najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2017-8-2-231-235najo-654Research ArticlePHYSICSФИЗИКАElectrical conductivity model for quasi-one-dimensional structuresBotmanS. A.

ul. Aleksandra Nevskogo, 14, Kaliningrad, 236016

sbotman@innopark.kantiana.ruLebleS. B.

ul. Aleksandra Nevskogo, 14, Kaliningrad, 236016

sleble@kantiana.ruImmanuel Kant Baltic Federal UniversityRussian Federation20171208202582231235Copyright © Botman S.A., Leble S.B., 20252025Botman S.A., Leble S.B.Botman S.A., Leble S.B.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/654

The electron-impurity scattering coefficient of Bloch waves for one dimensional Dirac comb potential is used for calculating the temperature dependence of conductivity within kinetic theory. We restrict ourselves by scattering on impurities that is also modelled by zero-range potential. The conductivity is obtained by standard averaging in momentum space, it is expressed by integral that is evaluated within temperature expansion.

Dirac combresistivitykinetic equationBloch wave scatteringReferencesDingle R.B. The electrical conductivity of thin wires. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1950, 201 (1067), P. 545.Dingle R.B. The electrical conductivity of thin wires. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1950, 201 (1067), P. 545.Lal R. Effect of electron-phonon interaction on the resistivity of metallic nanowires. Physical Review B, 2003, 68 (11), P. 115417.Lal R. Effect of electron-phonon interaction on the resistivity of metallic nanowires. Physical Review B, 2003, 68 (11), P. 115417.Zhang Z., Sun X., et al. Electronic transport properties of single-crystal bismuth nanowire arrays. Physical Review B, 2000, 61 (7), P. 4850–4861.Zhang Z., Sun X., et al. Electronic transport properties of single-crystal bismuth nanowire arrays. Physical Review B, 2000, 61 (7), P. 4850–4861.Lin Y., Sun X., Dresselhaus M.S. Theoretical investigation of thermoelectric transport properties of cylindrical Bi nanowires. Physical Review B, 2000, 62 (7), P. 4610.Lin Y., Sun X., Dresselhaus M.S. Theoretical investigation of thermoelectric transport properties of cylindrical Bi nanowires. Physical Review B, 2000, 62 (7), P. 4610.Wen W., Brongersma S.H., Van Hove M., Maex K. Influence of surface and grain-boundary scattering on the resistivity of copper in reduced dimensions. Applied physics letters, 2004, 84 (15), P. 2838–2840.Wen W., Brongersma S.H., Van Hove M., Maex K. Influence of surface and grain-boundary scattering on the resistivity of copper in reduced dimensions. Applied physics letters, 2004, 84 (15), P. 2838–2840.Natelson D., Willett R.L., West K.W., Pfeiffer L.N. Molecular-scale metal wires. Solid State Communications, 2004, 115 (5), P. 269–274.Natelson D., Willett R.L., West K.W., Pfeiffer L.N. Molecular-scale metal wires. Solid State Communications, 2004, 115 (5), P. 269–274.Botman S., Leble S. Bloch wave — ZRP scattering as a key element of solid state physics computation: 1D example. TASK Quarterly, 2016, 20 (2), P. 197–206.Botman S., Leble S. Bloch wave — ZRP scattering as a key element of solid state physics computation: 1D example. TASK Quarterly, 2016, 20 (2), P. 197–206.Kolmogoroff A. Uber die analytischen Methoden in der Wahrscheinlichkeitsrechnung ¨ Mathematische Annalen, 1931, 104 (1), P. 415–458.Kolmogoroff A. Uber die analytischen Methoden in der Wahrscheinlichkeitsrechnung ¨ Mathematische Annalen, 1931, 104 (1), P. 415–458.Newton R.G. Bloch-wave scattering by crystal defects. Journal of mathematical physics, 1991, 32 (2), P. 551–560.Newton R.G. Bloch-wave scattering by crystal defects. Journal of mathematical physics, 1991, 32 (2), P. 551–560.Boitsev A., Neidhardt H., Popov I. Dirac operator coupled to bosons. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (2), P. 332–339.Boitsev A., Neidhardt H., Popov I. Dirac operator coupled to bosons. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (2), P. 332–339.Rosch A., Andrei N. Conductivity of a clean one-dimensional wire. Physical review letters, 2000, 85 (5), P. 1092.Rosch A., Andrei N. Conductivity of a clean one-dimensional wire. Physical review letters, 2000, 85 (5), P. 1092.Popov I., Kurasov P., et al. A distinguished mathematical physicist Boris S. Pavlov. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (2), P. 782–788.Popov I., Kurasov P., et al. A distinguished mathematical physicist Boris S. Pavlov. Nanosystems: Physics, Chemistry, Mathematics, 2016, 7 (2), P. 782–788.Bid A., Bora A., Raychaudhuri A.K. Temperature dependence of the resistance of metallic nanowires of diameter ≥ 15 nm: Applicability of Bloch-Gr¨uneisen theorem. Physical Review B, 2006, 74 (3), P. 035426.Bid A., Bora A., Raychaudhuri A.K. Temperature dependence of the resistance of metallic nanowires of diameter ≥ 15 nm: Applicability of Bloch-Gr¨uneisen theorem. Physical Review B, 2006, 74 (3), P. 035426.

The authors declare that there are no conflicts of interest present.