Lectures: Difference between revisions

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*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].
*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].


==Band structure of graphene ==
==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]]
*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]
*[http://demonstrations.wolfram.com/GrapheneBrillouinZoneAndElectronicEnergyDispersion/ Visualization of graphene electronic energy dispersion using Mathematica]
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*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]]
*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]]
*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 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].
*'''Tight-binding Hamiltonian from physical intuition:'''
*'''Tight-binding Hamiltonian from 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]]
**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]]

Revision as of 12:59, 13 October 2020

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]
  • 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 from 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]

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

Graphene nanoribbons and carbon nanotubes

Additional references

  • Foa Torres et al. textbook Chapter 10

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

  • Example for two-terminal formula: Quantum interference effects in electronic transport---resonant tunneling, Anderson localization and Aharonov-Bohm ring
  • Example for multi-terminal formula: Quantum Hall and spin Hall effects

Additional references

  • Ryndyk textbook Chapters 2.3 and 2.4.
  • 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 in the nonlinear regime: Nonequilibrium Green function (NEGF) formalism

Additional references

Application of NEGF formalism to magnetic tunnel junctions

Additional references

  • W. H. Butler, Tunneling magnetoresistance from a symmetry filtering effect, Sci. Technol. Adv. Mater. 9, 014106 (2008). [PDF]
  • J. Walker and J. Gathright, Exploring one-dimensional quantum mechanics with transfer matrices, Am. J. Phys. 62, 408 (1994)]. [PDF]

Application of NEGF formalism to spin-transfer and spin-orbit torques

Additional references

  • 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]
  • 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, Nature Mater. 13, 11 (2014). [PDF]

Application of NEGF formalism 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]

NEGF+DFT formalism for first-principles quantum transport calculations

Additional references

  • 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]
  • K. K. Saha and B. K. Nikolić, Negative differential resistance in graphene-nanoribbon/carbon-nanotube crossbars: A first-principles multiterminal quantum transport study, J. Comput. Electron. 12, 542 (2013). [PDF]

NEGF for electronic transport in the presence of dephasing

Additional references

  • 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]

Coulomb blockade

Additional references

  • Ryndyk textbook Chapter 5.
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