Effect of Barrier’s Geometry on the Transport Properties of Gaussian Wave-Packet in the Presence of Rashba and Dresselhaus Spin-Orbit Interactions: Comparison of High-Energy and Low-Energy Wave-Packets

Document Type : Original Article


Department of Physics, Qom University of Technology, Qom, Iran


A Gaussian wave-packet quantum tunneling across a one-dimensional double-barrier structure has been explored in order to obtain the spin-based transport coefficients. We have used a split-step finite difference method to solve the resulting nonlinear coupled Schrodinger equations. The related behavior of scattering properties of the system as a function of the geometry of the barriers in the presence of Rashba and Dresselhaus spin-orbit interactions for High-energy and low-energy wave-packets have been compared. Evidence showed that the presence of Rashba or Dresselhaus SOIs leads to considerable spin polarization in the wave-packet components. Based on the results, it is found that the wave-packet velocity plays a significant role in the tunneling process of the Gaussian wave-packet through quantum barriers. In addition, by tuning the Rashba and the Dresselhaus coupling strengths, the energy of the wave-packet, and the characteristics of the system, one can control the spin polarization of the wave-packet and its propagation coefficients.


Main Subjects

© 2022 The Author(s). Journal of Progress in Physics of Applied Materials published by Semnan University Press. This is an open access article under the CC-BY 4.0 license. (https://creativecommons.org/licenses/by/4.0/)

[1] S. Franchi, G. Trevisi, L. Seravalli, and P. Frigeri, "Quantum dot nanostructures and molecular beam epitaxy." Progress in Crystal Growth and Characterization of Materials 47 (2003) 166-195.
[2] H. Wang, "Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations." Applied Mathematics and Computation170 (2005) 17-35.
[3] Li. Meng, "A high-order split-step finite difference method for the system of the space fractional CNLS." The European Physical Journal Plus134 (2019) 244.
[4] M. Dehghan, and A. Taleei, "A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients." Computer Physics Communications 181(1) (2010) 43-51.
[5] M. Solaimani, M. Ghalandari, and L. Lavaei. "Competition of parabolic and periodic sinusoidal potential in the propagation of a soliton." Optik 155 (2018) 185-189.
[6] I. Da, "A quadratic B-spline finite element method for solving nonlinear Schrödinger equation." Computer Methods in Applied Mechanics and Engineering 174 (1999) 247-258.
[7] J. Jin, N. Wei, and H. Zhang. "A two-grid finite-element method for the nonlinear Schiodinger equation." Journal of Computational Mathematics 33 (2015) 146.
[8] H. Hu, and Y. Chen. "Numerical solution of two-dimensional nonlinear Schrödinger equation using a new two-grid finite element method." Computational and Applied Mathematics 364 (2020) 112333.
[9] Y. Xu, and C. W. Shu. "Local discontinuous Galerkin methods for nonlinear Schrödinger equations." Journal of Computational Physics 205 (2005) 72-97.
[10] M. Solaimani, B. Farnam, M. Ghalandari, S. Z. SeyedShirazi. "Wave localization in two dimensional parabolic periodic refractive index profiles: a 4th order Runge–Kutta study." Optical and Quantum Electronics 50 (2018) 114.
[11] L. A. MacColl. "Note on the Transmission and Reflection of Wave Packets by Potential Barriers." Physical Review 40 (1932) 621-626.
[12] A. Jauho, and M. M. Nieto. "Time-dependent tunneling of wave-packets through heterostructures in an applied field." Superlattices and Microstructures 2 (1986) 407-
[13] F. Ancilotto, A. Selloni, A. F. Xu, and E. Tosatti. "Time- dependent tunneling of electron wave packets in a transverse magnetic field." Physical Review B 39 (1989) 8322-8335.
[14] D. Luis, H. Cruz H, and N. E. Capuj. "Suppression of the tunneling current in a bilayer electron system." Physical Review B 59 (1999) 9787-9790.
[15] D. Luis, J. P. Dı́az, N. E. Capuj, and H. Cruz. "Possibility of multiple tunnelling current peaks in a coupled quantum well system." Journal of Applied Physics 88 (2000) 943-947.
[16] H. Inaba, J. Nakagawa, K. Kurosawa, M. Okuda. "Dynamics of Resonant Tunneling in Double-Barrier Structures with Trapezoidal Potential Profile." Japanese Journal of Applied Physics 30 (1991) L544-L546.
[17] H. De Raedt, N. García, and J. Huyghebaert. "Tunneling through time-modulated barriers: Is there a crossover frequency?." Solid State Communications 76 (1990) 847-
[18] D. L. Haavig, and R. Reifenberger. "Dynamic transmission and reflection phenomena for a time-dependent rectangular potential." Physical Review B 26 (1982) 6408-
[19] R. M. Dimeo. "Wave packet scattering from time-varying potential barriers in one dimension." American Journal of Physics 82 (2014) 142-152.
[20] B. Jogai, K. L. Wang, and K. W. Brown. "High frequency amplification in quantum well oscillators." Superlattices and Microstructures 2 (1986) 259-265.
[21] N. Kiriushcheva, S. Kuzmin. "Scattering of a Gaussian wave packet by a reflectionless potential." American Journal of Physics 66 (1998) 867-872.
[22] V.I. Perel’, S.A. Tarasenko, I.N. Yassievich, S.D. Ganichev, V.V. Bel’kov, W. Prettl. "Spin-dependent tunneling through a
symmetric semiconductor barrier." Physical Review B 67 (2003) 201304(R).
[23] E. I. Rashba, and Y. A. Bychkov. "Oscillatory effects and the magnetic susceptibility of carriers in inversion layers." Journal of Physics C: Solid State Physics 17 (1984) 6039- 6045.
[24] G. Dresselhaus. "Spin-Orbit Coupling Effects in Zinc Blende Structures." Physical Review 100 (1955) 580-586.
[25] H. Cruz, and D. Luis. "Possibility of spin device in a triple quantum well system." Journal of Applied Physics 104 (2008) 083715.
[26] H. Dakhlaoui, M. Nefzi, N. S Al-Shameri, A. Al Suwaidan, H. Elmobkey, S. Almansour, & I. Alnaim. "Spin-polarized transmission across heterostructure based on an InAs/GaSb/InGaAs system: Effect of accelerating quantum wells." Chemical Physics Letters 757 (2020) 137866.
[27] H. Dakhlaoui, M. Nefzi, N. S. Al-Shameri, A. Al Suwaidan, H. Elmobkey, S. Almansour, & I. Alnaim. "Magnetic field effect on spin-polarized transport in asymmetric multibarrier based on InAs/GaAs/GaSb systems." Physica B: Condensed Matter 597 (2020) 412403.
[28] M.Solaimani,M.Izadifard,"Spinfilteringin GaAs/Al0.3Ga0.7As multiple quantum wells." Indian Journal of Physics (2020).
[29] M. W. Lu, S. Y. Chen, G. L. Zhang, X. H. Huang, "Spin Filter Based on Magnetically Confined and Spin-Orbit Coupled GaAs/AlxGa1–xAs Heterostructure." IEEE Transactions on Electron Devices 65 (2018) 3045–3049.
[30] E. Diez, F. Domínguez-Adame, A. Sánchez. "Nonlinear resonant tunnelling through double-barrier structures." Physics Letters A 198 (1995) 403–406.
[31] S. M. A. Aleomraninejad, M. Solaimani, M. Mohsenyzadeh,
L. Lavaei, "Discretized Euler–Lagrange variational study of nonlinear optical rectification coefficients." Physica Scripta 93 (2018) 095803.
[32] H. Cruz. "Wave-packet oscillations in a strongly driven InAs quantum well." Journal of Applied Physics 93 (2003) 1620–1623.
[33] G. A. Intronati, P. I. Tamborenea, D. Weinmann, R. A. Jalabert. "Spin-orbit effects in nanowire-based wurtzite semiconductor quantum dots." Physical Review B 88 (2013) 045303.
[34] M. Sabzevar, M. H. Ehsani, M. Solaimani, M. Ghorbani, "Optical properties of a few semiconducting heterostructures in the presence of Rashba spin-orbit interactions: a two-dimensional finite-difference numerical approach." Journal of the Optical Society of America B 36 (2019) 1774-1782.
[35] J. P. Loehr. "Physics of Strained Quantum Well Lasers." (1998) 143-144.
[36] I. V. Kozlov, Y. A. Kolesnichenko. "Magnetic field driven topological transitions in the noncentrosymmetric energy spectrum of the two-dimensional electron gas with Rashba-Dresselhaus spin-orbit interaction." Physical Review B 99 (2019) 085129.
[37] M. H. Bramhall, and B. M. Casper, "Reflections on a Wave Packet Approach to Quantum Mechanical Barrier Penetration." American Journal of Physics 38 (1970) 1136–1145.