Lectures: Difference between revisions

From phys824
Jump to navigationJump to search
(Created page with '== PDF Lectures == * Lecture 1: What is nanophysics: Introduction to course topics [PDF] * Lecture 10: Graphene nanoribbons * Lecture 11: Carbon nanotubes * Lecture 16: Quantum …')
 
 
(580 intermediate revisions by the same user not shown)
Line 1: Line 1:
== PDF Lectures ==
== What is nanophysics: Survey of course topics ==
*[[Media:what_is_nanophysics.pdf|PDF]]
* [http://nanohub.org/resources/9598 Video lectures on AFM and STM from nanohub.org]


* Lecture 1: What is nanophysics: Introduction to course topics [PDF]
===Additional references===
* Lecture 10: Graphene nanoribbons
*Foa Torres ''et al.'' textbook Chapters 1 and 3.
* Lecture 11: Carbon nanotubes
*M. Gibertini, M. Koperski, A. F. Morpurgo, and K. S. Novoselov, ''Magnetic 2D materials and heterostructures'', Nat. Nanotech. '''14''', (2019). [https://www.nature.com/articles/s41565-019-0438-6 [PDF]]
* Lecture 16: Quantum Hall effect
*A. Fert, [https://www.youtube.com/watch?v=vXXQI6u6C_E 2D magnets: From fundamentals to spintronic devices]
*Y. Ando, ''Topological insulator materials'', J. Phys. Soc. Jpn. '''82''', 102001 (2013).  [https://journals.jps.jp/doi/pdf/10.7566/JPSJ.82.102001 [PDF]]


== Survey of quantum statistical tools ==
*[[Media:PHYS824_lecture2_survey_quantum_statistical_tools.pdf|PDF]]
*[[Media:dos_in_2d_tight-binding.pdf|Density of states on square tight-binding lattice via Green functions]]


== Blackboard lectures ==
===Additional references===
*[http://www.worldscientific.com/doi/suppl/10.1142/9038/suppl_file/9038_chap01.pdf Dirac notation and mathematical prerequisites for quantum mechanics] (Chapter 1 from [http://www.worldscientific.com/worldscibooks/10.1142/9038 L. E. Ballentine: Quantum Mechanics - A modern development], second edition).
*[[Media:WYSIN=probability_current_and_current_operators_in_quantum_mechanics.pdf|Probability current and current operators in quantum mechanics]]
*B. K. Nikolić, L. P. Zarbo, and S. Souma, ''Imaging mesoscopic spin Hall fow: Spatial distribution of local spin currents and spin densities in and out of multiterminal spin-orbit coupled semiconductor nanostructures'', Phys. Rev. B '''73''', 075303 (2006). [https://wiki.physics.udel.edu/wiki_qttg/images/c/c4/Bond_spin_current.pdf [PDF]]
*M. M. Odashima, B. G. Prado, and E. Vernek, ''Pedagogical introduction to equilibrium Green's functions: Condensed matter examples with numerical implementations'', Rev. Bras. Ens. Fis. '''39''', e1303 (2017). [http://www.scielo.br/pdf/rbef/v39n1/1806-1117-rbef-39-01-e1303.pdf [PDF]]
*W. J. Herrera and H. Vinck-Posada, and S. Gómez Páez, Green's functions in quantum mechanics courses, Am. J. Phys. '''90''', 763 (2022). [https://doi.org/10.1119/5.0065733  [PDF]]


* Lecture 2: Survey of quantum statistical course tools
== From atoms to 1D nanowires: Tight-binding Hamiltonian ==
* Lecture 3: From atoms to one-dimensional nanowires
*[[Media:PHYS824_lecture3_atom_to_1D_nanowires.pdf|PDF]]
* Lecture 4: Landauer formula for 1D nanowires
*[[Discretization of 1D continuous Hamiltonian]]
* Lecture 4: Band structure of graphene
*[https://kwant-project.org/doc/1/tutorial/discretize Discretization of continuous Hamiltonian for any device shape and dimensionality in KWANT]
* Lecture 5: Introduction to Green functions in quantum physics
*[[How to put magnetic field into tight-binding Hamiltonian]]
* Lecture 6: Introduction to DFT
*[[Media:wannier1D.pdf|Wannier functions for 1D nanowires]]
* Lecture 7: Heterojunctions, interfaces, and band bending
 
* Lecture 8: Two-dimensional electron gas in semiconductor heterostructures
===Additional references===
* Lecture 9: Split gates and quantum nanowires
* Ryndyk textbook Chapter 3.
* Lecture 12: Semislassical transport
*J. G. Analytis, S. J. Blundell, and A. Ardavan, ''Landau levels, molecular orbitals, and the Hofstadter butterfly in finite systems'', Am. J. Phys. '''72''', 5 (2004)]. [http://dx.doi.org/10.1119/1.1615568 [PDF]]
* Lecture 13: Drif-diffusion approach to magnetic nanostructure
*E. Canadell, M.-L. Doublet, and C. Iung, [https://global.oup.com/academic/product/orbital-approach-to-the-electronic-structure-of-solids-9780199534937?cc=us&lang=en&# ''Orbital Approach to the Electronic Structure of Solids''] (Oxford University Press, Oxford, 2012).
* Lecture 14: Landauer-Buttiker scattering approach to quantum transport
*D. C. Ralph, Berry curvature, semiclassical electron dynamics, and topological materials: Lecture notes for Introduction to Solid State Physics, [https://arxiv.org/abs/2001.04797 arXiv:2001.04797].
* Lecture 15: Interference effects: double barrier junction, Aharonov-Bohm ring, localization
 
==Band structure of graphene via tight-binding Hamiltonian==
*P. B. Allen and B. K. Nikolic, [[Band structure of graphene, massless Dirac fermions as low-energy quasiparticles, Berry phase, and all that]]
*[http://demonstrations.wolfram.com/GrapheneBrillouinZoneAndElectronicEnergyDispersion/ Visualization of graphene electronic energy dispersion using Mathematica]
*[[How to construct matrix representation of tight-binding Hamiltonian of graphene for numerical calculations]]
*[[Media:OVERVIEW=effective_mass_in_graphene.pdf|Effective mass of electrons in graphene]]
*[[Media:TALK_KIM=hofstadter_butterfly_in_graphene.pdf|Hofstadter butterfly using graphene in magnetic field]]
 
===Additional references===
*Foa Torres ''et al.'' textbook Chapter 2.
*B. A. McKinnon and T. C. Choy, A tight-binding model for the density of states of graphite-like structures calculated using Green's functions, Aust. J. Phys. '''46''', 601 (1993). [https://www.publish.csiro.au/ph/pdf/ph930601 [PDF]]
*A. Matulis and F. M. Peeters, ''Analogy between one-dimensional chain models and graphene'', Am. J. Phys. '''77''', 595 (2009). [http://dx.doi.org/10.1119/1.3127143 [PDF]]
*'''Tight-binding Hamiltonian of other materials using physical intuition:'''
**S. Mao, A. Yamakage, and Y. Kuramoto, ''Tight-binding model for topological insulators: Analysis of helical surface modes over the whole Brillouin zone'', Phys. Rev. B '''84''', 115413 (2011). [https://doi.org/10.1103/PhysRevB.84.115413 [PDF]]
**T. M. McCormick, I. Kimchi, and N. Trivedi, ''Minimal models for topological Weyl semimetals'', Phys. Rev. B '''95''', 075133 (2017). [https://doi.org/10.1103/PhysRevB.95.075133 [PDF]]
 
== Density functional theory for first-principles band structure calculations==
*[[Media:intro_dft.pdf|PDF]]
*[https://molmod.ugent.be/deltacodesdft Delta benchmark of DFT codes]
 
===Additional references===
*Foa Torres ''et al.'' textbook Appendix A.
*Chapter 6 in C. Fiolhais, F. Nogueira, and M. A. L. Marques, ''A Primer in Density Functional Theory'' (Springer-Verlag, Berlin, 2003). [https://link.springer.com/book/10.1007/3-540-37072-2 [PDF]]
*'''Tight-binding Hamiltonian via fitting of density functional theory calculations:'''
 
<pre>Textbook tight-binding Hamiltonians are created by assuming the shape of the orbitals---for instance s, p or d orbitals centered around a particular atom---and then using symmetry to calculate orbital-orbital hopping up to a particular range. In a second step the parameters associated with the degrees of freedom are determined by fitting to experimental data or first-principles calculations.</pre>
 
**T. B. Boykin, M. Luisier, G. Klimeck, X. Jiang, N. Kharche, Yu. Zhou, and S. K. Nayak, ''Accurate six-band nearest-neighbor tight-binding model for the p-bands of bulk graphene and graphene nanoribbons'', J. Appl. Phys. '''109''', 104304 (2011). [https://doi.org/10.1063/1.3582136 [PDF]]
**J. M. Marmolejo-Tejada, J. H. García, M. Petrović, P.-H. Chang, X.-L. Sheng, A. Cresti, P. Plecháč, S. Roche, and B. K. Nikolić, ''Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents'', J. Phys.: Mater. '''1''', 0150061 (2018). [https://wiki.physics.udel.edu/wiki_qttg/images/0/09/Vhe_graphene_hbn.pdf [PDF]]
**E. Ridolfi, D. Le, T. S. Rahman, E. R. Mucciolo, and C. H. Lewenkopf, ''A tight-binding model for MoS<sub>2</sub> monolayers'', J. Phys.: Condens. Matter '''27''', 365501 (2015). [https://iopscience.iop.org/article/10.1088/0953-8984/27/36/365501/pdf [PDF]]
 
*'''Tight-binding Hamiltonian via Wannierization of density functional theory calculations:'''
 
<pre>Wannierization of density functional theory (DFT) calculations starts from the diagonal Kohn-Sham Hamiltonian in the Bloch state basis and transforms into a basis of maximally localized Wannier functions (typically via Wannier90 package). The first-principles Wannier tight-binding Hamiltonian preserves the phase and the orbital information from the DFT calculations.</pre>
 
**J. Kuneš, [[Media:REVIEW_KUNES=wannier_functions_and_construction_of_model_hamiltonians.pdf|''Wannier functions and construction of model Hamiltonians'']]
**S. Fang and E. Kaxiras, ''Electronic structure theory of weakly interacting bilayers'', Phys. Rev. B '''93''', 235153 (2016). [https://doi.org/10.1103/PhysRevB.93.235153 [PDF]]
**S. Carr, S. Fang, H. Chun Po, A. Vishwanath, and E. Kaxiras, ''Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach'', Phys. Rev. Res. '''1''', 033072 (2019). [https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.1.033072 [PDF]]
 
*'''Wannierization vs. fitting:'''
 
**A. C. Jacko, ''Deriving ab initio model Hamiltonians for molecular crystals'', [https://arxiv.org/abs/1508.07735 arXiv:1508.07735].
**J. Sifuna, P. García-Fernández, G. S. Manyali, G. Amolo, and J. Junquera, ''Comparison of band-fitting and Wannier-based model construction for WSe<sub>2</sub>'', [https://arxiv.org/abs/2001.05959 arXiv:2001.05959].
 
==Landauer formula for ballistic quasi-1D nanowires with application to edge state transport in 2D topological insulators==
*[[Media:PHYS824_lecture6_landauer_formula_ballistic_transport.pdf|PDF]]
*[[Media:double_step_f.pdf|Experiment on the electronic energy distribution along nanowire]]
*[[Media:crash_course_topologycm.pdf|Crash course on topology in condensed matter]]
*[https://topocondmat.org/w4_haldane/haldane_model.html Graphene goes topological -> Haldane model (introduced in video by Haldane himself)]
 
===Additional references===
*Ryndyk textbook Chapter 2.2.
*M. Payne, ''Electrostatic and electrochemical potentials in quantum transport'', J. Phys.: Condens. Matter '''1''', 4931 (1989). [https://iopscience.iop.org/article/10.1088/0953-8984/1/30/006 [PDF]]
*U. Bajpai, M. J. H. Ku, and B. K. Nikolić, ''Robustness of quantized transport through edge states of finite length: Imaging current density in Floquet topological versus quantum spin and anomalous Hall insulators'', Phys. Rev. Res. '''2''', 033438 (2020). [https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.2.033438 [PDF]]
*X.-L. Sheng and B. K. Nikolić, ''Monolayer of the 5d transition metal trichloride OsCl<sub>3</sub>: A playground for two-dimensional magnetism, room-temperature quantum anomalous Hall effect, and topological phase transitions'', Phys. Rev. B '''95''', 201402(R) (2017). [https://wiki.physics.udel.edu/wiki_qttg/images/8/89/Qahe_oscl3.pdf [PDF]]
 
== Graphene nanoribbons and carbon nanotubes ==
*[[Media:gnr_and_cnt.pdf|PDF]]
*[https://demonstrations.wolfram.com/ElectronicBandStructureOfArmchairAndZigzagGrapheneNanoribbon/ Subband structure of zigzag and armchair graphene nanoribbons]
*[https://demonstrations.wolfram.com/BrillouinZoneOfASingleWalledCarbonNanotube/ From Brillouin zone of graphene to that of single-wall carbon nanotube] 
*[https://demonstrations.wolfram.com/ElectronicBandStructureOfASingleWalledCarbonNanotubeByTheZon/ Subband structure of a single-wall carbon nanotube via the zone-folding method]
*[https://demonstrations.wolfram.com/ElectronicStructureOfASingleWalledCarbonNanotubeInTightBindi/ Subband structure of single-wall CNT via the Wannier tight-binding Hamiltonian]
 
===Additional references===
*Foa Torres ''et al.'' textbook Chapter 10
 
==Landauer-Büttiker formula for two-terminal and multi-terminal quantum-coherent nanostructures==
*[[Media:PHYS824_lecture8_landauer_buttiker_formula.pdf|PDF]]
 
===Additional references===
*Ryndyk textbook Chapters 2.3 and 2.4.
* J. Walker and J. Gathright, ''Exploring one-dimensional quantum mechanics with transfer matrices'', Am. J. Phys. '''62''', 408  (1994)].  [http://dx.doi.org/10.1119/1.17541 [PDF]]
 
==Application of Landauer-Büttiker formula to quantum interference effects in electronic transport==
*[[Media:PHYS824_lecture9_quantum_interference_effects_in_transport.pdf|PDF]]
 
===Additional references===
*G. B. Lesovik and I. A. Sadovskyy, ''Scattering matrix approach to the description of quantum electron transport'', Physics Uspekhi '''54''', 1007 (2011). [http://iopscience.iop.org/1063-7869/54/10/R02/pdf/1063-7869_54_10_R02.pdf [PDF]]
 
==Quantum transport via Nonequilibrium Green function (NEGF) formalism==
*[[Media:PHYS824_lecture10_negf.pdf|PDF]]
*[[Media:self_energy_lead.pdf|Self-energy for semi-infinite electrodes modeled on a cubic tight-binding lattice]]
*[[Media:negf_formulas_in_pictures.pdf|How to use NEGF matrix formulas: Step-by-step tutorial in pictures]]
 
===Additional references===
*Ryndyk textbook Chapter 3
*S. Datta, [[Media:DATTA=nanoscale_device_modeling_green_function_method.pdf|Nanoscale device modeling: The Green's function method]]
*R. Golizadeh-Mojarad and S. Datta, ''Nonequilibrium Green’s function based models for dephasing in quantum transport'', Phys. Rev. B '''75''', 081301(R) (2007).  [http://link.aps.org/doi/10.1103/PhysRevB.75.081301 [PDF]]
*C.-L. Chen, C.-R. Chang, and B. K. Nikolić, ''Quantum coherence and its dephasing in the giant spin Hall effect and nonlocal voltage generated by magnetotransport through multiterminal graphene bars'', Phys. Rev. B '''85''', 155414 (2012). [https://wiki.physics.udel.edu/wiki_qttg/images/b/b0/Giant_nonlocality_graphene.pdf [PDF]]
 
==Application of NEGF and NEGF+DFT to magnetic tunnel junctions==
*[[Media:negf_mtj.pdf|PDF]]
 
===Additional references===
*'''NEGF+DFT:'''
**Foa Torres ''et al.'' textbook Appendix C.
**S. Sanvito, [http://pubs.rsc.org/en/content/chapter/bk9781849731331-00179/978-1-84973-133-1#!divabstract Electron transport theory for large systems].
**D. A. Areshkin and B. K. Nikolić, ''Electron density and transport in top-gated graphene nanoribbon devices: First-principles Green function algorithms for systems containing a large number of atoms'', Phys. Rev. B '''81''', 155450 (2010). [https://wiki.physics.udel.edu/wiki_qttg/images/d/dc/Negf_dft_gnr.pdf [PDF]]
*'''MTJs:'''
** W. H. Butler, ''Tunneling magnetoresistance from a symmetry filtering effect'', Sci. Technol. Adv. Mater. '''9''',  014106 (2008). [https://doi.org/10.1088/1468-6996/9/1/014106  [PDF]]
**K. K. Saha, A. Blom, K. S. Thygesen, and B. K. Nikolić, ''Magnetoresistance and negative differential resistance in Ni/Graphene/Ni vertical heterostructures driven by finite bias voltage: A first-principles study'', Phys. Rev. B '''85''', 184426 (2012). [https://wiki.physics.udel.edu/wiki_qttg/images/7/70/Ni-gr-ni_mj.pdf [PDF]]
**M. Piquemal-Banci, R. Galceran, M.-B. Martin, F. Godel, A. Anane, F. Petroff, B. Dlubak, and P. Seneor, ''2D-MTJs: Introducing 2D materials in magnetic tunnel junctions'', J. Phys. D: Appl. Phys. '''50''', 203002 (2017). [https://iopscience.iop.org/article/10.1088/1361-6463/aa650f/pdf [PDF]]
 
==Application of NEGF and NEGF+DFT to spin torque and spin pumping==
*[[Media:negf_stt_sot.pdf|PDF]]
 
===Additional references===
*D. C. Ralph and M. D. Stiles, [http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.4608v3.pdf Tutorial on spin transfer torque] [NOTE:  arXiv:0711.4608 version linked here is corrected and contains additional material compared to the officially published J. Magn. Magn. Mater. '''320''', 1190 (2008)].
*N. Locatelli, V. Cros, and J. Grollier, ''Spin-torque building blocks'', Nat. Mater. '''13''', 11 (2014). [http://www.nature.com/nmat/journal/v13/n1/full/nmat3823.html [PDF]]
*B. K. Nikolić, K. Dolui, M. Petrović, P. Plecháč, T. Markussen, and K. Stokbro, ''First-principles quantum transport modeling of spin-transfer and spin-orbit torques in magnetic multilayers'' (Chapter of Handbook of Materials Modeling, Volume 2 Applications: Current and Emerging Materials (Springer, Cham, 2018). [https://wiki.physics.udel.edu/wiki_qttg/images/9/94/Review_stt_sot.pdf [PDF]]
*S.-H. Chen, C.-R. Chang, J. Q. Xiao, and B. K. Nikolić, ''Spin and charge pumping in magnetic tunnel junctions with precessing magnetization: A nonequilibrium Green function approach'', Phys. Rev. B. '''79''', 054424 (2009). [https://wiki.physics.udel.edu/wiki_qttg/images/3/35/Spin_pumping_mtj.pdf [PDF]]
 
==Application of NEGF and NEGF+DFT  to nanoscale thermoelectrics==
*[[Media:nano_thermoelectrics.pdf|PDF]]
 
===Additional references===
*B. K. Nikolić, K. K. Saha, T. Markussen, and K. S. Thygesen, ''First-principles quantum transport modeling of thermoelectricity in single-molecule nanojunctions with graphene nanoribbon electrodes'', J. Comp. Electronics '''11''', 78 (2012). [https://wiki.physics.udel.edu/wiki_qttg/images/5/53/Jcel_review_nanothermoelectrics.pdf [PDF]]
 
==Coulomb blockade==
 
===Additional references===
*Ryndyk textbook Chapter 5.

Latest revision as of 20:21, 12 March 2023

What is nanophysics: Survey of course topics

Additional references

  • Foa Torres et al. textbook Chapters 1 and 3.
  • M. Gibertini, M. Koperski, A. F. Morpurgo, and K. S. Novoselov, Magnetic 2D materials and heterostructures, Nat. Nanotech. 14, (2019). [PDF]
  • A. Fert, 2D magnets: From fundamentals to spintronic devices
  • Y. Ando, Topological insulator materials, J. Phys. Soc. Jpn. 82, 102001 (2013). [PDF]

Survey of quantum statistical tools

Additional references

From atoms to 1D nanowires: Tight-binding Hamiltonian

Additional references

  • Ryndyk textbook Chapter 3.
  • J. G. Analytis, S. J. Blundell, and A. Ardavan, Landau levels, molecular orbitals, and the Hofstadter butterfly in finite systems, Am. J. Phys. 72, 5 (2004)]. [PDF]
  • E. Canadell, M.-L. Doublet, and C. Iung, Orbital Approach to the Electronic Structure of Solids (Oxford University Press, Oxford, 2012).
  • D. C. Ralph, Berry curvature, semiclassical electron dynamics, and topological materials: Lecture notes for Introduction to Solid State Physics, arXiv:2001.04797.

Band structure of graphene via tight-binding Hamiltonian

Additional references

  • Foa Torres et al. textbook Chapter 2.
  • B. A. McKinnon and T. C. Choy, A tight-binding model for the density of states of graphite-like structures calculated using Green's functions, Aust. J. Phys. 46, 601 (1993). [PDF]
  • A. Matulis and F. M. Peeters, Analogy between one-dimensional chain models and graphene, Am. J. Phys. 77, 595 (2009). [PDF]
  • Tight-binding Hamiltonian of other materials using physical intuition:
    • S. Mao, A. Yamakage, and Y. Kuramoto, Tight-binding model for topological insulators: Analysis of helical surface modes over the whole Brillouin zone, Phys. Rev. B 84, 115413 (2011). [PDF]
    • T. M. McCormick, I. Kimchi, and N. Trivedi, Minimal models for topological Weyl semimetals, Phys. Rev. B 95, 075133 (2017). [PDF]

Density functional theory for first-principles band structure calculations

Additional references

  • Foa Torres et al. textbook Appendix A.
  • Chapter 6 in C. Fiolhais, F. Nogueira, and M. A. L. Marques, A Primer in Density Functional Theory (Springer-Verlag, Berlin, 2003). [PDF]
  • Tight-binding Hamiltonian via fitting of density functional theory calculations:
Textbook tight-binding Hamiltonians are created by assuming the shape of the orbitals---for instance s, p or d orbitals centered around a particular atom---and then using symmetry to calculate orbital-orbital hopping up to a particular range. In a second step the parameters associated with the degrees of freedom are determined by fitting to experimental data or first-principles calculations.
    • T. B. Boykin, M. Luisier, G. Klimeck, X. Jiang, N. Kharche, Yu. Zhou, and S. K. Nayak, Accurate six-band nearest-neighbor tight-binding model for the p-bands of bulk graphene and graphene nanoribbons, J. Appl. Phys. 109, 104304 (2011). [PDF]
    • J. M. Marmolejo-Tejada, J. H. García, M. Petrović, P.-H. Chang, X.-L. Sheng, A. Cresti, P. Plecháč, S. Roche, and B. K. Nikolić, Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents, J. Phys.: Mater. 1, 0150061 (2018). [PDF]
    • E. Ridolfi, D. Le, T. S. Rahman, E. R. Mucciolo, and C. H. Lewenkopf, A tight-binding model for MoS2 monolayers, J. Phys.: Condens. Matter 27, 365501 (2015). [PDF]
  • Tight-binding Hamiltonian via Wannierization of density functional theory calculations:
Wannierization of density functional theory (DFT) calculations starts from the diagonal Kohn-Sham Hamiltonian in the Bloch state basis and transforms into a basis of maximally localized Wannier functions (typically via Wannier90 package). The first-principles Wannier tight-binding Hamiltonian preserves the phase and the orbital information from the DFT calculations.
    • J. Kuneš, Wannier functions and construction of model Hamiltonians
    • S. Fang and E. Kaxiras, Electronic structure theory of weakly interacting bilayers, Phys. Rev. B 93, 235153 (2016). [PDF]
    • S. Carr, S. Fang, H. Chun Po, A. Vishwanath, and E. Kaxiras, Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: First-principles approach, Phys. Rev. Res. 1, 033072 (2019). [PDF]
  • Wannierization vs. fitting:
    • A. C. Jacko, Deriving ab initio model Hamiltonians for molecular crystals, arXiv:1508.07735.
    • J. Sifuna, P. García-Fernández, G. S. Manyali, G. Amolo, and J. Junquera, Comparison of band-fitting and Wannier-based model construction for WSe2, arXiv:2001.05959.

Landauer formula for ballistic quasi-1D nanowires with application to edge state transport in 2D topological insulators

Additional references

  • Ryndyk textbook Chapter 2.2.
  • M. Payne, Electrostatic and electrochemical potentials in quantum transport, J. Phys.: Condens. Matter 1, 4931 (1989). [PDF]
  • U. Bajpai, M. J. H. Ku, and B. K. Nikolić, Robustness of quantized transport through edge states of finite length: Imaging current density in Floquet topological versus quantum spin and anomalous Hall insulators, Phys. Rev. Res. 2, 033438 (2020). [PDF]
  • X.-L. Sheng and B. K. Nikolić, Monolayer of the 5d transition metal trichloride OsCl3: A playground for two-dimensional magnetism, room-temperature quantum anomalous Hall effect, and topological phase transitions, Phys. Rev. B 95, 201402(R) (2017). [PDF]

Graphene nanoribbons and carbon nanotubes

Additional references

  • Foa Torres et al. textbook Chapter 10

Landauer-Büttiker formula for two-terminal and multi-terminal quantum-coherent nanostructures

Additional references

  • Ryndyk textbook Chapters 2.3 and 2.4.
  • J. Walker and J. Gathright, Exploring one-dimensional quantum mechanics with transfer matrices, Am. J. Phys. 62, 408 (1994)]. [PDF]

Application of Landauer-Büttiker formula to quantum interference effects in electronic transport

Additional references

  • G. B. Lesovik and I. A. Sadovskyy, Scattering matrix approach to the description of quantum electron transport, Physics Uspekhi 54, 1007 (2011). [PDF]

Quantum transport via Nonequilibrium Green function (NEGF) formalism

Additional references

  • Ryndyk textbook Chapter 3
  • S. Datta, Nanoscale device modeling: The Green's function method
  • R. Golizadeh-Mojarad and S. Datta, Nonequilibrium Green’s function based models for dephasing in quantum transport, Phys. Rev. B 75, 081301(R) (2007). [PDF]
  • C.-L. Chen, C.-R. Chang, and B. K. Nikolić, Quantum coherence and its dephasing in the giant spin Hall effect and nonlocal voltage generated by magnetotransport through multiterminal graphene bars, Phys. Rev. B 85, 155414 (2012). [PDF]

Application of NEGF and NEGF+DFT to magnetic tunnel junctions

Additional references

  • NEGF+DFT:
    • Foa Torres et al. textbook Appendix C.
    • S. Sanvito, Electron transport theory for large systems.
    • D. A. Areshkin and B. K. Nikolić, Electron density and transport in top-gated graphene nanoribbon devices: First-principles Green function algorithms for systems containing a large number of atoms, Phys. Rev. B 81, 155450 (2010). [PDF]
  • MTJs:
    • W. H. Butler, Tunneling magnetoresistance from a symmetry filtering effect, Sci. Technol. Adv. Mater. 9, 014106 (2008). [PDF]
    • K. K. Saha, A. Blom, K. S. Thygesen, and B. K. Nikolić, Magnetoresistance and negative differential resistance in Ni/Graphene/Ni vertical heterostructures driven by finite bias voltage: A first-principles study, Phys. Rev. B 85, 184426 (2012). [PDF]
    • M. Piquemal-Banci, R. Galceran, M.-B. Martin, F. Godel, A. Anane, F. Petroff, B. Dlubak, and P. Seneor, 2D-MTJs: Introducing 2D materials in magnetic tunnel junctions, J. Phys. D: Appl. Phys. 50, 203002 (2017). [PDF]

Application of NEGF and NEGF+DFT to spin torque and spin pumping

Additional references

  • D. C. Ralph and M. D. Stiles, Tutorial on spin transfer torque [NOTE: arXiv:0711.4608 version linked here is corrected and contains additional material compared to the officially published J. Magn. Magn. Mater. 320, 1190 (2008)].
  • N. Locatelli, V. Cros, and J. Grollier, Spin-torque building blocks, Nat. Mater. 13, 11 (2014). [PDF]
  • B. K. Nikolić, K. Dolui, M. Petrović, P. Plecháč, T. Markussen, and K. Stokbro, First-principles quantum transport modeling of spin-transfer and spin-orbit torques in magnetic multilayers (Chapter of Handbook of Materials Modeling, Volume 2 Applications: Current and Emerging Materials (Springer, Cham, 2018). [PDF]
  • S.-H. Chen, C.-R. Chang, J. Q. Xiao, and B. K. Nikolić, Spin and charge pumping in magnetic tunnel junctions with precessing magnetization: A nonequilibrium Green function approach, Phys. Rev. B. 79, 054424 (2009). [PDF]

Application of NEGF and NEGF+DFT to nanoscale thermoelectrics

Additional references

  • B. K. Nikolić, K. K. Saha, T. Markussen, and K. S. Thygesen, First-principles quantum transport modeling of thermoelectricity in single-molecule nanojunctions with graphene nanoribbon electrodes, J. Comp. Electronics 11, 78 (2012). [PDF]

Coulomb blockade

Additional references

  • Ryndyk textbook Chapter 5.
Retrieved from "https://wiki.physics.udel.edu/wiki_phys824/index.php?title=Lectures&oldid=3146"