«Bottom – up» nanoelectronics: the hall effects, measurement of electrochemical potentials and spin transport in the NEGF model
DOI:
https://doi.org/10.15587/2313-8416.2015.51353Keywords:
nanoelectronics, Hall effects, chemical potential measurement, spin transport, NEGF method, grapheneAbstract
The Hall effects, measurement of electrochemical potentials, the Landauer and Buttiker approaches, an account of magnetic field in the non-equilibrium Green’s functions (NEGF) method, spin transport by the NEGF method in the spinor representation, in particular, rotating magnetic contacts and spins, Zeeman and Rashba spin Hamiltonians, calculation of the spin potential, and four-component description of spin transport are discussed in the «bottom – up» approach of modern nanoelectronics
References
Hall, E. H. (1879). On a New Action of the Magnet on Electric Currents. American Journal of Mathematics, 2 (3), 287–292. doi: 10.2307/2369245
Klitzing, K. v., Dorda, G., Pepper, M. (1980). New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance. Physical Review Letters, 45 (6), 494–497. doi: 10.1103/physrevlett.45.494
fon Klitcing, K. (1985). Kvantovyj jeffekt Holla: Nobelevskie lekcii po fizike. UFN, 150 (1), 107–126.
Reedtz, G. M., Cage, M. E. (1987). An automated potentiometric system for precision measurement of the quantized hall resistance. Journal of Research of the National Bureau of Standards, 92 (5), 303–310. doi: 10.6028/jres.092.030
Tsui, D. C., Stormer, H. L., Gossard, A. C. (1982). Two-Dimensional Magnetotransport in the Extreme Quantum Limit. Physical Review Letters, 48 (22), 1559–1562. doi: 10.1103/physrevlett.48.1559
Stepanovskij, Ju. P. (1998). Drobnyj kvantovyj jeffekt Holla. Jelektromagnitnye javlenija,1 (3), 427–442.
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H., Ong, N. P. (2010). Anomalous Hall effect. Reviews of Modern Physics, 82 (2), 1539–1592. doi: 10.1103/revmodphys.82.1539
Dyakonov, M. I., Perel, V. I. (1971). Possibility of orientating electron spins with current. Sov. Phys. JETP Lett., 13, 467.
Dyakonov, M. I., Perel, V. I. (1971). Current-induced spin orientation of electrons in semiconductors. Physics Letters A, 35 (6), 459–460. doi: 10.1016/0375-9601(71)90196-4
Kane, C. L., Mele, E. J. (2005). Quantum Spin Hall Effect in Graphene. Physical Review Letters, 95 (22). doi: 10.1103/physrevlett.95.226801
Srinivasan, S., Sarkar, A., Behin-Aein, B., Datta, S. (2011). All-Spin Logic Device With Inbuilt Nonreciprocity. IEEE Transactions on Magnetics, 47 (10), 4026–4032. doi: 10.1109/tmag.2011.2159106
Kane, C., Moore, J. (2011). Topological insulators. Physics World, 24 (02), 32–36. doi: 10.1088/2058-7058/24/02/36
Datta, S. (2012). Lessons from Nanoelectronics: A New Perspective on Transport. Hackensack, New Jersey: World Scientific Publishing Company, 492. doi: 10.1142/8029
Krugljak, Ju. A. (2015). Nanoelectronics «bottom – up»: current generation, generalized Ohm’s law, elastic resistors, conductivity modes, thermoelectricity. ScienceRise, 7/2 (12), 76–100. doi: 10.15587/2313-8416.2015.45700
Krugljak Ju. O., Krugljak, N. Ju., Striha, M. V. (2012). Uroky nanoelektroniky: vynyknennja strumu, formuljuvannja zakonu Oma i mody providnosti v koncepcii' «znyzu – vgoru». Sensor. elektr. mikrosyst. tehn., 9 (4), 5–29. Available at: http://dspace.onu.edu.ua:8080/handle/123456789/3643
Ashkroft N., Mermin N. (1979). Fizika tverdogo tela. Vol. 1-2. Moscow: Mir, 458; 486.
Rashba, E. I. (2003). Spin currents in thermodynamic equilibrium: The challenge of discerning transport currents. Physical Review B, 68 (24). doi: 10.1103/physrevb.68.241315
Buttiker, M. (1988). Symmetry of electrical conduction. IBM Journal of Research and Development, 32 (3), 317–334. doi: 10.1147/rd.323.0317
Krugljak, Ju. A. (2015). Nanoelectronics «bottom – up»: non-equillibrium Green’s functions method, model transport problems and quantum interference. ScienceRise, 9/2 (14), 41–72. doi: 10.15587/2313-8416.2015.48827
Krugljak, Ju. A. (2015). Nanoelectronics «bottom – up»: non-equillibrium Green’s functions method, model transport problems and quantum interference. ScienceRise, 2/2 (7), 93–106. doi: 10.15587/2313-8416.2015.36443
Krugljak, Ju. A. (2015). The «bottom – up» nanoelectronics: elements of spintronics and magnetronics. ScienceRise, 8/2 (13), 51–68. doi: 10.15587/2313-8416.2015.47792
Sears, F. W., Salinger, G. L. (1975). Thermodynamics, Kinetic Theory, and Statistical Thermodynamics. Boston: Addison-Wesley.
Landauer, R. (1957). Spatial Variation of Currents and Fields Due to Localized Scatterers in Metallic Conduction. IBM Journal of Research and Development, 1 (3), 223–231. doi: 10.1147/rd.13.0223
Landauer, R. (1970). Electrical resistance of disordered one-dimensional lattices. Philosophical Magazine, 21 (172), 863–867. doi: 10.1080/14786437008238472
Landauer, R. (1988). Spatial variation of currents and fields due to localized scatterers in metallic conduction. IBM Journal of Research and Development, 32 (3), 306–316. doi: 10.1147/rd.323.0306
Landauer, R. (1996). Spatial variation of currents and fields due to localized scatterers in metallic conduction (and comment). Journal of Mathematical Physics, 37 (10), 5259. doi: 10.1063/1.531590
Buttiker, M. (1986). Four-Terminal Phase-Coherent Conductance. Physical Review Letters, 57 (14), 1761–1764. doi: 10.1103/physrevlett.57.1761
Sharvin, Ju. V. (1965). Ob odnom vozmozhnom metode issledovanija poverhnosti Fermi. ZhJeTF,. 48 (3), 984–985.
Sharvin, Yu. V., Bogatina, N. I. (1969). Investigation of Focusing of Electron Beams in a Metal by a Longitudinal Magnetic Field. Sov. Phys. JETP, 29 (3), 419–423.
Imry, Y.; Grinstein, G., Mazenko, G. (Eds.) (1986). In Directions in Condensed Matter Physics. Singapore: World Scientific, 101.
Imry, Y., Landauer, R. (1999). Conductance viewed as transmission. Reviews of Modern Physics, 71 (2), 306–312. doi: 10.1103/revmodphys.71.s306
Lesovik, G. B., Sadovskij, I. A. (2011). Opisanie kvantovogo jelektronnogo transporta s pomoshh'ju matric rassejanija. UFN., 181 (10), 1041–1096. doi: 10.3367/ufnr.0181.201110b.1041
Stone, A. D., Szafer, A. (1988). What is measured when you measure a resistance? – The Landauer formula revisited. IBM Journal of Research and Development, 32 (3), 384–413. doi: 10.1147/rd.323.0384
Golizadeh-Mojarad, R., Zainuddin, A. N. M., Klimeck, G., Datta, S. (2008). Atomistic non-equilibrium Green’s function simulations of Graphene nano-ribbons in the quantum hall regime. Journal of Computational Electronics, 7 (3), 407–410. doi: 10.1007/s10825-008-0190-x
Haug, R. J. (1993). Edge-state transport and its experimental consequences in high magnetic fields. Semicond. Semiconductor Science and Technology, 8 (2), 131–153. doi: 10.1088/0268-1242/8/2/001
Cage, M. E. (1997). Current distributions in quantum Hall effect devices. Journal of Research of the National Institute of Standards and Technology, 102 (6), 677–691. doi: 10.6028/jres.102.045
Martines-Duart, Dzh. M., Martin-Palma, R. Dzh., Agullo-Rueda, F. (2007). Nanotehnologii dlja mikro- i optojelektroniki. Moscow: Tehnosfera, 368.
Berger, C., Song, Z., Li, X., Wu, X., Brown, N., Naud, C. et. al (2006). Electronic Confinement and Coherence in Patterned Epitaxial Graphene. Science, 312 (5777), 1191–1196. doi: 10.1126/science.1125925
Brey, L., Fertig, H. A. (2006). Edge states and the quantized Hall effect in graphene. Physical Review B, 73 (19). doi: 10.1103/physrevb.73.195408
Peres, N. M. R., Castro Neto, A. H., Guinea, F. (2006). Conductance quantization in mesoscopic graphene. Physical Review B, 73 (19). doi: 10.1103/physrevb.73.195411
Abanin, D. A., Lee, P. A., Levitov, L. S. (2006). Spin-Filtered Edge States and Quantum Hall Effect in Graphene. Physical Review Letters, 96 (17). doi: 10.1103/physrevlett.96.176803
Kubo, R. (1957). Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems. Journal of the Physical Society of Japan, 12 (6), 570–586. doi: 10.1143/jpsj.12.570
Yourgrau, W., van der Merwe, A., Raw, G. (1982). Treatise on Irreversible and Statistical Thermophysics. Dover, New York.
Krugljak, Ju. A. (2015). Model' provodimosti Landaujera – Datty – Lundstroma v mikro- i nanojelektronike i transportnoe uravnenie Bol'cmana. ScienceRise, 3/2 (8), 108–116. doi: 10.15587/2313-8416.2015.38848
Doniach, S., Sondheimer, E. H. (1998). Green’s Functions for Solid State Physicists. College Press London, 336. doi: 10.1142/p067
Blanter, Y. M., Büttiker, M. (2000). Shot noise in mesoscopic conductors. Physics Reports, 336 (1-2), 1–166. doi: 10.1016/s0370-1573(99)00123-4
Hasan, M. Z., Kane, C. L. (2010). Colloquium: Topological insulators. Reviews of Modern Physics, 82 (4), 3045–3067. doi: 10.1103/revmodphys.82.3045
Krugljak, Ju. A., Prejss, H., Janoshek, R. (1971). Raschet jelektronnyh obolochek benzil'nogo radikala neogranichennym metodom Hartri – Foka na gaussovom bazise. Zh. strukt. him., 12 (4), 689–696.
Krugljak, Ju. A. (2014). Generalized Landauer-Datta-Lundstrom model of electron and heat transport for micro- and nanoelectronics. ScienceRise, 5/3 (5), 6–21. doi: 10.15587/2313-8416.2014.30726
Kruglyak, Y. A., Ukrainsky, I. I. (1970). Study of the electronic structure of alternant radicals by theDODS method. International Journal of Quantum Chemistry, 4 (1), 57–72. doi: 10.1002/qua.560040106
Kruglyak, Yu. A. (2015). Quantum-chemical studies of quasi-one-dimensional electron systems. 1. Polyenes. ScienceRise, 5/2 (10), 69–105. doi: 10.15587/2313-8416.2015.42643
Rashba, E. I. (1960). Properties of semiconductors with an extremum loop . 1. Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop. Sov. Phys. Solid. State., 2, 1109.
Bychkov, Y. A., Rashba, E. I. (1984). Oscillatory effects and the magnetic susceptibility of carriers in inversion layers. Journal of Physics C: Solid State Physics, 17 (33), 6039–6045. doi: 10.1088/0022-3719/17/33/015
Winkler, R. (2003). Spin-Orbit Coupling Effects in Two-Dimensional Electron and Hole Systems. Berlin: Springer, 228. doi: 10.1007/b13586
Hanle, W. (1924). Uber magnetische Beeinflussung der Polarisation der Resonanzfluoreszenz. Zeitschrift for Physik, 30 (1), 93–105. doi: 10.1007/bf01331827
Van Dyck, R., Stoltenberg, J. Pengra, D. (2006). The Hanle Effect. – Washington: The University of Washington.
Huang, B., Jang, H.-J., Appelbaum, I. (2008). Geometric dephasing-limited Hanle effect in long-distance lateral silicon spin transport devices. Applied Physics Letters, 93 (16), 162508. doi: 10.1063/1.3006333
Koo, H. C., Kwon, J. H., Eom, J., Chang, J., Han, S. H., Johnson, M. (2009). Control of Spin Precession in a Spin-Injected Field Effect Transistor. Science, 325 (5947), 1515–1518. doi: 10.1126/science.1173667
Wunderlich, J., Park, B.-G., Irvine, A. C., Zarbo, L. P., Rozkotova, E., Nemec, P et. al (2010). Spin Hall Effect Transistor. Science, 330 (6012), 1801–1804. doi: 10.1126/science.1195816
Sih, V., Lau, W. H., Myers, R. C., Horowitz, V. R., Gossard, A. C., Awschalom, D. D. (2006). Generating Spin Currents in Semiconductors with the Spin Hall Effect. Physical Review Letters, 97 (9). doi: 10.1103/physrevlett.97.096605
Fundamentals of nanoelectronics – quantum models. Available at: http://nanohub.org/courses/FoN2
PurdueX. Free online courses from Purdue University. Available at: https://www.edx.org/school/purduex
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