时间周期双阱势中光子辅助Dirac电子的Fano共振隧穿
Fano Resonance in Photon-Assisted Dirac Electron Transmission through a Time-Periodic Double-Well Potential
DOI: 10.12677/CMP.2017.64012, PDF, HTML, XML, 下载: 1,703  浏览: 4,179  国家自然科学基金支持
作者: 彭坦, 周斌*:湖北大学物理与电子科学学院,湖北 武汉
关键词: Fano共振光子辅助隧穿Dirac电子Floquet散射矩阵Fano Resonance Photon-Assisted Tunneling Dirac Electron Floquet Scattering Matrix
摘要: 在具有时间周期双阱势的石墨烯体系中,我们研究了光子辅助Dirac电子的Fano型共振隧穿。研究结果表明,由于双阱势中束缚态能级的劈裂,Fano型共振谱会分裂成两个不对称的共振峰。这两个非对称Fano型共振峰的形状不同。并且,两个振荡场的相对相位可以调制非对称Fano型共振峰的形状。此外,我们还可以通过改变振荡场的频率、振幅以及静势阱的结构来调制Fano峰的轮廓。
Abstract: The photon-assisted Fano-type resonance transmission of a Dirac electron through a time-periodic double-well potential in graphene is investigated. It is shown that the Fano-type resonance spectra through double wells are divided into two asymmetric resonance peaks due to the level splitting of bound state in double wells. The line shapes of two asymmetric Fano-type resonance peaks are different. Moreover, the relative phase of the two oscillating fields can adjust the line shapes of the asymmetry Fano-type resonance peaks. Additionally, the profile of Fano-type resonance can be also controlled by adjusting the frequency and amplitude of the applied oscillating fields, and the structure of the static quantum wells.
文章引用:彭坦, 周斌. 时间周期双阱势中光子辅助Dirac电子的Fano共振隧穿[J]. 凝聚态物理学进展, 2017, 6(4): 86-95. https://doi.org/10.12677/CMP.2017.64012

参考文献

[1] Novoselov, K.S., Geim, A.K., Morozov, S.V., et al. (2005) Two-Dimensional Gas of Massless Dirac Fermions in Graphene. Nature, 438, 197-200.
https://doi.org/10.1038/nature04233
[2] Neto, A.H.C., Guinea, F., Peres, N.M.R., et al. (2009) The Electronic Properties of Graphene. Reviews of modern physics, 81, 109.
https://doi.org/10.1103/RevModPhys.81.109
[3] Rozhkov, A.V., Giavaras, G., Bliokh, Y.P., et al. (2011) Electronic Properties of Mesoscopic Graphene Structures: Charge Confinement and Control of Spin and Charge Transport. Physics Reports, 503, 77-114.
https://doi.org/10.1016/j.physrep.2011.02.002
[4] Semenoff, G.W. (1984) Condensed-Matter Simulation of a Three-Dimensional Anomaly. Physical Review Letters, 53, 2449.
https://doi.org/10.1103/PhysRevLett.53.2449
[5] Luk’yanchuk, I.A. and Kopelevich, Y. (2004) Phase Analysis of Quantum Oscilla-tions in Graphite. Physical Review Letters, 93, Article ID: 166402.
https://doi.org/10.1103/PhysRevLett.93.166402
[6] Zawadzki, W. and Rusin, T.M. (2011) Zitterbewegung (Trembling Motion) of Electrons in Semiconductors: A Review. Journal of Physics: Condensed Matter, 23, Article ID: 143201.
https://doi.org/10.1088/0953-8984/23/14/143201
[7] Cserti, J. and Dávid, G. (2006) Unified Description of Zitterbewegung for Spintronic, Graphene, and Superconducting systems. Physical Review B, 74, Article ID: 172305.
https://doi.org/10.1103/PhysRevB.74.172305
[8] Allain, P.E. and Fuchs, J.N. (2011) Klein Tunneling in Graphene: Optics with Massless Electrons. The European Physical Journal B, 83, 301.
https://doi.org/10.1140/epjb/e2011-20351-3
[9] De Leo, S. and Rotelli, P.P. (2006) Barrier Paradox in the Klein Zone. Physical Review A, 73, Article ID: 042107.
https://doi.org/10.1103/PhysRevA.73.042107
[10] De Leo, S. and Rotelli, P.P. (2007) Dirac Equation Studies in the Tunneling Energy Zone. The European Physical Journal C-Particles and Fields, 51, 241-247.
https://doi.org/10.1140/epjc/s10052-007-0297-4
[11] Sarma, S.D., Adam, S., Hwang, E.H., et al. (2011) Electronic Transport in Two-Dimensional Graphene. Reviews of Modern Physics, 83, 407.
https://doi.org/10.1103/RevModPhys.83.407
[12] Klein, O. (1929) Die Reflexion von Elektronen an Einem Potentialsprung Nach der Relativistischen Dynamik von Dirac. Zeitschriftfür Physik A Hadrons and Nuclei, 53, 157-165.
https://doi.org/10.1007/BF01339716
[13] Katsnelson, M.I., Novoselov, K.S. and Geim, A.K. (2006) Chiral Tunnelling and the Klein Paradox in Graphene. Nature Physics, 2, 620.
https://doi.org/10.1038/nphys384
[14] Barbiër, M., Papp, G., Peeters, F.M. (2012) Snake States and Klein Tunneling in a Gra-phene Hall Bar with a Pn-Junction. Applied Physics Letters, 100, Article ID: 163121.
https://doi.org/10.1063/1.4704667
[15] Pereira Jr, J.M., Mlinar, V., Peeters, F.M., et al. (2006) Confined States and Direc-tion-Dependent Transmission in Graphene Quantum Wells. Physical Review B, 74, Article ID: 045424.
https://doi.org/10.1103/PhysRevB.74.045424
[16] Bai, C. and Zhang, X. (2007) Klein Paradox and Resonant Tunneling in a Graphene Superlattice. Physical Review B, 76, Article ID: 075430.
https://doi.org/10.1103/PhysRevB.76.075430
[17] Park, C.H., Yang, L., Son, Y.W., et al. (2008) Anisotropic Behaviours of Massless Dirac Fermions in Graphene under Periodic Potentials. Nature Physics, 4.
[18] Barbier, M., Vasilopoulos, P. and Peeters, F.M. (2010) Extra Dirac Points in the Energy Spectrum for Superlattices on Single-Layer Graphene. Physical Review B, 81, Article ID: 075438.
https://doi.org/10.1103/PhysRevB.81.075438
[19] Tan, L.Z., Park, C.H. and Louie, S.G. (2010) Graphene Dirac Fermions in One-Dimensional Inhomogeneous Field Profiles: Transforming Mag-netic to Electric Field. Physical Review B, 81, Article ID: 195426.
https://doi.org/10.1103/PhysRevB.81.195426
[20] Bliokh, Y.P., Freilikher, V., Savel’ev, S., et al. (2009) Transport and Localiza-tion in Periodic and Disordered Graphene Superlattices. Physical Review B, 79, Article ID: 075123.
https://doi.org/10.1103/PhysRevB.79.075123
[21] Cheianov, V.V., Fal’ko, V. and Altshuler, B.L. (2007) The Focusing of Elec-tron Flow and a Veselago Lens in Grapheme p-n Junctions. Science, 315, 1252-1255.
https://doi.org/10.1126/science.1138020
[22] Chiu, H.Y., Perebeinos, V., Lin, Y.M., et al. (2010) Controllable p-n Junction Formation in Monolayer Graphene using Electrostatic Substrate Engineering. Nano Letters, 10, 4634-4639.
https://doi.org/10.1021/nl102756r
[23] Han, M.Y., Özyilmaz, B., Zhang, Y., et al. (2007) Energy Band-Gap Engineering of Graphemenanoribbons. Physical Review Letters, 98, Article ID: 206805.
https://doi.org/10.1103/PhysRevLett.98.206805
[24] Huard, B., Sulpizio, J.A., Stander, N., et al. (2007) Transport Measurements across a Tunable Potential Barrier in Graphene. Physical Review Letters, 98, Article ID: 236803.
https://doi.org/10.1103/PhysRevLett.98.236803
[25] Ghosh, T.K., De Martino, A., Häusler, W., et al. (2008) Conductance Quantiza-tion and Snake States in Graphene Magnetic Waveguides. Physical Review B, 77, Article ID: 081404.
https://doi.org/10.1103/PhysRevB.77.081404
[26] Fano, U. (1961) Effects of Configuration Interaction on Intensities and Phase Shifts. Physical Review, 124, 1866.
https://doi.org/10.1103/PhysRev.124.1866
[27] Miroshnichenko, A.E., Flach, S. and Kivshar, Y.S. (2010) Fano Resonances in Nanoscale Structures. Reviews of Modern Physics, 82, 2257.
https://doi.org/10.1103/RevModPhys.82.2257
[28] Dayem, A.H. and Martin, R.J. (1962) Quantum Interaction of Microwave Radiation with Tunneling between Superconductors. Physical Review Let-ters, 8, 246.
https://doi.org/10.1103/PhysRevLett.8.246
[29] Tien, P.K. and Gordon, J.P. (1963) Multiphoton Process Observed in the Interaction of Microwave Fields with the Tunneling between Superconductor Films. Physical Review, 129, 647.
https://doi.org/10.1103/PhysRev.129.647
[30] Büttiker, M. and Landauer, R. (1982) Traversal Time for Tunneling. Physical Re-view Letters, 49, 1739.
https://doi.org/10.1103/PhysRevLett.49.1739
[31] Wagner, M. (1996) Strongly Driven Quantum Wells: An Analytical Solution to the Time-Dependent Schrödinger Equation. Physical Review Letters, 76, 4010.
https://doi.org/10.1103/PhysRevLett.76.4010
[32] Wagner, M. and Zwerger, W. (1997) Characteristic Scaling Parameters for Tunnel-ing in Strong Time-Dependent Electric Fields. Physical Review B, 55, R10217.
https://doi.org/10.1103/PhysRevB.55.R10217
[33] Burmeister, G. and Maschke, K. (1998) Scattering by Time-Periodic Potentials in One Dimension and Its Influence on Electronic Transport. Physical Review B, 57, 13050.
https://doi.org/10.1103/PhysRevB.57.13050
[34] Burmeister, G. and Maschke, K. (1999) Bound States Revealed by Time-Periodic Perturbing Scattering Potentials. Physical Review B, 59, 4612.
https://doi.org/10.1103/PhysRevB.59.4612
[35] Li, W. and Reichl, L.E. (1999) Floquet Scattering through a Time-Periodic Potential. Physical Review B, 60, Article ID: 15732.
https://doi.org/10.1103/PhysRevB.60.15732
[36] Moskalets, M. and Büttiker, M. (2002) Floquet scattering Theory of Quantum Pumps. Physical Review B, 66, Article ID: 205320.
https://doi.org/10.1103/PhysRevB.66.205320
[37] Shelykh, I.A. and Galkin, N.G. (2004) Fano and Breit-Wigner Resonances in Carrier Transport through Datta and Das Spin Modulators. Physical Review B, 70, Article ID: 205328.
https://doi.org/10.1103/PhysRevB.70.205328
[38] Ho, C.L. and Lee, C.C. (2005) Stabilizing Quantum Met-astable States in a Time-Periodic Potential. Physical Review A, 71, Article ID: 012102.
https://doi.org/10.1103/PhysRevA.71.012102
[39] Zhang, C.X., Nie, Y.H. and Liang, J.Q. (2006) Photon-Assisted Electron Trans-mission Resonance through a Quantum Well with Spin-Orbit Coupling. Physical Review B, 73, Article ID: 085307.
https://doi.org/10.1103/PhysRevB.73.085307
[40] Ye, C.Z., Zhang, C.X., Nie, Y.H., et al. (2007) Field-Assisted Resonance Tunneling through a Symmetric Double-Barrier Structure with Spin-Orbit Coupling. Physical Review B, 76, Article ID: 035345.
https://doi.org/10.1103/PhysRevB.76.035345
[41] Zhang, C.X., Nie, Y.H. and Liang, J.Q. (2008) Field-Assisted Electron Transport through a Symmetric Double-Well Structure with Spin Orbit Coupling and the Fano-Resonance Induced Spin Filtering. Chi-nese Physics B, 17, 2670-2677.
https://doi.org/10.1088/1674-1056/17/7/052
[42] Hu, L.Y. and Zhou, B. (2011) Spin-Dependent Breit-Wigner and Fano Reso-nances in Photon-Assisted Electron Transport through a Semiconductor Heterostructure. Chinese Physics B, 20, Article ID: 067201.
https://doi.org/10.1088/1674-1056/20/6/067201
[43] Reinhardt, J. and Greiner, W. (1977) Quantum Electrodynamics of Strong Fields. Reports on Progress in Physics, 40, 219.
https://doi.org/10.1088/0034-4885/40/3/001
[44] Petrillo, V. and Janner, D. (2003) Relativistic Analysis of a Wave Packet Interacting with a Quantum-Mechanical Barrier. Physical Review A, 67, Article ID: 012110.
https://doi.org/10.1103/PhysRevA.67.012110
[45] Trauzettel, B., Blanter, Y.M. and Morpurgo, A.F. (2007) Pho-ton-Assisted Electron Transport in Graphene: Scattering Theory Analysis. Physical Review B, 75, Article ID: 035305.
https://doi.org/10.1103/PhysRevB.75.035305
[46] Zeb, M.A., Sabeeh, K. and Tahir, M. (2008) Chiral Tunneling through a Time-Periodic Potential in Monolayer Graphene. Physical Review B, 78, Article ID: 165420.
https://doi.org/10.1103/PhysRevB.78.165420
[47] Cao, Z., Cheng, Y. and Li, G.Q. (2011) Massive Dirac Electron Tunneling through a Time-Periodic Potential in Single Layer Graphene. Physics Letters A, 375, 4065-4069.
https://doi.org/10.1016/j.physleta.2011.08.074
[48] Wu, Z., Li, J. and Chan, K.S. (2012) Charge Pumping in Monolayer Graphene Driven by a Series of Time-Periodic Potentials. Physics Letters A, 376, 1159-1165.
https://doi.org/10.1016/j.physleta.2012.01.043
[49] Savel’ev, S.E., Häusler, W. and Hänggi, P. (2012) Current Resonances in Gra-phene with Time-Dependent Potential Barriers. Physical Review Letters, 109, Article ID: 226602.
https://doi.org/10.1103/PhysRevLett.109.226602
[50] Lu, W.T., Wang, S.J., Li, W., et al. (2012) Fano-Type Resonance through a Time-Periodic Potential in Graphene. Journal of Applied Physics, 111, Article ID: 103717.
https://doi.org/10.1063/1.4721653
[51] Sinha, C. and Biswas, R. (2012) Transmission of Electron through Monolayer Graphene Laser Barrier. Applied Physics Letters, 100, Article ID: 183107.
https://doi.org/10.1063/1.4710525
[52] Myoung, N., Seo, K. and Ihm, G. (2013) Demonstration of Magnetic Confinement in Graphene with Fano-Type Resonances. Journal of the Korean Physical Society, 62, 275-283.
https://doi.org/10.3938/jkps.62.275
[53] Szabó, L.Z., Benedict, M.G., Czirják, A., et al. (2013) Relativistic Electron Transport through an Oscillating Barrier: Wave-Packet Generation and Fano-Type Resonances. Physical Review B, 88, Article ID: 075438.
https://doi.org/10.1103/PhysRevB.88.075438
[54] Biswas, R. and Sinha, C. (2013) Photon Induced Tunneling of Electron through a Graphene Electrostatic Barrier. Journal of Applied Physics, 114, Article ID: 183706.
https://doi.org/10.1063/1.4829446
[55] Biswas, R. and Sinha, C. (2014) Spin Orbit Splitting of the Photon Induced Fano Reso-nance in an Oscillating Graphene Electrostatic Barrier. Journal of Applied Physics, 115, Article ID: 133705.
https://doi.org/10.1063/1.4869846
[56] Zhang, C., Liu, J. and Fu, L. (2015) Anomalous Fano Resonance of Massive Dirac Parti-cle through a Time-Dependent Barrier. Europhysics Letters, 110, Article ID: 61001.
https://doi.org/10.1209/0295-5075/110/61001
[57] Biswas, R., Maity, S. and Sinha, C. (2016) Beating Oscillation and Fano Resonance in the Laser Assisted Electron Transmission through Graphene δ-Function Magnetic Barriers. Physica E: Low-Dimensional Systems and Nanostructures, 84, 235-243.
https://doi.org/10.1016/j.physe.2016.06.010
[58] Biswas, R., Maiti, S., Mukhopadh-yay, S, et al. (2017) Electron Transmission through a Periodically Driven Graphene Magnetic Barrier. Physics Letters A, 381, 1582-1591.
https://doi.org/10.1016/j.physleta.2017.02.045
[59] Shirley, J.H. (1965) Solution of the Schrödinger Equation with a Hamiltonian Periodic in Time. Physical Review, 138, B979.
https://doi.org/10.1103/PhysRev.138.B979
[60] Holthaus, M. and Hone, D. (1993) Quantum Wells and Superlattices in Strong Time-Dependent Fields. Physical Review B, 47, 6499.
https://doi.org/10.1103/PhysRevB.47.6499
[61] Fromherz, T. (1997) Floquet States and Intersubband Absorption in Strongly Driven Double Quantum Wells. Physical Review B, 56, 4772.
https://doi.org/10.1103/PhysRevB.56.4772
[62] Bagwell, P.F. and Lake, R.K. (1992) Resonances in Transmission through an Oscillating Barrier. Physical Review B, 46, Article ID: 15329.
https://doi.org/10.1103/PhysRevB.46.15329
[63] Landauer, R. (1989) Conductance Determined by Transmission: Probes and Quantised Constriction Resistance. Journal of Physics: Condensed Matter, 1, 8099.
https://doi.org/10.1088/0953-8984/1/43/011
[64] Büttiker, M. (1986) Four-Terminal Phase-Coherent Conductance. Physical Re-view Letters, 57, 1761.
https://doi.org/10.1103/PhysRevLett.57.1761
[65] Christen, T. and Büttiker, M. (1996) Low Frequency Admittance of a Quantum Point Contact. Physical Review Letters, 77, 143.
https://doi.org/10.1103/PhysRevLett.77.143
[66] Bulgakov, E.N. and Sadreev, A.F. (1996) Current-Voltage Characteristics of the Resonant Tunnelling Double-Barrier Structure under Time-Periodical Perturbation. Journal of Physics: Condensed Matter, 8, 8869.
https://doi.org/10.1088/0953-8984/8/45/020
[67] Göres, J., Goldhaber-Gordon, D., Heemeyer, S., et al. (2000) Fano Resonances in Electronic Transport through a Single-Electron Transistor. Physical Review B, 62, 2188.
https://doi.org/10.1103/PhysRevB.62.2188
[68] Kobayashi, K., Aikawa, H., Katsumoto, S., et al. (2002) Tuning of the Fano Effect through a Quantum Dot in an Aharonov-Bohm Interferometer. Physical Review Letters, 88, Article ID: 256806.
https://doi.org/10.1103/PhysRevLett.88.256806
[69] Kobayashi, K., Aikawa, H., Katsumoto, S., et al. (2003) Mesoscopic Fano Effect in a Quantum Dot Embedded in an Aharonov-Bohmring. Physical Review B, 68, Article ID: 235304.
https://doi.org/10.1103/PhysRevB.68.235304
[70] Racec, E.R. and Wulf, U. (2001) Resonant Quantum Transport in Semiconductor Nanostructures. Physical Review B, 64, Article ID: 115318.
https://doi.org/10.1103/PhysRevB.64.115318