اثر کرنش بر روی زمان تونل‌زنی و قطبش‌پذیری اسپینی در ابرشبکه‌ی گرافینی

نویسنده

گروه فیزیک، دانشکده علوم دانشگاه محقق اردبیلی، اردبیل

چکیده

در این مقاله زمان تونل زنی وابسته به اسپین و قطبش پذیری اسپینی را در یک ابرشبکه‌ی تک لایه‌ی گرافینی با برهمکنش اسپین - مدار راشبا در حضور کرنش در راستای زیگزاگ و دسته صندلی بررسی می‌کنیم. مشاهده می‌شود دامنه‌ی نوسان زمان تونل زنی با افزایش قدرت کرنش افزایش می‌یابد. علاوه بر این زمانی که کرنش در راستای زیگزاگ باشد اثر هارتمن برای اسپین بالا و پایین قابل مشاهده خواهد بود. برای کرنش در راستای دسته صندلی قطبش پذیری اسپینی با افزایش قدرت کرنش زیاد می‌شود در حالی که قطبش پذیری اسپینی برای کرنش زیگزاگ صفر است. وقتی کرنش در راستای دسته صندلی باشد بر خلاف کرنش در راستای زیگزاگ زمان تونل زنی برای فرود عمود به اسپین الکترون وابسته خواهد بود.

کلیدواژه‌ها


عنوان مقاله [English]

Effects of Strain on the Tunneling Time and Spin Polarization in Graphene Superlattice

نویسنده [English]

  • F. Sattari
چکیده [English]

In this paper, we investigate spin-dependent tunneling time and spin polarization through monolayer graphene superlattice with Rashba spin–orbit interaction in the presence of zigzag and armchair direction strain. It is found that the oscillation amplitude of the dwell time increases by increasing the strain strength. In addition, for the zigzag direction strain the Hartman effect can be observed for the both spin-up and spin-down electrons. When the armchair direction strain is applied to a monolayer graphene the spin polarization increases with increasing the strain strength, whereas for the zigzag direction strain it is zero. In this case, unlike the zigzag direction strain tunneling time for the normal incident angle depends on the spin state of electron.

کلیدواژه‌ها [English]

  • Superlattice
  • Rashba spin–orbit interaction
  • Tunneling time
  • Spin polarization
  • Strained graphene
[1] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Griegorieva, A. A. Firsov, “Electric Field Effect in Atomically Thin Carbon Films”, Science, vol. 306, pp. 666-669, 2004.
[2] K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Griegorieva, A. A. Firsov, “Two-dimensional gas of massless Dirac fermions in graphene”, Nature (London), vol. 438, pp. 197-200, 2005.
[3] Y. Zhang, Y. Wen Tan, H. L. Stormer, P. Kim, “Experimental observation of the quantum Hall effect and Berry's phase in graphene” Nature, vol. 438, pp. 201-204, 2005.
[4] A. R. Wright, X. G. Xu, J. C. Cao, C. Zhang, “Strong nonlinear optical response of graphene in the terahertz regime” Appl. Phys. Lett., vol. 95, pp. 072101-072104, 2009.
[5] M. I. Katsnelson, K. S. Nososelov, A. K. Geim, “Chiral tunnelling and the Klein paradox in graphene”, Nat. phys., vol. 2, pp. 620-625, 2006.
[6] R. Tsu, L. Esaki, “Tunneling in a finite superlattice”, Appl. Phys. Lett., vol. 22, pp. 562-564, 1973.
[7] J. C. Meyer, C. O. Girit, M. F. Crommie, A. Zettl, “Hydrocarbon lithography on graphene membranes”, Appl. Phys. Lett., vol. 92, pp.123110-123113, 2008.
[8] S. Marchini, S. Günther, J. Wintterlin, “Scanning tunneling microscopy of graphene on Ru(0001)” Phys. Rev. B, vol. 76, pp. 075429-075437, 2007.
[9] C. Bai, X. Zhang, “Klein paradox and resonant tunneling in a graphene superlattice”, Phys. Rev. B, vol. 76, pp. 075430-075437, 2007.
[10] E. Faizabadi, M. Esmaeilzadeh, F. Sattari. “Spin filtering in a ferromagnetic graphene superlattice”, Eur. Phys. J. B, vol. 85, pp. 30073-30077, 2012.
[11] F. Sattari, E. Faizabadi, “Transport in magnetic graphene superlattice with Rashba spin-orbit interaction”, Eur. Phys. J. B, vol. 86, pp. 40275-40280 (2013).
[12] F. Khoeini, “Effect of uniaxial strain on electrical conductance and band gap of superlattice-graphene nanoribbons”, Superlattices Microstruct, vol. 81, pp. 202- 214, 2015.
[13] T. Nemati Aram, A. Asgari, “Influence of Fermi velocity engineering on electronic and optical properties of graphene superlattices, Physics Letters A, vol. 379, pp. 974-978, 2015.
[14] E. I. Rashba, “Cyclotron and combinational resonance in a magnetic field perpendicular to the plane of the loop”, Sov. Phys. Solid State, vol. 2, pp. 1109-1122, 1960.
[15] S. Datta, B. Das, “Electronic analog of the electro?optic modulator”, Appl. Phys. Lett., vol. 56, pp. 665-667, 1990.
[16] J. C. Boettger, S. B. Trickey, “First-principles calculation of the spin-orbit splitting in graphene”, Phys. Rev. B, vol. 75, pp.121402(R)-121405(R), 2007.
[17] M. Kariminezhad, A. Namiranian, “Spin-polarized transport in zigzag graphene nanoribbons with Rashba spin–orbit interaction”, J. Appl. Phys., vol. 110, pp. 103702- 103706, 2011.
[18] Yu. S. Dedkov, M. Fonin, U. Rüdiger, C. Laubschat, “Rashba Effect in the Graphene/Ni(111) System”, Phys. Rev. Lett., vol. 100, pp. 107602-1076 06, 2008.
[19] E. U. Condon, “Quantum Mechanics of Collision Processes I. scattering of particles in a definite force field”, Rev. Mod. Phys., vol. 3, pp. 43-88, 1931.
[20] L. A. MacColl, “Note on the Transmission and Reflection of Wave Packets by Potential Barriers”, Phys. Rev., vol. 40, pp. 621-626, 1932.
[21] T. E. Hartman, “Tunneling of a Wave Packet”, J. Appl. Phys., vol. 33, pp. 3427-3433, 1962.
[22] J. C. Martinez, E. Polatdemir, “Origin of the Hartman effect”, Phys. Lett. A, vol. 351, pp. 31-36, 2006.
[23] J. R. Fletcher, “Time delay in tunnelling through a potential barrier”, J. Phys. C, vol. 18, pp. L55-l59, 1985.
[24] E. H. Hauge, J. A. St?vneng, “Tunneling times: a critical review”, Rev. Mod. Phys., vol. 61, pp. 917-936, 1989.
[25] A. Enders, G. Nimtz, “On superluminal barrier traversal”, J. Phys. I, vol. 2, pp. 1693-1698, 1992, “Zero-time tunneling of evanescent mode packets”, J. Phys. I, vol. 3, pp. 1089-1092, 1993.
[26] H. G. Winful, “Delay Time and the Hartman Effect in Quantum Tunneling”, Phys. Rev. Lett., vol. 91, pp. 260401-260404, 2003.
[27] H. G. Winful, “Tunneling time, the Hartman effect, and superluminality: A proposed resolution of an old paradox”, Phys. Rep., vol. 436, pp.1-69, 2006.
[28] C. R. Leavens, G. C. Aers, “Dwell time and phase times for transmission and reflection”,
Phys. Rev. B, vol. 39, pp. 1202-1206, 1989.
[29] F. T. Smith, “Lifetime Matrix in Collision Theory”, Phys. Rev., vol. 118, pp. 349-356, 1960.
[30] X. Chen, Z-Yong Deng, Y. Ban, “Delay time and Hartman effect in strain engineered graphene”, J. Appl. Phys, vol 115, pp. 173703-173708, 2014.
[31] Y. Ban, L.-J. Wang, X. Chen, “Tunable delay time and Hartman effect in graphene magnetic barriers”, J. Appl. Phys., vol. 117, pp. 164307-164313, 2015.
[32] Z.-J. Li, H. Zhao, Y.-H. Nie, J.-Q. Liang, “Barrier tunneling time of an electron in graphene”, J. Appl. Phys., vol. 113, pp. 043714-043722, 2013.
[33] F. Sattari, “Rashba spin–orbit effect on dwell time in graphene asymmetrical barrier”, Appl Phys A, vol. 117, pp.1963-1969, 2014.
[34] C.-S. Park, “Chiral tunneling, tunneling times, and Hartman effect in bilayer graphene”, Phys. Rev. B, vol. 89, pp. 115423-115435, 2014.
[35] D. Jahani, “Note on Hartman effect in gapped graphene”, Physica B, vol. 423, pp.10-15, 2013.
[36] V. Pereira, A. Castro Neto, “Strain Engineering of Graphene’s Electronic Structure”, Phys. Rev. Lett., vol. 103, pp. 046801-046804, 2009.
[37] M. Farjam, H. Rafii-Tabar, “Comment on Band structure engineering of graphene by strain: First-principles calculations’’, Phys. Rev. B, vol. 80, pp.167401-167404, 2009.
[38] F. M. D. Pellegrino, G. G. N. Angilella, R. Pucci, “Transport properties of graphene across strain-induced nonuniform velocity profiles’’, Phys. Rev. B, vol. 84, pp.195404-195415, 2011.
[39] F. M. D. Pellegrino, G. G. N. Angilella, R. Pucci, “Resonant modes in strain-induced graphene superlattices’’, Phys. Rev. B, vol. 85, pp. 195409-19513, 2012.
[40] M. Büttiker, “Four-Terminal Phase-Coherent Conductance’’, Phys. Rev. Lett., vol. 57, pp. 1761-1764, 1986.
[41] Z .Wu, K. Chang, J. T. Liu, X. J. Li, K. S. Chan, “The Hartman effect in graphene’’, J. Appl. Phys., vol. 105, pp. 043702-043707, 2009.
[42] Y .Gong, Y. Guo, “Dwell time in graphene-based magnetic barrier nanostructures’’, J. Appl. Phys., vol. 106, pp. 064317-064323, 2009.
[43] A. T. Ngo, J. M. Villas-Boas, S. E. Ulloa, “Spin polarization control via magnetic barriers and spin-orbit effects’’, Phys. Rev. B, vol. 78, pp. 245310-245315, 2008.
[44] D. Bercioux, A. De Martino, “Spin-resolved scattering through spin-orbit nanostructures in graphene’’, Phys. Rev. B, vol. 81, pp.165410-165415 (2010).
[45] E. Faizabadi, F. Sattari, “Rashba spin-orbit effect on tunneling time in graphene superlattice’’, J. Appl. Phys., vol. 111, pp. 093724-093729, 2012.