مقالۀ پژوهشی: ترابرد سطحی عایق توپولوژیک با تابیدگی (وارپینگ) شش ضلعی در حضور سدهای الکتریکی و مغناطیسی

نوع مقاله : مقاله پژوهشی

نویسنده

استادیار گروه فیزیک، دانشگاه پیام نور، تهران، ایران

چکیده

ویژگی­های ترابرد فرمیون­های دیراک در سطح یک عایق توپولوژیک سه بعدی با آثار وارپینگ در حضور سدهای الکتریکی و مغناطیسی با استفاده از روش ماتریس انتقال بررسی شده است. نتایج بیانگر این است که احتمال عبور و رسانندگی با ولتاژ هدایت، زاویة فرودی الکترون­ها، تعداد سدها و شدت میدان تبادلی قابل تنظیم است. در احتمال عبور نسبت به زاویة فرودی الکترون­ها مشخص شده است که برای الکترون­های فرودی عمودی، عبور کامل وجود ندارد. این رفتار، نقش اثر مجاورت مغناطیسی در کم شدن شدت عبور را تأیید می­کند. در طیف رسانندگی، میدان مغناطیسی می­تواند یک شکاف نواری در نقطه دیراک باز کند که به جهت مغناطش بستگی داشته و تا زمانی که جهت­های مغناطش کامل موازی با سطح عایق نباشد، تقارن وارونی زمان شکسته باقی می­ماند. مکان و شدّت قلّه­های تشدیدی به مقادیر ولتاژ هدایت و انرژی فرودی بستگی دارد. با افزایش تعداد کل سدها مشخص شده است که تعداد قلّه­‌های عبور افزایش می­یابد. در حضور آثار وارپینگ شش ضلعی نشان داده شده است که با افزایش انرژی، ترابرد الکتریکی نیز افزایش یافته است. نتایج به دست آمده از این مطالعه با نتایجی که از پیش در این زمینه در اختیار است، همخوانی دارد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Research Paper: Transport Through Potential and Magnetic Barriers on Topological Insulator Surfaces with Hexagonal Warping Effects

نویسنده [English]

  • Masomeh Arabikhah
Assistant Professor, Department of Physics, Payame Noor University, Tehran, Iran
چکیده [English]

The transport properties of the Dirac fermions through the electric and magnetic barriers on the surface of a 3D topological insulator with a hexagonal warping effect have been investigated using the transfer matrix method. It was found that the transmission probability and the electric conductance are strongly modulated by the gate voltage, incident energy, number of barriers, and the exchange field strength. It was remarkable that the Dirac fermion is not perfectly transmitted at the normal incidence, confirming the role of the proximity effect in the suppression of transmission for normal incident electrons. The magnetic field can open up a band gap in the conductance spectrum at the Dirac point, depending on the magnetization orientation. The time-reversal symmetry remains broken as long as the magnetization orientations in modulated regions are not entirely parallel to the surface of a topological insulator. The resonant states and the position of resonant peaks are dependent on the gate voltage and incident energy values. It is shown that the number of tunneling resonances increases with increasing the number of barriers. The hexagonal warping effect can increase electronic transport at high energies. The results found here are consistent with those obtained previously.

کلیدواژه‌ها [English]

  • Topological Insulators
  • Surface States
  • Electronic Transport
  • Potential and Magnetic Barriers
  • Hexagonal Warping Effect
[1] Hasan M.Z., Kane C.L., Colloquim: Topological Insulators, Reviews of Modern Physics, 82, 3045-3067, 2010.
[2] Qi X. L., Zhange S.C., Topological insulator and superconductors, Reviews of Modern Physics, 83, 1057-1110, 2011.
[3] Ando Y., Topological Insulator Materials, Journal of the Physical Society of Japan, 82, 102001-32, 2013.
[4] Wang H.Y., Chen X.W., Zhou X.Y., Zhang L.B., and Zhou G.H., Electronic structure and transport on the surface of topological insulator attached to an electromagnetic superlattice, Phys. B, 407, 3664-3670, 2012.
[5] Zhang Y., Zhai F., Tunneling magnetoresistance on the surface of a topological insulator with periodic magnetic modulations, Applied Physics Letters, 96, 172109-3, 2010.
[6] Song J.T., Li Y.X., and Sun Q.F., Transport through quantum wells and superlattice on topological insulator surfaces, Journal of Physics: Condensed Matte, 26, 185007, 2014.
[7] Vali M., Dideban D., and Moezi N., Quantum well resonant tunneling FET based on topological insulator, Super. Micro, 100, 1256-1262, 2016.
[8] Zhang K. H., Wang Z. C., Zheng Q. R., and Su G., Gate-Voltage controlled electronic transport through a ferromagnet/normal/ferromagnet junction on the surface of a topological insulator, Physical Review B, 86, 174416-7, 2012.
[9] Chen Y. L., Analytis J. G., Chu J.-H., Liu Z. K., Mo S.-K., Qi X. L., Zhang H. J., Lu D. H., Dai X., Fang Z., Zhang S. C., Fisher I. R., Hussain Z., and Shen Z. X., Experimental Realization of a Tree-Dimensional Topological Insulator  , Science, 325, 178-259, 2009.
[10] Fu L., Hexagonal Warping Effects in Surface States of the Topological Insulator, Physical Review Letters, 103, 266801-4, 2009.
[11] Nomura M., Souma S., Takayama A., Sato T., Takahashi T., Eto K., Segawa K., and Ando Y., Relationship between Fermi surface waping and out-of-plane spin polarization in topological insulators: A view from spin-and angle-resolved photoemission, Physical Review B, 89, 045134, 2014.
[12] Wang C. M., Yu F. J., Effects of hexagonal warping on surface transport in topological insulators, Physical Review B, 84, 155440, 2011.
[13] Li Z., Carbotte J. P., Hexagonal warping on optical conductivity of surface states in Topological insulator    , Physical Review B, 87, 155416, 2013.
[14] An J., Ting C. S., Surface state scattering from a step defect in the topological insulator   , Physical Review B, 86, 165313, 2012.
[15] Li H., Shao J. M., Zhang H. B., Yao D. X., and Yang G. W., Resonant tunneling in a topological insulator supperlattice, Journal of Applied Physics, 114, 093703-6, 2013.
[16] Akzyanov R. S., Rakhmanov A. L., Surface charge conductivity of a topological insulator in a magnetic field: The effect of hexagonal warping, Physical Review B, 97, 075421, 2018.
[17] Fu Z. G., Zhang P., Chen M., Wang Z., Zheng F. W., and Lin H. Q., Anisotropic Fabry-Perot resonant states confined within nano-steps on the toplological insulator surface, Scientific Reports, 4, 5544, 2014.
[18] Siu Z. B., Jalil M. B. A., and Tan S. G., Topological state transport in topological insulators under the influence of hexagonal warping and exchange coupling to in-plane magnetizations, Scientific Reports, 4, 5062-7, 2014.
[19] Yu, Z. M., Ma, D. S., Pan, H., Yao, Y., Double reflection and tunneling resonance in a topological insulator: Towards the quantification of warping strength by transport, Physical Review B, 96, 125152, 2017.
[20] Arabikhah M., Saffarzadeh A., Surface state transport in double-gated and magnetized topological insulators with hexagonal warping effects, Journal of Physics: Condensed Matter, 31, 445001-8, 2019.
[21] Dehnavi H., Masoudi A.A., Saadat M., Ghadiri H., and Saffarzadeh A., Electron scattering in a superlattice of line defects on the surface of topological insulator, Journal of Physics: Condensed Matter, 32, 415002-10, 2020.
[22] Saffarzadeh A., Bahar M., and Banihasan M., Spin-dependent resonant tunneling in ZnSe/ZnMnSe heterostructure, Phys. E, 27, 462, 2005.
[23] Katsnelson M. I., Novoselov K. S., and Geim A. K., Chiral tunneling and the Klein paradox in graphene, Nature. Physics, 2, 620-625, 2006.
[24] Klein O., The reflection of electrons at a potential jump according to Dirac’s relativistic dynamics, Phys. Z, 53, 157, 1929.
[25] Li Y., Wan Q., Peng Y., Wang G., Qian Z., Zhou G., and Jalil M. B. A., The effect of magnetic field on chiral transmission in p-n-p graphene junctions, Scientific Reports, 5, 18458-10, 2015.
[26] Stephen G.M., Vail O.A., Lu J., Beck W.A., Taylor P.J., and Friedman A.L., Weak Antilocalization and Anisotropic Magnetoresistance as a Probe of Surface States in Topological  Thin Films, Scientific Reports, 10, 4845-7 ,2020.