najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2025-16-2-199-208najo-16Research ArticlePHYSICSФИЗИКАThermal and magnetic properties and density of state of in 3D SnTe (001) surface state under combined exchange and strain effectsТепловые и магнитные свойства и плотность состояний в 3D поверхностном состоянии SnTe (001) при комбинированных эффектах обмена и деформацииАбдулхакХ.AbdulhaqK.

Халед Абдулхак

Khaled Abdulhaq – Physics department, An-Najah National University

Nablus

khaled.j.abdulhaq@gmail.comhttps://orcid.org/0000-0002-1392-3192ЭльсаидМ. К.ElsaidM. K.

Мохаммад К. Эльсаид

Mohammad K. Elsaid – Physics department, An-Najah National University

Nablus

mkelsaid@najah.eduhttps://orcid.org/0000-0002-6919-3539ДалияД.DahliahD.

Диана Далия

Diana Dahliah – Physics department, An-Najah National University

Nablus

diana.dahliah@najah.eduPhysics department, An-Najah National UniversityPalestinian Territory, Occupied202519052025162199208Copyright © Abdulhaq K., Elsaid M.K., Dahliah D., 20252025Абдулхак Х., Эльсаид М.К., Далия Д.Abdulhaq K., Elsaid M.K., Dahliah D.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/16

This paper presents a comprehensive investigation of the essential properties of topological insulator materials like electronic, thermal, and magnetic quantities. We considered crystalline topological insulators tin telluride (SnTe), deposited on a magnetic substrate material. The anisotropic mass Hamiltonian is considered to obtain eigenenergy spectra expression in the presence of exchange proximity and strain effects. We showed that the strain has an important effect in shifting the position of the valley or Dirac points in the reciprocal space; an important result that leads to significant role in using the topological material as an electronic component in the new hot research area called valley electronics. We displayed the dependences of the computed density of states, heat capacity, and the magnetic susceptibility of the crystalline topological material, SnTe, on the Hamiltonian physical parameters.

В этой статье представлено всестороннее исследование основных свойств, таких как электронные, тепловые и магнитные, топологических изоляторов. Мы рассмотрели кристаллические топологические изоляторы теллурида олова (SnTe), нанесенные на магнитный материал подложки. Анизотропный массовый гамильтониан рассматривается для получения выражения спектра энергии при наличии эффектов обмена и деформации. Мы показали, что деформация оказывает важное влияние на смещение положения точек долины или Дирака в обратном пространстве; важный результат, который приводит к значительной роли в использовании топологического материала в качестве электронного компонента в новой актуальной области исследований, называемой электроникой долин. Мы показали зависимости вычисленной плотности состояний, теплоемкости и магнитной восприимчивости кристаллического топологического материала SnTe от физических параметров гамильтониана.

ТопологияSnTeТепловые свойстваМагнитные свойстваtopologySnTethermal propertiesmagnetic propertiesReferencesMoore J.E. The birth of topological insulators. Nature, 2010, 464 (7286), P. 194–198.Moore J.E. The birth of topological insulators. Nature, 2010, 464 (7286), P. 194–198.Qi, Xiao-Liang, Shou-Cheng Zhang. Topological insulators and superconductors. Reviews of Modern Physics, 2011, 83 (4), P. 1057–1110.Qi, Xiao-Liang, Shou-Cheng Zhang. Topological insulators and superconductors. Reviews of Modern Physics, 2011, 83 (4), P. 1057–1110.Moore J. The next generation. Nature Physics, 2009, 5 (6), P. 378–380.Moore J. The next generation. Nature Physics, 2009, 5 (6), P. 378–380.Zhang, Haijun, et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Physics, 2009, 5 (6), P. 438–442.Zhang, Haijun, et al. Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface. Nature Physics, 2009, 5 (6), P. 438–442.Hasan, Zahid M., Moore J.E. Three-dimensional topological insulators. Annu. Rev. Condens. Matter Phys., 2011, 2 (1), P. 55–78.Hasan, Zahid M., Moore J.E. Three-dimensional topological insulators. Annu. Rev. Condens. Matter Phys., 2011, 2 (1), P. 55–78.Batra, Navketan, Goutam Sheet. Physics with coffee and doughnuts: Understanding the physics behind topological insulators through SuSchrieffer-Heeger model. Resonance, 2020, 25 (6), P. 765–786.Batra, Navketan, Goutam Sheet. Physics with coffee and doughnuts: Understanding the physics behind topological insulators through SuSchrieffer-Heeger model. Resonance, 2020, 25 (6), P. 765–786.Boothroyd A.T. Topological electronic bands in crystalline solids. Contemporary Physics, 2022, 63 (4), P. 305–327.Boothroyd A.T. Topological electronic bands in crystalline solids. Contemporary Physics, 2022, 63 (4), P. 305–327.Furchi, Marco, et al. Microcavity-integrated graphene photodetector. Nano Letters, 2012, 12 (6), P. 2773–2777.Furchi, Marco, et al. Microcavity-integrated graphene photodetector. Nano Letters, 2012, 12 (6), P. 2773–2777.Ma, Eric Yue, et al. Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry. Nature Communications, 2015, 6 (1), 7252.Ma, Eric Yue, et al. Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry. Nature Communications, 2015, 6 (1), 7252.Xu, Su-Yang, et al. Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe. Nature Communications, 2012, 3 (1), 1192.Xu, Su-Yang, et al. Observation of a topological crystalline insulator phase and topological phase transition in Pb1−xSnxTe. Nature Communications, 2012, 3 (1), 1192.Tanaka Y., et al. Experimental realization of a topological crystalline insulator in SnTe. Nature Physics, 2012, 8 (11), P. 800–803.Tanaka Y., et al. Experimental realization of a topological crystalline insulator in SnTe. Nature Physics, 2012, 8 (11), P. 800–803.Dziawa P., et al. Topological crystalline insulator states in Pb1−xSnxSe. Nature Materials, 2012, 11 (12), P. 1023–1027.Dziawa P., et al. Topological crystalline insulator states in Pb1−xSnxSe. Nature Materials, 2012, 11 (12), P. 1023–1027.Hsieh, Timothy H., et al. Topological crystalline insulators in the SnTe material class. Nature Communications, 2012, 3 (1), 982.Hsieh, Timothy H., et al. Topological crystalline insulators in the SnTe material class. Nature Communications, 2012, 3 (1), 982.Ngo B.V.Q., et al. Exchange field effects on the electronic properties of heterostructured ferromagnetic/topological crystalline insulator. Physica E: Low-dimensional Systems and Nanostructures, 2021, 126, 114441.Ngo B.V.Q., et al. Exchange field effects on the electronic properties of heterostructured ferromagnetic/topological crystalline insulator. Physica E: Low-dimensional Systems and Nanostructures, 2021, 126, 114441.Liu, Junwei, Wenhui Duan, Liang Fu. Two types of surface states in topological crystalline insulators. Physical Review B – Condensed Matter and Materials Physics, 2013, 88 (24), 241303.Liu, Junwei, Wenhui Duan, Liang Fu. Two types of surface states in topological crystalline insulators. Physical Review B – Condensed Matter and Materials Physics, 2013, 88 (24), 241303.Hsieh D., Xia Y., Wray L., Qian D., Pal A., Dil J. H., Osterwalder J., Meier F., Bihlmayer G., Hasan M.Z. Observation of unconventional quantum spin textures in topological insulators. Science, 2009, 323 (5916), P. 919–922.Hsieh D., Xia Y., Wray L., Qian D., Pal A., Dil J. H., Osterwalder J., Meier F., Bihlmayer G., Hasan M.Z. Observation of unconventional quantum spin textures in topological insulators. Science, 2009, 323 (5916), P. 919–922.Pham, Khang D., et al. Controlling anisotropic surface group velocity and effective mass in topological crystalline insulator SnTe by Rashba effect. Physica E: Low-dimensional Systems and Nanostructures, 2020, 120, 114118.Pham, Khang D., et al. Controlling anisotropic surface group velocity and effective mass in topological crystalline insulator SnTe by Rashba effect. Physica E: Low-dimensional Systems and Nanostructures, 2020, 120, 114118.Mitchell D.L., Wallis R.F. Theoretical energy-band parameters for the lead salts. Physical Review, 1966, 151 (2), 581. [19] Ando, Yoichi, Liang Fu. Topological crystalline insulators and topological superconductors: From concepts to materials. Annu. Rev. Condens. Matter Phys., 2015, 6 (1), P. 361–381.Mitchell D.L., Wallis R.F. Theoretical energy-band parameters for the lead salts. Physical Review, 1966, 151 (2), 581. [19] Ando, Yoichi, Liang Fu. Topological crystalline insulators and topological superconductors: From concepts to materials. Annu. Rev. Condens. Matter Phys., 2015, 6 (1), P. 361–381.Tang, Evelyn, Liang Fu. Strain-induced partially flat band, helical snake states and interface superconductivity in topological crystalline insulators. Nature Physics, 2014, 10 (12), P. 964–969.Tang, Evelyn, Liang Fu. Strain-induced partially flat band, helical snake states and interface superconductivity in topological crystalline insulators. Nature Physics, 2014, 10 (12), P. 964–969.Tien, Tong S., Pham TC Van, Le P.T.T. The strain and electric field modulation of magnetic properties in topological crystalline insulator thin films. Chemical Physics Letters, 2020, 751, 137512.Tien, Tong S., Pham TC Van, Le P.T.T. The strain and electric field modulation of magnetic properties in topological crystalline insulator thin films. Chemical Physics Letters, 2020, 751, 137512.

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