Lectures: Difference between revisions

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*Foa Torres ''et al.'' textbook Chapters 1 and 3.
*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). [https://www.nature.com/articles/s41565-019-0438-6 [PDF]]
*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]]
*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]]
*Y. Ando, ''Topological insulator materials'', J. Phys. Soc. Jpn. '''82''', 102001 (2013).  [https://journals.jps.jp/doi/pdf/10.7566/JPSJ.82.102001 [PDF]]


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*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]]
*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]]
*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]]


== From atoms to 1D nanowires: Tight-binding Hamiltonian ==
== From atoms to 1D nanowires: Tight-binding Hamiltonian ==
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==Landauer formula for ballistic quasi-1D nanowires with application to edge state transport in 2D topological insulators==
==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:PHYS824_lecture6_landauer_formula_ballistic_transport.pdf|PDF]]
*[[Media:double_step_f.pdf|Experiment on the electronic energy distribution along mesoscopic wire]]
*[[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]]
*[[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)]
*[https://topocondmat.org/w4_haldane/haldane_model.html Graphene goes topological -> Haldane model (introduced in video by Haldane himself)]
Line 82: Line 84:
===Additional references===
===Additional references===
*Ryndyk textbook Chapter 2.2.
*Ryndyk textbook Chapter 2.2.
*M. Payne, ''Electrostatic and electrochemical potentials in quantum transport'', J. Phys.: Condens. Matter '''1''', 4931 (1989). [http://www.iop.org/EJ/abstract/0953-8984/1/30/006/ [PDF]]
*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]]
*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]]
*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]]
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*[[Media:PHYS824_lecture10_negf.pdf|PDF]]
*[[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: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===
===Additional references===
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*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]]
*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 formalism to magnetic tunnel junctions==
==Application of NEGF and NEGF+DFT to magnetic tunnel junctions==
*[[Media.xyz.pdf|PDF]]
*[[Media:negf_mtj.pdf|PDF]]


===Additional references===
===Additional references===
*Foa Torres ''et al.'' textbook Appendix C.
*'''NEGF+DFT:'''
* W. H. Butler, ''Tunneling magnetoresistance from a symmetry filtering effect'', Sci. Technol. Adv. Mater. '''9''',  014106 (2008). [http://www.iop.org/EJ/abstract/-search=67129383.1/1468-6996/9/1/014106  [PDF]]
**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].
**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]]
**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]]
*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). [https://wiki.physics.udel.edu/wiki_qttg/images/d/dd/Jcel_gnr_cnt_crossbar.pdf [PDF]]
*'''MTJs:'''
*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]
** 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 formalism to spin-transfer and spin-orbit torques==
==Application of NEGF and NEGF+DFT to spin torque and spin pumping==
*[[Media:stt_phys824.pdf|PDF]]
*[[Media:negf_stt_sot.pdf|PDF]]


===Additional references===
===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). [https://wiki.physics.udel.edu/wiki_qttg/images/9/94/Review_stt_sot.pdf | [PDF]]
*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)].
*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'', Nature Mater. '''13''', 11 (2014). [http://www.nature.com/nmat/journal/v13/n1/full/nmat3823.html [PDF]]
*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 formalism to nanoscale thermoelectrics==
==Application of NEGF and NEGF+DFT  to nanoscale thermoelectrics==
*[[Media:nano_thermoelectrics.pdf|PDF]]
*[[Media:nano_thermoelectrics.pdf|PDF]]


Latest revision as of 19:21, 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.
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