Effective Hamiltonians for phosphorene and silicene

Lew Yan Voon, L. C.; Lopez-Bezanilla, A.; Wang, J.; Zhang, Y.; Willatzen, M.

doi:10.1088/1367-2630/17/2/025004

Title: Effective Hamiltonians for phosphorene and silicene

Abstract

We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene. We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector. We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k center dot p parameters.

Authors:

Lew Yan Voon, L. C. ^[1]; Lopez-Bezanilla, A. ^[2]; Wang, J. ^[3]; Zhang, Y. ^[3]; Willatzen, M. ^[4]

The Citadel, Charleston, SC (United States)
Argonne National Lab., Lomont, IL (United States)
Univ. of North Carolina, Charlotte, NC (United States)
Univ. of Denmark, Lyngby (Denmark)

Publication Date:: Wed Feb 04 00:00:00 EST 2015

Research Org.:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science - Office of Basic Energy Sciences - Materials Sciences and Engineering Division; The Citadel

OSTI Identifier:: 1194161

Alternate Identifier(s):: OSTI ID: 1352839

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: New Journal of Physics

Additional Journal Information:: Journal Volume: 17; Journal Issue: 2; Journal ID: ISSN 1367-2630

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Lew Yan Voon, L. C., Lopez-Bezanilla, A., Wang, J., Zhang, Y., and Willatzen, M. Effective Hamiltonians for phosphorene and silicene.  United States: N. p., 2015. 
Web.  doi:10.1088/1367-2630/17/2/025004.

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                    Lew Yan Voon, L. C., Lopez-Bezanilla, A., Wang, J., Zhang, Y., & Willatzen, M. Effective Hamiltonians for phosphorene and silicene.  United States.  https://doi.org/10.1088/1367-2630/17/2/025004

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                    Lew Yan Voon, L. C., Lopez-Bezanilla, A., Wang, J., Zhang, Y., and Willatzen, M. Wed .  
"Effective Hamiltonians for phosphorene and silicene".  United States.  https://doi.org/10.1088/1367-2630/17/2/025004.  https://www.osti.gov/servlets/purl/1194161.

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@article{osti_1194161,

  title        = {Effective Hamiltonians for phosphorene and silicene},

  author       = {Lew Yan Voon, L. C. and Lopez-Bezanilla, A. and Wang, J. and Zhang, Y. and Willatzen, M.},

  abstractNote = {We derived the effective Hamiltonians for silicene and phosphorene with strain, electric field and magnetic field using the method of invariants. Our paper extends the work of Geissler et al 2013 (New J. Phys. 15 085030) on silicene, and Li and Appelbaum 2014 (Phys. Rev. B 90, 115439) on phosphorene. Our Hamiltonians are compared to an equivalent one for graphene. For silicene, the expression for band warping is obtained analytically and found to be of different order than for graphene. We prove that a uniaxial strain does not open a gap, resolving contradictory numerical results in the literature. For phosphorene, it is shown that the bands near the Brillouin zone center only have terms in even powers of the wave vector. We predict that the energies change quadratically in the presence of a perpendicular external electric field but linearly in a perpendicular magnetic field, as opposed to those for silicene which vary linearly in both cases. Preliminary ab initio calculations for the intrinsic band structures have been carried out in order to evaluate some of the k center dot p parameters.},

  doi          = {10.1088/1367-2630/17/2/025004},

  journal      = {New Journal of Physics},

  number       = 2,

  volume       = 17,

  place        = {United States},

  year         = {Wed Feb 04 00:00:00 EST 2015},

  month        = {Wed Feb 04 00:00:00 EST 2015}

}

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Works referencing / citing this record:

Computational study of silicene nanoribbon tunnel field-effect transistor
journal, May 2019

Srivastava, Ashok; Fahad, Md. S.; Sharma, Ashwani K.
Microsystem Technologies
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A tight binding and $$\overrightarrow{{\boldsymbol{k}}}\cdot \overrightarrow{{\boldsymbol{p}}}$$ k → ⋅ p → study of monolayer stanene
journal, September 2017

Jiang, Liming; Marconcini, Paolo; Hossian, Md Sharafat
Scientific Reports, Vol. 7, Issue 1
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Silicene: Recent theoretical advances
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Lew Yan Voon, L. C.; Zhu, Jiajie; Schwingenschlögl, Udo
Applied Physics Reviews, Vol. 3, Issue 4
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Spin-dependent k.p Hamiltonian of black phosphorene based on Löwdin partitioning method
journal, July 2018

Kafaei, Narges; Beiranvand, Khadijeh; Sabaeian, Mohammad
Journal of Applied Physics, Vol. 124, Issue 3
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Functionalization of group-14 two-dimensional materials
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Focus on silicene and other 2D materials
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Ezawa, Motohiko; Le Lay, Guy
New Journal of Physics, Vol. 17, Issue 9
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$k \cdot p$ theory for phosphorene: Effective $g$ -factors, Landau levels, and excitons
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Faria Junior, Paulo E.; Kurpas, Marcin; Gmitra, Martin
Physical Review B, Vol. 100, Issue 11
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Origin of the electromagnetic anisotropy in monolayer black phosphorus
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Li, Pengke
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Normal and skewed phosphorene nanoribbons in combined magnetic and electric fields
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Arsoski, Vladimir V.; Grujić, Marko M.; Čukarić, Nemanja A.
Physical Review B, Vol. 96, Issue 12
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Strain-engineered Majorana zero energy modes and $φ_{0}$ Josephson state in black phosphorus
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Alidoust, Mohammad; Willatzen, Morten; Jauho, Antti-Pekka
Physical Review B, Vol. 98, Issue 8
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Fraunhofer response and supercurrent spin switching in black phosphorus with strain and disorder
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Alidoust, Mohammad; Willatzen, Morten; Jauho, Antti-Pekka
Physical Review B, Vol. 98, Issue 18
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Spin Orbit Coupling Gap and Indirect Gap in Strain-Tuned Topological Insulator-Antimonene
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Cheung, Chi-Ho; Fuh, Huei-Ru; Hsu, Ming-Chien
Nanoscale Research Letters, Vol. 11, Issue 1
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k.p theory for phosphorene: Effective g-factors, Landau levels, and excitons
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Faria Junior, Paulo E.; Kurpas, Marcin; Gmitra, Martin
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Spin Orbit Coupling Gap and Indirect Gap in Strain-Tuned Topological Insulator-Antimonene
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Cheung, Chi-Ho; Fuh, Huei-Ru; Hsu, Ming-Chien
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Title: Effective Hamiltonians for phosphorene and silicene

Abstract

Citation Formats

The electronic properties of graphene journal, January 2009

Electronic structure of silicon-based nanostructures journal, August 2007

Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility journal, March 2014

Theoretical possibility of stage corrugation in Si and Ge analogs of graphite journal, November 1994

Electronic structure of black phosphorus: Tight binding approach journal, May 1981

The Band Theory of Graphite journal, May 1947

Invariant expansion for the trigonal band structure of graphene journal, December 2010

Group theoretical and topological analysis of the quantum spin Hall effect in silicene journal, August 2013

Strain-Induced Gap Modification in Black Phosphorus journal, May 2014

Electrons and holes in phosphorene journal, September 2014

Quantum Spin Hall Effect in Silicene and Two-Dimensional Germanium journal, August 2011

Projector augmented-wave method journal, December 1994

Generalized Gradient Approximation Made Simple journal, October 1996

Ab initio molecular dynamics for open-shell transition metals journal, November 1993

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set journal, October 1996

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

Strain and chirality effects on the mechanical and electronic properties of silicene and silicane under uniaxial tension journal, October 2012

Electronic and optical properties of silicene under uni-axial and bi-axial mechanical strains: A first principle study journal, July 2014

First-principles calculations of mechanical and electronic properties of silicene under strain journal, June 2012

Phonon instability and ideal strength of silicene under tension journal, December 2014

Uniaxial strain-induced mechanical and electronic property modulation of silicene journal, September 2014

Electrically tunable band gap in silicene journal, February 2012

Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus journal, June 2014

Strain-Engineering the Anisotropic Electrical Conductance of Few-Layer Black Phosphorus journal, April 2014

Modulation of the Electronic Properties of Ultrathin Black Phosphorus by Strain and Electrical Field journal, October 2014

Strain-engineered direct-indirect band gap transition and its mechanism in two-dimensional phosphorene journal, August 2014

Strain Engineering for Phosphorene: The Potential Application as a Photocatalyst journal, November 2014

Computational study of silicene nanoribbon tunnel field-effect transistor journal, May 2019

A tight binding and $$\overrightarrow{{\boldsymbol{k}}}\cdot \overrightarrow{{\boldsymbol{p}}}$$ k → ⋅ p → study of monolayer stanene journal, September 2017

Silicene: Recent theoretical advances journal, December 2016

Spin-dependent k.p Hamiltonian of black phosphorene based on Löwdin partitioning method journal, July 2018

Functionalization of group-14 two-dimensional materials journal, May 2018

Focus on silicene and other 2D materials journal, September 2015

k · p theory for phosphorene: Effective g -factors, Landau levels, and excitons journal, September 2019

Origin of the electromagnetic anisotropy in monolayer black phosphorus journal, November 2019

Normal and skewed phosphorene nanoribbons in combined magnetic and electric fields journal, September 2017

Strain-engineered Majorana zero energy modes and φ 0 Josephson state in black phosphorus journal, August 2018

Fraunhofer response and supercurrent spin switching in black phosphorus with strain and disorder journal, November 2018

Spin Orbit Coupling Gap and Indirect Gap in Strain-Tuned Topological Insulator-Antimonene journal, October 2016

k.p theory for phosphorene: Effective g-factors, Landau levels, and excitons text, January 2019

Spin Orbit Coupling Gap and Indirect Gap in Strain-Tuned Topological Insulator-Antimonene journal, October 2016

The electronic properties of graphene
journal, January 2009

Electronic structure of silicon-based nanostructures
journal, August 2007

Phosphorene: An Unexplored 2D Semiconductor with a High Hole Mobility
journal, March 2014

Theoretical possibility of stage corrugation in Si and Ge analogs of graphite
journal, November 1994

Electronic structure of black phosphorus: Tight binding approach
journal, May 1981

The Band Theory of Graphite
journal, May 1947

Invariant expansion for the trigonal band structure of graphene
journal, December 2010

Group theoretical and topological analysis of the quantum spin Hall effect in silicene
journal, August 2013

Strain-Induced Gap Modification in Black Phosphorus
journal, May 2014

Electrons and holes in phosphorene
journal, September 2014

Quantum Spin Hall Effect in Silicene and Two-Dimensional Germanium
journal, August 2011

Projector augmented-wave method
journal, December 1994

Generalized Gradient Approximation Made Simple
journal, October 1996

Ab initio molecular dynamics for open-shell transition metals
journal, November 1993

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996

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

Strain and chirality effects on the mechanical and electronic properties of silicene and silicane under uniaxial tension
journal, October 2012

Electronic and optical properties of silicene under uni-axial and bi-axial mechanical strains: A first principle study
journal, July 2014

First-principles calculations of mechanical and electronic properties of silicene under strain
journal, June 2012

Phonon instability and ideal strength of silicene under tension
journal, December 2014

Uniaxial strain-induced mechanical and electronic property modulation of silicene
journal, September 2014

Electrically tunable band gap in silicene
journal, February 2012

Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus
journal, June 2014

Strain-Engineering the Anisotropic Electrical Conductance of Few-Layer Black Phosphorus
journal, April 2014

Modulation of the Electronic Properties of Ultrathin Black Phosphorus by Strain and Electrical Field
journal, October 2014

Strain-engineered direct-indirect band gap transition and its mechanism in two-dimensional phosphorene
journal, August 2014

Strain Engineering for Phosphorene: The Potential Application as a Photocatalyst
journal, November 2014

Computational study of silicene nanoribbon tunnel field-effect transistor
journal, May 2019

A tight binding and $$\overrightarrow{{\boldsymbol{k}}}\cdot \overrightarrow{{\boldsymbol{p}}}$$ k → ⋅ p → study of monolayer stanene
journal, September 2017

Silicene: Recent theoretical advances
journal, December 2016

Spin-dependent k.p Hamiltonian of black phosphorene based on Löwdin partitioning method
journal, July 2018

Functionalization of group-14 two-dimensional materials
journal, May 2018

Focus on silicene and other 2D materials
journal, September 2015

$k \cdot p$ theory for phosphorene: Effective $g$ -factors, Landau levels, and excitons
journal, September 2019

Origin of the electromagnetic anisotropy in monolayer black phosphorus
journal, November 2019

Normal and skewed phosphorene nanoribbons in combined magnetic and electric fields
journal, September 2017

Strain-engineered Majorana zero energy modes and $φ_{0}$ Josephson state in black phosphorus
journal, August 2018

Fraunhofer response and supercurrent spin switching in black phosphorus with strain and disorder
journal, November 2018

Spin Orbit Coupling Gap and Indirect Gap in Strain-Tuned Topological Insulator-Antimonene
journal, October 2016

k.p theory for phosphorene: Effective g-factors, Landau levels, and excitons
text, January 2019

Spin Orbit Coupling Gap and Indirect Gap in Strain-Tuned Topological Insulator-Antimonene
journal, October 2016