Lectures
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What is nanophysics: Survey of course topics
Additional references
- Foa Torres et al. textbook Chapters 1 and 3.
Survey of quantum statistical tools
Additional references
- Dirac notation and mathematical prerequisites for quantum mechanics (Chapter 1 from L. E. Ballentine: Quantum Mechanics - A modern development, second edition).
- G. M. Wysin, Probability current and current operators in quantum mechanics. [PDF]
- 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). [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). [PDF]
- Density of states in square tight-binding lattice via Green functions
From atoms to 1D nanowires
- Discretization of 1D continuous Hamiltonian
- Discretization of 1D continuous Hamiltonian in KWANT
- How to put magnetic field into discretized 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).
Landauer formula for ballistic 1D nanowires with application to edge states in topological phases
- Crash course on topological phases of quantum matter
- Experiment on the electronic energy distribution along mesoscopic wire
Additional references
- Ryndyk textbook Chapter 2.2.
Band structure of graphene
- P. B. Allen and B. K. Nikolic, Band structure of graphene, massless Dirac fermions as low-energy quasiparticles, Berry phase, and all that
- How to construct tight-binding Hamiltonian for numerical calculations on graphene
- Visualization of graphene electronic energy dispersion using Mathematica
Additional references
- Foa Torres et al. textbook Chapter 2.
- A. Matulis and F. M. Peeters, Analogy between one-dimensional chain models and graphene, Am. J. Phys. 77, 595 (2009). [PDF]
- Effective mass in graphene
- J. M. Marmolejo-Tejada, J. H. García, M. Petrović, P.-H. Chang, X.-L. Sheng, A. Cresti, P. Plecháč, S. Roche, 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]
- J. M. Marmolejo-Tejada, J. H. García, M. Petrović, P.-H. Chang, X.-L. Sheng, A. Cresti, P. Plecháč, S. Roche, 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]
Graphene nanoribbons and carbon nanotubes
Density functional theory for first-principles band structure calculations
Additional references
- Foa Torres et al. textbook Appendix A.
- K. Capelle, A bird's-eye view of density-functional theory, arXiv:cond-mat/0211443 [PDF]
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]
- M. Payne, Electrostatic and electrochemical potentials in quantum transport, J. Phys.: Condens. Matter 1, 4931 (1989). [PDF]
Quantum transport in the nonlinear regime: Nonequilibrium Green function (NEGF) formalism
Additional references
- Ryndyk textbook Chapter 3
- S. Datta, Nanoscale device modeling: The Green's function method
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
- 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.
