<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2024-15-5-658-669</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-135</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>Effect of structural parameters, and spin-orbit interaction on the electronic properties of double quantum wire systems in the presence of external magnetic field</article-title><trans-title-group xml:lang="ru"><trans-title>Влияние структурных параметров и спин-орбитального взаимодействия на электронные свойства систем с двойными квантовыми проводами в присутствии внешнего магнитного поля</trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3738-5851</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Али</surname><given-names>Махмуд</given-names></name><name name-style="western" xml:lang="en"><surname>Ali</surname><given-names>Mahmoud</given-names></name></name-alternatives><bio xml:lang="ru"><p>Махмуд Али, Физический факультет </p><p> </p></bio><bio xml:lang="en"><p>Mahmoud Ali – Physics Department</p><p> </p></bio><email xlink:type="simple">mahmoud.Ali@najah.edu</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-1392-3192</contrib-id><name-alternatives><name name-style="eastern" xml:lang="ru"><surname>Эль-Саид</surname><given-names>Мохаммад</given-names></name><name name-style="western" xml:lang="en"><surname>Elsaid</surname><given-names>Mohammad</given-names></name></name-alternatives><bio xml:lang="ru"><p>Мохаммад Эль-Саид, Физический факультет </p><p> </p></bio><bio xml:lang="en"><p>Mohammad Elsaid – Physics Department</p><p> </p></bio><email xlink:type="simple">mkelsaid@najah.edu</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>Национальный университет Ан-Наджах</institution></aff><aff xml:lang="en"><institution>An-Najah National University</institution></aff></aff-alternatives><pub-date pub-type="collection"><year>2024</year></pub-date><pub-date pub-type="epub"><day>03</day><month>06</month><year>2025</year></pub-date><volume>15</volume><issue>5</issue><fpage>658</fpage><lpage>669</lpage><permissions><copyright-statement>Copyright &amp;#x00A9; Ali M., Elsaid M., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Али М., Эль-Саид М.</copyright-holder><copyright-holder xml:lang="en">Ali M., Elsaid M.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/135">https://nanojournal.ifmo.ru/jour/article/view/135</self-uri><abstract><p>This study explores the effect of the structural parameters of the confining potential and external magnetic field on the electronic properties of a double quantum wire (DQW) system. Using theoretical analysis and graphical representations, we investigate the effects of varying parameters such as structural parameters (µ and λ) on the confinement potential profiles, probability density distributions and energy spectra of DQWs. Furthermore, we investigate the effect of variation of the confinement potential, the Rashba spin-orbit coupling and the external magnetic field on the energy spectra and the local density of states of the system. The changes in the energy spectra and the local density of states of the system due to Rashba spin-orbit coupling, and the external magnetic field were highlighted. The shifts and variations in energy and in the local density of states were discussed in detail. Our research results provide valuable insights into possibility of using the structural parameters and the external magnetic fields for control the electronic properties of the double quantum wire system.</p></abstract><trans-abstract xml:lang="ru"><p>В этом исследовании изучается влияние структурных параметров ограниченного потенциала и внешнего магнитного поля на электронные свойства системы с двойными квантовыми проводами (DQW). С помощью комплексного теоретического анализа и графических представлений мы исследуем влияние изменяющихся параметров, таких как структурные параметры (μ и λ), на профили потенциала ограничения, распределения плотности вероятности и энергетические спектры DQW. Кроме того, мы исследуем влияние изменения потенциала ограничения, спин-орбитальной связи Рашбы и внешнего магнитного поля на энергетические спектры и локальную плотность состояний системы. Были выделены изменения в энергетических спектрах и локальной плотности состояний системы из-за спин-орбитальной связи Рашбы и внешнего магнитного поля. Подробно обсуждались сдвиги и изменения в энергии и локальной плотности состояний. Результаты наших исследований дают ценную информацию о том, как можно использовать индивидуальные структурные параметры и внешние магнитные поля для управления электронными свойствами системы двойной квантовой проволоки.</p></trans-abstract><kwd-group xml:lang="ru"><kwd>Двойная квантовая проволока</kwd><kwd>Спин-орбитальное взаимодействие</kwd><kwd>Локальная плотность состояний</kwd></kwd-group><kwd-group xml:lang="en"><kwd>double quantum wire</kwd><kwd>spin-orbit interaction</kwd><kwd>local density of states</kwd></kwd-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Baghramyan H.M., Barseghyan M.G., Kirakosyan A.A., Restrepo R.L., Mora-Ramos M.E., Duque C.A. Donor impurity-related linear and nonlinear optical absorption coefficients in GaAs/Ga1−xAlxAs concentric double quantum rings: Effects of geometry, hydrostatic pressure, and aluminum concentration. J. of Luminescence, 2014, 145, P. 676-683.</mixed-citation><mixed-citation xml:lang="en">Baghramyan H.M., Barseghyan M.G., Kirakosyan A.A., Restrepo R.L., Mora-Ramos M.E., Duque C.A. Donor impurity-related linear and nonlinear optical absorption coefficients in GaAs/Ga1−xAlxAs concentric double quantum rings: Effects of geometry, hydrostatic pressure, and aluminum concentration. J. of Luminescence, 2014, 145, P. 676-683.</mixed-citation></citation-alternatives></ref><ref id="cit2"><label>2</label><citation-alternatives><mixed-citation xml:lang="ru">Dakhlaoui H. Linear and nonlinear optical absorption coefficients and refractive index changes in GaN/AlxGa(1−x)N double quantum wells operating at 1.55 µm. J. of Applied Physics, 2015, 117 (13), 135705.</mixed-citation><mixed-citation xml:lang="en">Dakhlaoui H. Linear and nonlinear optical absorption coefficients and refractive index changes in GaN/AlxGa(1−x)N double quantum wells operating at 1.55 µm. J. of Applied Physics, 2015, 117 (13), 135705.</mixed-citation></citation-alternatives></ref><ref id="cit3"><label>3</label><citation-alternatives><mixed-citation xml:lang="ru">Kolokolov K.I., Beneslavski S.D., Minina N.Y., Savin A.M. Far-infrared intersubband absorption in p-type GaAs/AlxGa1−xAs single heterojunctions under uniaxial compression. Physical Review B, 2001, 63 (19), 195308.</mixed-citation><mixed-citation xml:lang="en">Kolokolov K.I., Beneslavski S.D., Minina N.Y., Savin A.M. Far-infrared intersubband absorption in p-type GaAs/AlxGa1−xAs single heterojunctions under uniaxial compression. Physical Review B, 2001, 63 (19), 195308.</mixed-citation></citation-alternatives></ref><ref id="cit4"><label>4</label><citation-alternatives><mixed-citation xml:lang="ru">Panda M., Das T., Panda B.K. Nonlinear optical properties in the laser-dressed two-level AlxGa1−xN/GaN single quantum well. Int. J. of Modern Physics B, 2018, 32 (4), 1850032.</mixed-citation><mixed-citation xml:lang="en">Panda M., Das T., Panda B.K. Nonlinear optical properties in the laser-dressed two-level AlxGa1−xN/GaN single quantum well. Int. J. of Modern Physics B, 2018, 32 (4), 1850032.</mixed-citation></citation-alternatives></ref><ref id="cit5"><label>5</label><citation-alternatives><mixed-citation xml:lang="ru">Liao Q.L., Jiang H., Zhang X.W., Qiu Q.F., Tang Y., Yang X.K., Liu Y.L., Huang W.H. A single nanowire sensor for intracellular glucose detection. Nanoscale, 2019, 11 (22), P. 10702–10708.</mixed-citation><mixed-citation xml:lang="en">Liao Q.L., Jiang H., Zhang X.W., Qiu Q.F., Tang Y., Yang X.K., Liu Y.L., Huang W.H. A single nanowire sensor for intracellular glucose detection. Nanoscale, 2019, 11 (22), P. 10702–10708.</mixed-citation></citation-alternatives></ref><ref id="cit6"><label>6</label><citation-alternatives><mixed-citation xml:lang="ru">Chen W., Cabarrocas P.R. Rational design of nanowire solar cells: from single nanowire to nanowire arrays. Nanotechnology, 2019, 30 (19), 194002.</mixed-citation><mixed-citation xml:lang="en">Chen W., Cabarrocas P.R. Rational design of nanowire solar cells: from single nanowire to nanowire arrays. Nanotechnology, 2019, 30 (19), 194002.</mixed-citation></citation-alternatives></ref><ref id="cit7"><label>7</label><citation-alternatives><mixed-citation xml:lang="ru">Robertson K.W., LaPierre R.R., Krich J.J. Efficient wave optics modeling of nanowire solar cells using rigorous coupled-wave analysis. Optics Express, 2019, 27 (4), A133–147.</mixed-citation><mixed-citation xml:lang="en">Robertson K.W., LaPierre R.R., Krich J.J. Efficient wave optics modeling of nanowire solar cells using rigorous coupled-wave analysis. Optics Express, 2019, 27 (4), A133–147.</mixed-citation></citation-alternatives></ref><ref id="cit8"><label>8</label><citation-alternatives><mixed-citation xml:lang="ru">Espinet-Gonzalez P., Barrigon E., Otnes G., Vescovi G., Mann C., France R.M., Welch A.J., Hunt M.S., Walker D., Kelzenberg M.D., ´ Aberg I. ˚ Radiation tolerant nanowire array solar cells. ACS Nano, 2019, 13 (11), P. 12860–12869.</mixed-citation><mixed-citation xml:lang="en">Espinet-Gonzalez P., Barrigon E., Otnes G., Vescovi G., Mann C., France R.M., Welch A.J., Hunt M.S., Walker D., Kelzenberg M.D., ´ Aberg I. ˚ Radiation tolerant nanowire array solar cells. ACS Nano, 2019, 13 (11), P. 12860–12869.</mixed-citation></citation-alternatives></ref><ref id="cit9"><label>9</label><citation-alternatives><mixed-citation xml:lang="ru">Hsu C.L., Wang Y.C., Chang S.P., Chang S.J. Ultraviolet/visible photodetectors based on p–n NiO/ZnO nanowires decorated with Pd nanoparticles. ACS Applied Nano Materials, 2019, 2 (10), P. 6343–6351.</mixed-citation><mixed-citation xml:lang="en">Hsu C.L., Wang Y.C., Chang S.P., Chang S.J. Ultraviolet/visible photodetectors based on p–n NiO/ZnO nanowires decorated with Pd nanoparticles. ACS Applied Nano Materials, 2019, 2 (10), P. 6343–6351.</mixed-citation></citation-alternatives></ref><ref id="cit10"><label>10</label><citation-alternatives><mixed-citation xml:lang="ru">Chen Y., Hrachowina L., Barrigon E., Beech J.P., Alcer D., Lyttleton R., Jam R.J., Samuelson L., Linke H., Borgstrom M. Semiconductor nanowire ¨ array for transparent photovoltaic applications. Applied Physics Letters, 2021, 118 (19).</mixed-citation><mixed-citation xml:lang="en">Chen Y., Hrachowina L., Barrigon E., Beech J.P., Alcer D., Lyttleton R., Jam R.J., Samuelson L., Linke H., Borgstrom M. Semiconductor nanowire ¨ array for transparent photovoltaic applications. Applied Physics Letters, 2021, 118 (19).</mixed-citation></citation-alternatives></ref><ref id="cit11"><label>11</label><citation-alternatives><mixed-citation xml:lang="ru">Wu Y., Yang P. Direct observation of vapor- liquid- solid nanowire growth. J. of the American Chemical Society, 2001, 123 (13), P. 3165–3166.</mixed-citation><mixed-citation xml:lang="en">Wu Y., Yang P. Direct observation of vapor- liquid- solid nanowire growth. J. of the American Chemical Society, 2001, 123 (13), P. 3165–3166.</mixed-citation></citation-alternatives></ref><ref id="cit12"><label>12</label><citation-alternatives><mixed-citation xml:lang="ru">Pevzner A., Engel Y., Elnathan R., Ducobni T., Ben-Ishai M., Reddy K., Shpaisman N., Tsukernik A., Oksman M., Patolsky F. Knocking down highly-ordered large-scale nanowire arrays. Nano letters, 2010, 10 (4), P. 1202–1208.</mixed-citation><mixed-citation xml:lang="en">Pevzner A., Engel Y., Elnathan R., Ducobni T., Ben-Ishai M., Reddy K., Shpaisman N., Tsukernik A., Oksman M., Patolsky F. Knocking down highly-ordered large-scale nanowire arrays. Nano letters, 2010, 10 (4), P. 1202–1208.</mixed-citation></citation-alternatives></ref><ref id="cit13"><label>13</label><citation-alternatives><mixed-citation xml:lang="ru">Madaria A.R., Yao M., Chi C., Huang N., Lin C., Li R., Povinelli M.L., Dapkus P.D., Zhou C. Toward optimized light utilization in nanowire arrays using scalable nanosphere lithography and selected area growth. Nano Letters, 2012, 12 (6), P. 2839–2845.</mixed-citation><mixed-citation xml:lang="en">Madaria A.R., Yao M., Chi C., Huang N., Lin C., Li R., Povinelli M.L., Dapkus P.D., Zhou C. Toward optimized light utilization in nanowire arrays using scalable nanosphere lithography and selected area growth. Nano Letters, 2012, 12 (6), P. 2839–2845.</mixed-citation></citation-alternatives></ref><ref id="cit14"><label>14</label><citation-alternatives><mixed-citation xml:lang="ru">No Y.S., Gao R., Mankin M.N., Day R.W., Park H.G., Lieber C.M. Encoding active device elements at nanowire tips. Nano Letters, 2016, 16 (7), P. 4713–4719.</mixed-citation><mixed-citation xml:lang="en">No Y.S., Gao R., Mankin M.N., Day R.W., Park H.G., Lieber C.M. Encoding active device elements at nanowire tips. Nano Letters, 2016, 16 (7), P. 4713–4719.</mixed-citation></citation-alternatives></ref><ref id="cit15"><label>15</label><citation-alternatives><mixed-citation xml:lang="ru">Chaure S., Chaure N.B., Pandey R.K. Self-assembled nanocrystalline CdSe thin films. Physica E: Low-dimensional Systems and Nanostructures, 2005, 28 (4), P. 439–446.</mixed-citation><mixed-citation xml:lang="en">Chaure S., Chaure N.B., Pandey R.K. Self-assembled nanocrystalline CdSe thin films. Physica E: Low-dimensional Systems and Nanostructures, 2005, 28 (4), P. 439–446.</mixed-citation></citation-alternatives></ref><ref id="cit16"><label>16</label><citation-alternatives><mixed-citation xml:lang="ru">Fischer S.F., Apetrii G., Kunze U., Schuh D., Abstreiter G. Tunnel-coupled one-dimensional electron systems with large subband separations. Physical Review B, 2006, 74 (11), 115324.</mixed-citation><mixed-citation xml:lang="en">Fischer S.F., Apetrii G., Kunze U., Schuh D., Abstreiter G. Tunnel-coupled one-dimensional electron systems with large subband separations. Physical Review B, 2006, 74 (11), 115324.</mixed-citation></citation-alternatives></ref><ref id="cit17"><label>17</label><citation-alternatives><mixed-citation xml:lang="ru">Wang D.W., Mishchenko E.G., Demler E. Pseudospin ferromagnetism in double-quantum-wire systems. Physical Review Letters, 2005, 95 (8), 086802.</mixed-citation><mixed-citation xml:lang="en">Wang D.W., Mishchenko E.G., Demler E. Pseudospin ferromagnetism in double-quantum-wire systems. Physical Review Letters, 2005, 95 (8), 086802.</mixed-citation></citation-alternatives></ref><ref id="cit18"><label>18</label><citation-alternatives><mixed-citation xml:lang="ru">Karaaslan Y., Gisi B., Sakiroglu S.E., Kasapoglu E.S., Sari H.U., Sokmen I. Rashba spin-orbit coupling effects on the optical properties of double ¨ quantum wire under magnetic field. Superlattices and Microstructures, 2016, 93, P. 32–39.</mixed-citation><mixed-citation xml:lang="en">Karaaslan Y., Gisi B., Sakiroglu S.E., Kasapoglu E.S., Sari H.U., Sokmen I. Rashba spin-orbit coupling effects on the optical properties of double ¨ quantum wire under magnetic field. Superlattices and Microstructures, 2016, 93, P. 32–39.</mixed-citation></citation-alternatives></ref><ref id="cit19"><label>19</label><citation-alternatives><mixed-citation xml:lang="ru">Gudmundsson V., Tang C.S. Magnetotransport in a double quantum wire: Modeling using a scattering formalism built on the Lippmann-Schwinger equation. Physical Review B-Condensed Matter and Materials Physics, 2006, 74 (12), 125302.</mixed-citation><mixed-citation xml:lang="en">Gudmundsson V., Tang C.S. Magnetotransport in a double quantum wire: Modeling using a scattering formalism built on the Lippmann-Schwinger equation. Physical Review B-Condensed Matter and Materials Physics, 2006, 74 (12), 125302.</mixed-citation></citation-alternatives></ref><ref id="cit20"><label>20</label><citation-alternatives><mixed-citation xml:lang="ru">Abdullah N.R., Tang C.S., Gudmundsson V. Time-dependent magnetotransport in an interacting double quantum wire with window coupling. Physical Review B – Condensed Matter and Materials Physics, 2010, 82 (19), 195325.</mixed-citation><mixed-citation xml:lang="en">Abdullah N.R., Tang C.S., Gudmundsson V. Time-dependent magnetotransport in an interacting double quantum wire with window coupling. Physical Review B – Condensed Matter and Materials Physics, 2010, 82 (19), 195325.</mixed-citation></citation-alternatives></ref><ref id="cit21"><label>21</label><citation-alternatives><mixed-citation xml:lang="ru">Liu G., Liu R., Chen G., Zhang Z., Guo K., Lu L. Nonlinear optical rectification and electronic structure in asymmetric coupled quantum wires. Results in Physics, 2020, 17, 103027.</mixed-citation><mixed-citation xml:lang="en">Liu G., Liu R., Chen G., Zhang Z., Guo K., Lu L. Nonlinear optical rectification and electronic structure in asymmetric coupled quantum wires. Results in Physics, 2020, 17, 103027.</mixed-citation></citation-alternatives></ref><ref id="cit22"><label>22</label><citation-alternatives><mixed-citation xml:lang="ru">Su Y., Guo K., Liu G., Yang T., Yu Q., Hu M., Yang Y. Nonlinear optical properties of semiconductor double quantum wires coupled to a quantum-sized metal nanoparticle. Optics Letters, 2020, 45 (2), P. 379–382.</mixed-citation><mixed-citation xml:lang="en">Su Y., Guo K., Liu G., Yang T., Yu Q., Hu M., Yang Y. Nonlinear optical properties of semiconductor double quantum wires coupled to a quantum-sized metal nanoparticle. Optics Letters, 2020, 45 (2), P. 379–382.</mixed-citation></citation-alternatives></ref><ref id="cit23"><label>23</label><citation-alternatives><mixed-citation xml:lang="ru">Gisi B., Karaaslan Y., Sakiroglu S.E., Kasapoglu E.S., Sari H.U., Sokmen I. Effects of an in-plane magnetic field on the energy dispersion, spin ¨ texturing and conductance of double quantum wires. Superlattices and Microstructures, 2016, 91, P. 391–400.</mixed-citation><mixed-citation xml:lang="en">Gisi B., Karaaslan Y., Sakiroglu S.E., Kasapoglu E.S., Sari H.U., Sokmen I. Effects of an in-plane magnetic field on the energy dispersion, spin ¨ texturing and conductance of double quantum wires. Superlattices and Microstructures, 2016, 91, P. 391–400.</mixed-citation></citation-alternatives></ref><ref id="cit24"><label>24</label><citation-alternatives><mixed-citation xml:lang="ru">Moon J.S., Blount M.A., Simmons J.A., Wendt J.R., Lyo S.K., Reno J.L. Magnetoresistance of one-dimensional subbands in tunnel-coupled double quantum wires. Physical Review B, 1999, 60 (16), 11530.</mixed-citation><mixed-citation xml:lang="en">Moon J.S., Blount M.A., Simmons J.A., Wendt J.R., Lyo S.K., Reno J.L. Magnetoresistance of one-dimensional subbands in tunnel-coupled double quantum wires. Physical Review B, 1999, 60 (16), 11530.</mixed-citation></citation-alternatives></ref><ref id="cit25"><label>25</label><citation-alternatives><mixed-citation xml:lang="ru">Bielejec E., Reno J.L., Lyo S.K., Lilly M.P. Tunneling spectroscopy in vertically coupled quantum wires. Solid State Communications, 2008, 147 (3–4), P. 79–82.</mixed-citation><mixed-citation xml:lang="en">Bielejec E., Reno J.L., Lyo S.K., Lilly M.P. Tunneling spectroscopy in vertically coupled quantum wires. Solid State Communications, 2008, 147 (3–4), P. 79–82.</mixed-citation></citation-alternatives></ref><ref id="cit26"><label>26</label><citation-alternatives><mixed-citation xml:lang="ru">Huang D., Lyo S.K., Thomas K.J., Pepper M. Field-induced modulation of the conductance, thermoelectric power, and magnetization in ballistic coupled double quantum wires under a tilted magnetic field. Physical Review B, 2008, 77 (8), 085320.</mixed-citation><mixed-citation xml:lang="en">Huang D., Lyo S.K., Thomas K.J., Pepper M. Field-induced modulation of the conductance, thermoelectric power, and magnetization in ballistic coupled double quantum wires under a tilted magnetic field. Physical Review B, 2008, 77 (8), 085320.</mixed-citation></citation-alternatives></ref><ref id="cit27"><label>27</label><citation-alternatives><mixed-citation xml:lang="ru">Karaaslan Y., Gisi B., Sakiroglu S.E., Kasapoglu E.S., Sari H.U., Sokmen I. Electric and magnetic field modulated energy dispersion, conductivity ¨ and optical response in double quantum wire with spin-orbit interactions. Physics Letters A, 2018, 382 (7), P. 507–515.</mixed-citation><mixed-citation xml:lang="en">Karaaslan Y., Gisi B., Sakiroglu S.E., Kasapoglu E.S., Sari H.U., Sokmen I. Electric and magnetic field modulated energy dispersion, conductivity ¨ and optical response in double quantum wire with spin-orbit interactions. Physics Letters A, 2018, 382 (7), P. 507–515.</mixed-citation></citation-alternatives></ref><ref id="cit28"><label>28</label><citation-alternatives><mixed-citation xml:lang="ru">Kumar S., Kumar M., Kumar A. Combined effect of rashba spin-orbit interaction, hydrostatic pressure and temperature on energy dispersion based ballistic conductance of InAs tunnel-coupled (double) quantum wire under exterior magnetic and electric field. Physica B: Condensed Matter, 2024, 677, 415715.</mixed-citation><mixed-citation xml:lang="en">Kumar S., Kumar M., Kumar A. Combined effect of rashba spin-orbit interaction, hydrostatic pressure and temperature on energy dispersion based ballistic conductance of InAs tunnel-coupled (double) quantum wire under exterior magnetic and electric field. Physica B: Condensed Matter, 2024, 677, 415715.</mixed-citation></citation-alternatives></ref><ref id="cit29"><label>29</label><citation-alternatives><mixed-citation xml:lang="ru">Korepov S.V., Liberman M.A. Tunnel-coupled double quantum wires in a magnetic field: electron scattering on impurities and boundary roughness. Physica B: Condensed Matter, 2002, 322 (1–2), P. 92–109.</mixed-citation><mixed-citation xml:lang="en">Korepov S.V., Liberman M.A. Tunnel-coupled double quantum wires in a magnetic field: electron scattering on impurities and boundary roughness. Physica B: Condensed Matter, 2002, 322 (1–2), P. 92–109.</mixed-citation></citation-alternatives></ref><ref id="cit30"><label>30</label><citation-alternatives><mixed-citation xml:lang="ru">Sharma R. Impurity-modulated physical and transport properties in a InxGa1−xAs double quantum wire. Physica B: Condensed Matter, 2023, 659, 414845.</mixed-citation><mixed-citation xml:lang="en">Sharma R. Impurity-modulated physical and transport properties in a InxGa1−xAs double quantum wire. Physica B: Condensed Matter, 2023, 659, 414845.</mixed-citation></citation-alternatives></ref><ref id="cit31"><label>31</label><citation-alternatives><mixed-citation xml:lang="ru">Naydenov B., Boland J.J. Variable-height scanning tunneling spectroscopy for local density of states recovery based on the one-dimensional WKB approximation. Physical Review B, 2010, 82 (24), 245411.</mixed-citation><mixed-citation xml:lang="en">Naydenov B., Boland J.J. Variable-height scanning tunneling spectroscopy for local density of states recovery based on the one-dimensional WKB approximation. Physical Review B, 2010, 82 (24), 245411.</mixed-citation></citation-alternatives></ref><ref id="cit32"><label>32</label><citation-alternatives><mixed-citation xml:lang="ru">Widmer R., Groning P., Feuerbacher M., Gr ¨ oning O. Experimental signatures of spiky local density of states in quasicrystals. ¨ Physical Review B, 2009, 79 (10), 104202.</mixed-citation><mixed-citation xml:lang="en">Widmer R., Groning P., Feuerbacher M., Gr ¨ oning O. Experimental signatures of spiky local density of states in quasicrystals. ¨ Physical Review B, 2009, 79 (10), 104202.</mixed-citation></citation-alternatives></ref><ref id="cit33"><label>33</label><citation-alternatives><mixed-citation xml:lang="ru">Mart´ın-Jimenez A., Fern ´ andez-Dom ´ ´ınguez A.I., Lauwaet K., Granados D., Miranda R., Garc´ıa-Vidal F.J., Otero R. Unveiling the radiative local density of optical states of a plasmonic nanocavity by STM. Nature Communications, 2020, 11 (1), P. 1–8.</mixed-citation><mixed-citation xml:lang="en">Mart´ın-Jimenez A., Fern ´ andez-Dom ´ ´ınguez A.I., Lauwaet K., Granados D., Miranda R., Garc´ıa-Vidal F.J., Otero R. Unveiling the radiative local density of optical states of a plasmonic nanocavity by STM. Nature Communications, 2020, 11 (1), P. 1–8.</mixed-citation></citation-alternatives></ref><ref id="cit34"><label>34</label><citation-alternatives><mixed-citation xml:lang="ru">Ivanov D.A., Ostrovsky P.M., Skvortsov M.A. Correlations of the local density of states in quasi-one-dimensional wires. Physical Review B – Condensed Matter and Materials Physics, 2009, 79 (20), 205108.</mixed-citation><mixed-citation xml:lang="en">Ivanov D.A., Ostrovsky P.M., Skvortsov M.A. Correlations of the local density of states in quasi-one-dimensional wires. Physical Review B – Condensed Matter and Materials Physics, 2009, 79 (20), 205108.</mixed-citation></citation-alternatives></ref><ref id="cit35"><label>35</label><citation-alternatives><mixed-citation xml:lang="ru">Ignatchenko V.A., Tsikalov D.S. Local density of states in one-dimensional photonic crystals and sinusoidal superlattices. Physics Procedia, 2017, 86, P. 113–116.</mixed-citation><mixed-citation xml:lang="en">Ignatchenko V.A., Tsikalov D.S. Local density of states in one-dimensional photonic crystals and sinusoidal superlattices. Physics Procedia, 2017, 86, P. 113–116.</mixed-citation></citation-alternatives></ref><ref id="cit36"><label>36</label><citation-alternatives><mixed-citation xml:lang="ru">Segovia-Chaves F., Vinck-Posada H., Navarro-Baron E.P. Local density of states in a one-dimensional photonic crystal with a semiconducting ´ cavity. Results in Physics, 2022, 33, 105129.</mixed-citation><mixed-citation xml:lang="en">Segovia-Chaves F., Vinck-Posada H., Navarro-Baron E.P. Local density of states in a one-dimensional photonic crystal with a semiconducting ´ cavity. Results in Physics, 2022, 33, 105129.</mixed-citation></citation-alternatives></ref><ref id="cit37"><label>37</label><citation-alternatives><mixed-citation xml:lang="ru">Bena C., Kivelson S.A. Quasiparticle scattering and local density of states in graphite. Physical Review B, 2005, 72 (12), 125432.</mixed-citation><mixed-citation xml:lang="en">Bena C., Kivelson S.A. Quasiparticle scattering and local density of states in graphite. Physical Review B, 2005, 72 (12), 125432.</mixed-citation></citation-alternatives></ref><ref id="cit38"><label>38</label><citation-alternatives><mixed-citation xml:lang="ru">Shimomura Y., Takane Y., Wakabayashi K. Electronic states and local density of states in graphene with a corner edge structure. J. of the Physical Society of Japan, 2011, 80 (5), 054710.</mixed-citation><mixed-citation xml:lang="en">Shimomura Y., Takane Y., Wakabayashi K. Electronic states and local density of states in graphene with a corner edge structure. J. of the Physical Society of Japan, 2011, 80 (5), 054710.</mixed-citation></citation-alternatives></ref><ref id="cit39"><label>39</label><citation-alternatives><mixed-citation xml:lang="ru">Karaaslan Y., Gisi B., Sakiroglu S., Kasapoglu E.S., Sari H.U., Sokmen I. Spin–orbit interaction and magnetic field effects on the energy dispersion ¨ of double quantum wire. Superlattices and Microstructures, 2015, 85, P. 401–409.</mixed-citation><mixed-citation xml:lang="en">Karaaslan Y., Gisi B., Sakiroglu S., Kasapoglu E.S., Sari H.U., Sokmen I. Spin–orbit interaction and magnetic field effects on the energy dispersion ¨ of double quantum wire. Superlattices and Microstructures, 2015, 85, P. 401–409.</mixed-citation></citation-alternatives></ref><ref id="cit40"><label>40</label><citation-alternatives><mixed-citation xml:lang="ru">Hosseinpour P. Effect of Gaussian impurity parameters on the valence and conduction subbands and thermodynamic quantities in a doped quantum wire. Solid State Communications, 2020, 322, 114061.</mixed-citation><mixed-citation xml:lang="en">Hosseinpour P. Effect of Gaussian impurity parameters on the valence and conduction subbands and thermodynamic quantities in a doped quantum wire. Solid State Communications, 2020, 322, 114061.</mixed-citation></citation-alternatives></ref><ref id="cit41"><label>41</label><citation-alternatives><mixed-citation xml:lang="ru">Chen Q., Li L.L., Peeters F.M. Magnetic field dependence of electronic properties of MoS2 quantum dots with different edges. Physical Review B, 2018, 97 (8), 085437.</mixed-citation><mixed-citation xml:lang="en">Chen Q., Li L.L., Peeters F.M. Magnetic field dependence of electronic properties of MoS2 quantum dots with different edges. Physical Review B, 2018, 97 (8), 085437.</mixed-citation></citation-alternatives></ref><ref id="cit42"><label>42</label><citation-alternatives><mixed-citation xml:lang="ru">Gradshteyn I.S., Ryzhik I.M., Romer R.H. Tables of Integrals, Series, and Products. American Association of Physics Teachers: College Park, MD, USA, 1988.</mixed-citation><mixed-citation xml:lang="en">Gradshteyn I.S., Ryzhik I.M., Romer R.H. Tables of Integrals, Series, and Products. American Association of Physics Teachers: College Park, MD, USA, 1988.</mixed-citation></citation-alternatives></ref><ref id="cit43"><label>43</label><citation-alternatives><mixed-citation xml:lang="ru">Nilsson H.A., Samuelsson P., Caroff P., Xu H.Q. Supercurrent and multiple Andreev reflections in an InSb nanowire Josephson junction. Nano Letters, 2012, 12 (1), P. 228–233.</mixed-citation><mixed-citation xml:lang="en">Nilsson H.A., Samuelsson P., Caroff P., Xu H.Q. Supercurrent and multiple Andreev reflections in an InSb nanowire Josephson junction. Nano Letters, 2012, 12 (1), P. 228–233.</mixed-citation></citation-alternatives></ref></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
