly twisted bilayer graphene: Tight-binding calculations
journal, September 2010

Coupling-constant dependence of atomization energies
journal, January 1997

Twisted Bilayer Graphene: Moiré with a Twist
journal, August 2016

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995

Origin of van Hove singularities in twisted bilayer graphene
journal, August 2015

Exact continuum model for low-energy electronic states of twisted bilayer graphene
journal, August 2019

Moiré structures in twisted bilayer graphene studied by transmission electron microscopy
journal, February 2019

Maximized electron interactions at the magic angle in twisted bilayer graphene
journal, July 2019

Moire bands in twisted double-layer graphene
journal, July 2011

Structural and electron diffraction scaling of twisted graphene bilayers
journal, March 2018

Theory of the scanning tunneling microscope
journal, January 1985

Fourier transform analysis of STM images of multilayer graphene moiré patterns
journal, March 2015

Local spectroscopy of moiré-induced electronic structure in gate-tunable twisted bilayer graphene
journal, October 2015

Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions
journal, August 2018

Atomic simulations of the formation of twist grain boundary and mechanical properties of graphene/aluminum nanolaminated composites
journal, February 2020

Strongly correlated Chern insulators in magic-angle twisted bilayer graphene
journal, December 2020

Localization of lattice dynamics in low-angle twisted bilayer graphene
journal, February 2021

Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene
journal, April 2019

The electronic properties of bilayer graphene
journal, April 2013

Semiempirical GGA-type density functional constructed with a long-range dispersion correction
journal, January 2006

Higher-Order Topological Insulator in Twisted Bilayer Graphene
journal, November 2019

Tkatchenko-Scheffler van der Waals correction method with and without self-consistent screening applied to solids
journal, February 2013

$G$ -band Raman double resonance in twisted bilayer graphene: Evidence of band splitting and folding
journal, September 2009

Raman Spectrum of Graphene and Graphene Layers
journal, October 2006

Energy and moiré patterns in 2D bilayers in translation and rotation: A study using an efficient discrete–continuum interlayer potential
journal, July 2017

Electronic localization in small-angle twisted bilayer graphene
journal, June 2021

Atomic Structure and Mechanical Properties of Twisted Bilayer Graphene
journal, December 2018

Periodic overlayers and moiré patterns: theoretical studies of geometric properties
journal, July 2012

Toward Moiré engineering in 2D materials via dislocation theory
journal, December 2017

Raman spectra of twisted CVD bilayer graphene
journal, October 2017

Abnormal conductivity in low-angle twisted bilayer graphene
journal, November 2020

Angle-Dependent van Hove Singularities in a Slightly Twisted Graphene Bilayer
journal, September 2012