Nonlinear dynamics in a terahertz-driven double-layer graphene diode

Wei Feng; Lijuan Shi

doi:10.1088/1674-4926/39/12/124012

J. Semicond. > 2018, Volume 39 > Issue 12 > 124012

SEMICONDUCTOR DEVICES

Nonlinear dynamics in a terahertz-driven double-layer graphene diode

Wei Feng and Lijuan Shi

+ Author Affiliations

Corresponding author: Wei Feng, wfeng@ujs.edu.cn

DOI: 10.1088/1674-4926/39/12/124012

Abstract: By using the time-dependent hydrodynamic equations, we carry out a theoretical study of nonlinear dynamics in an n⁺nn⁺ double-layer graphene diode driven by terahertz radia-tion. A cooperative nonlinear oscillatory mode shows up due to the negative differential conductance effect. We use different chaos-detecting methods, such as the Poincaré bifurcation diagram and the first return map, to examine the transitions between the periodic and chaotic states. The double-layer graphene diode shows typical nonlinear dynamical behavior with the DC bias, AC amplitudes and the AC frequency as the control parameters.

Key words: nonlinear, terahertz, double-layer graphene

References

[1]	Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306: 666 doi: 10.1126/science.1102896
[2]	Apalkov V M, hakraborty T. Fractal butterflies in buckled graphenelike materials. Phys Rev B, 2015, 91: 235447 doi: 10.1103/PhysRevB.91.235447
[3]	Semnani B, Majedi A H, Safavi-Naeini S. Nonlinear quantum optical properties of graphene: the role of chirality and symmetry. Appl Phys Lett, 2015, 85: 115438
[4]	Katsnelson M. Graphene: carbon in two dimensions. Cambridge: Cambridge University Press, 2012
[5]	Bonaccorso F, Sun Z, Hasan T, et al. Graphene photonics and optoelectronics. Nat Photonics, 2010, 4: 611 doi: 10.1038/nphoton.2010.186
[6]	Zheng Y, Ni G X, Toh C T, et al. Graphene field-effect transistors with ferroelectric gating. Phys Rev Lett, 2010, 105: 166602 doi: 10.1103/PhysRevLett.105.166602
[7]	Ferreira A, Peres N M R, Ribeiro R M, et al. Graphene-based photodetector with two cavities. Phys Rev B, 2012, 85: 115438 doi: 10.1103/PhysRevB.85.115438
[8]	Bae S, Kim H, Lee Y B, et al. Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nat Nanotech, 2010, 5: 574 doi: 10.1038/nnano.2010.132
[9]	Britnell L, Gorbachev R V, Geim A K, et al. Resonant tunneling and negative differential conductance in graphene transistors. Nat Commun, 2013, 4: 1794 doi: 10.1038/ncomms2817
[10]	Nguyen V H, Mazzamuto F, Bournel A, et al. Resonant tunneling diodes based on graphene/h-BN heterostructure. J Phys D, 2012, 45: 325104 doi: 10.1088/0022-3727/45/32/325104
[11]	Song Y, Wu H C, Guo Y. Negative differential resistances in graphene double barrier resonant tunneling diodes. Appl Phys Lett, 2013, 102: 093118 doi: 10.1063/1.4794952
[12]	Ferreira G J, Leuenberger M N, Loss D, et al. Low-bias negative differential resistance in graphene nanoribbon superlattices. Phys Rev B, 2011, 84: 125453 doi: 10.1103/PhysRevB.84.125453
[13]	Yamasue K, Fukidome H, Funakubo K, et al. Interfacial charge states in graphene on SiC studied by noncontact scanning nonlinear dielectric potentiometry. Phys Rev Lett, 2015, 114: 226103 doi: 10.1103/PhysRevLett.114.226103
[14]	Kuroda M A, Tersoff J, Martyna G J. Nonlinear screening in multilayer graphene systems. Phys Rev Lett, 2011, 106: 116804 doi: 10.1103/PhysRevLett.106.116804
[15]	Bykov A Y, Murzina T V, Rybin M G, et al. Second harmonic generation in multilayer graphene induced by direct electric current. Phys Rev B, 2012, 85: 121413 doi: 10.1103/PhysRevB.85.121413
[16]	Petrone N, McMillan J F, van der Zande A, et al. Regenerative oscillation and four-wave mixing in graphene optoelectronics. Nat Photonics, 2012, 6: 554 doi: 10.1038/nphoton.2012.147
[17]	Entin M V, Magarill L I, Shepelyansky D L. Theory of resonant photon drag in mono-layer graphene. Phys Rev B, 2010, 81: 165441 doi: 10.1103/PhysRevB.81.165441
[18]	Mai S, Syzranov S V, Efetov K B. Photocurrent in a visible-light graphene photodiode. Phys Rev B, 2011, 83: 033402
[19]	Chu S, Wang S, Gong Q. Ultrafast third-order nonlinear optical properties of graphene in aqueous solution and polyvinyl alcohol film. Chem Phys Lett, 2012, 523: 104 doi: 10.1016/j.cplett.2011.12.024
[20]	Cao J C, Lei X L. Synchronization and chaos in miniband semiconductor superlattices. Phys Rev B, 1999, 60: 1871 doi: 10.1103/PhysRevB.60.1871
[21]	Cao J C, Liu H C, Lei X L, et al. Chaotic dynamics in terahertz-driven semiconductors with negative effective mass. Phys Rev B, 2001, 63: 115308 doi: 10.1103/PhysRevB.63.115308
[22]	Feng W, Cao J C. Nonlinear dynamics in GaAs_1–xN_x diodes under terahertz radiation. J Appl Phys, 2009, 106: 033708 doi: 10.1063/1.3177345
[23]	Cao J C. Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures. Phys Rev Lett, 2003, 91: 237401 doi: 10.1103/PhysRevLett.91.237401

Fig. 1. (Color online) Analytical fit for the velocity-field relation of double-layer graphene at lattice temperature T = 300 K.

DownLoad: Full-Size Img PowerPoint

Fig. 2. (a) Poincaré bifurcation diagram and first return maps at (b) ${V_{{\rm{ac}}}} = 0.035$ V, (c) 0.1 V, (d) 0.1355 V, respectively, for the NDC n⁺nn⁺ double-layer graphene at ${V_{{\rm{dc}}}} = 0.88$ V.

DownLoad: Full-Size Img PowerPoint

Fig. 3. (a) Poincaré bifurcation diagram and first return maps at (b) ${V_{{\rm{ac}}}} = 0.015$ V, (c) 0.12 V, (d) 0.245 V, respectively, for the NDC n⁺nn⁺ double-layer graphene at ${V_{{\rm{dc}}}} = 1.2$ V.

DownLoad: Full-Size Img PowerPoint

[1]	Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306: 666 doi: 10.1126/science.1102896
[2]	Apalkov V M, hakraborty T. Fractal butterflies in buckled graphenelike materials. Phys Rev B, 2015, 91: 235447 doi: 10.1103/PhysRevB.91.235447
[3]	Semnani B, Majedi A H, Safavi-Naeini S. Nonlinear quantum optical properties of graphene: the role of chirality and symmetry. Appl Phys Lett, 2015, 85: 115438
[4]	Katsnelson M. Graphene: carbon in two dimensions. Cambridge: Cambridge University Press, 2012
[5]	Bonaccorso F, Sun Z, Hasan T, et al. Graphene photonics and optoelectronics. Nat Photonics, 2010, 4: 611 doi: 10.1038/nphoton.2010.186
[6]	Zheng Y, Ni G X, Toh C T, et al. Graphene field-effect transistors with ferroelectric gating. Phys Rev Lett, 2010, 105: 166602 doi: 10.1103/PhysRevLett.105.166602
[7]	Ferreira A, Peres N M R, Ribeiro R M, et al. Graphene-based photodetector with two cavities. Phys Rev B, 2012, 85: 115438 doi: 10.1103/PhysRevB.85.115438
[8]	Bae S, Kim H, Lee Y B, et al. Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nat Nanotech, 2010, 5: 574 doi: 10.1038/nnano.2010.132
[9]	Britnell L, Gorbachev R V, Geim A K, et al. Resonant tunneling and negative differential conductance in graphene transistors. Nat Commun, 2013, 4: 1794 doi: 10.1038/ncomms2817
[10]	Nguyen V H, Mazzamuto F, Bournel A, et al. Resonant tunneling diodes based on graphene/h-BN heterostructure. J Phys D, 2012, 45: 325104 doi: 10.1088/0022-3727/45/32/325104
[11]	Song Y, Wu H C, Guo Y. Negative differential resistances in graphene double barrier resonant tunneling diodes. Appl Phys Lett, 2013, 102: 093118 doi: 10.1063/1.4794952
[12]	Ferreira G J, Leuenberger M N, Loss D, et al. Low-bias negative differential resistance in graphene nanoribbon superlattices. Phys Rev B, 2011, 84: 125453 doi: 10.1103/PhysRevB.84.125453
[13]	Yamasue K, Fukidome H, Funakubo K, et al. Interfacial charge states in graphene on SiC studied by noncontact scanning nonlinear dielectric potentiometry. Phys Rev Lett, 2015, 114: 226103 doi: 10.1103/PhysRevLett.114.226103
[14]	Kuroda M A, Tersoff J, Martyna G J. Nonlinear screening in multilayer graphene systems. Phys Rev Lett, 2011, 106: 116804 doi: 10.1103/PhysRevLett.106.116804
[15]	Bykov A Y, Murzina T V, Rybin M G, et al. Second harmonic generation in multilayer graphene induced by direct electric current. Phys Rev B, 2012, 85: 121413 doi: 10.1103/PhysRevB.85.121413
[16]	Petrone N, McMillan J F, van der Zande A, et al. Regenerative oscillation and four-wave mixing in graphene optoelectronics. Nat Photonics, 2012, 6: 554 doi: 10.1038/nphoton.2012.147
[17]	Entin M V, Magarill L I, Shepelyansky D L. Theory of resonant photon drag in mono-layer graphene. Phys Rev B, 2010, 81: 165441 doi: 10.1103/PhysRevB.81.165441
[18]	Mai S, Syzranov S V, Efetov K B. Photocurrent in a visible-light graphene photodiode. Phys Rev B, 2011, 83: 033402
[19]	Chu S, Wang S, Gong Q. Ultrafast third-order nonlinear optical properties of graphene in aqueous solution and polyvinyl alcohol film. Chem Phys Lett, 2012, 523: 104 doi: 10.1016/j.cplett.2011.12.024
[20]	Cao J C, Lei X L. Synchronization and chaos in miniband semiconductor superlattices. Phys Rev B, 1999, 60: 1871 doi: 10.1103/PhysRevB.60.1871
[21]	Cao J C, Liu H C, Lei X L, et al. Chaotic dynamics in terahertz-driven semiconductors with negative effective mass. Phys Rev B, 2001, 63: 115308 doi: 10.1103/PhysRevB.63.115308
[22]	Feng W, Cao J C. Nonlinear dynamics in GaAs_1–xN_x diodes under terahertz radiation. J Appl Phys, 2009, 106: 033708 doi: 10.1063/1.3177345
[23]	Cao J C. Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures. Phys Rev Lett, 2003, 91: 237401 doi: 10.1103/PhysRevLett.91.237401

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Received: 18 July 2018 Revised: 30 August 2018 Online: Accepted Manuscript: 09 November 2018Uncorrected proof: 12 November 2018Published: 13 December 2018

Article Navigation > Journal of Semiconductors > 2018 > 39(12): 124012

Wei Feng, Lijuan Shi. Nonlinear dynamics in a terahertz-driven double-layer graphene diode[J]. Journal of Semiconductors, 2018, 39(12): 124012. doi: 10.1088/1674-4926/39/12/124012 ****W Feng, L J Shi, Nonlinear dynamics in a terahertz-driven double-layer graphene diode[J]. J. Semicond., 2018, 39(12): 124012. doi: 10.1088/1674-4926/39/12/124012.

Citation:

Wei Feng, Lijuan Shi. Nonlinear dynamics in a terahertz-driven double-layer graphene diode[J]. Journal of Semiconductors, 2018, 39(12): 124012. doi: 10.1088/1674-4926/39/12/124012 ****

W Feng, L J Shi, Nonlinear dynamics in a terahertz-driven double-layer graphene diode[J]. J. Semicond., 2018, 39(12): 124012. doi: 10.1088/1674-4926/39/12/124012.

Citation:

Wei Feng, Lijuan Shi. Nonlinear dynamics in a terahertz-driven double-layer graphene diode[J]. Journal of Semiconductors, 2018, 39(12): 124012. doi: 10.1088/1674-4926/39/12/124012 ****

W Feng, L J Shi, Nonlinear dynamics in a terahertz-driven double-layer graphene diode[J]. J. Semicond., 2018, 39(12): 124012. doi: 10.1088/1674-4926/39/12/124012.

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Nonlinear dynamics in a terahertz-driven double-layer graphene diode

DOI: 10.1088/1674-4926/39/12/124012

Department of Physics, Jiangsu University, Zhenjiang 212013, China

Funds:

Project supported by the National Natural Science Foundation of China (No. 11604126), the National Natural Science Foundation of China (No. 61601205), the Basic Research Program of Jiangsu Province (Natural Science Foundation for Young Scholars) (No. BK20160541), and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (No. 16KJB140003).

More Information

Corresponding author: wfeng@ujs.edu.cn
Received Date: 2018-07-18
Revised Date: 2018-08-30
Published Date: 2018-12-01

Abstract

Abstract

By using the time-dependent hydrodynamic equations, we carry out a theoretical study of nonlinear dynamics in an n⁺nn⁺ double-layer graphene diode driven by terahertz radia-tion. A cooperative nonlinear oscillatory mode shows up due to the negative differential conductance effect. We use different chaos-detecting methods, such as the Poincaré bifurcation diagram and the first return map, to examine the transitions between the periodic and chaotic states. The double-layer graphene diode shows typical nonlinear dynamical behavior with the DC bias, AC amplitudes and the AC frequency as the control parameters.
- nonlinear,
- terahertz,
- double-layer graphene

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References(23)

References

[1]	Novoselov K S, Geim A K, Morozov S V, et al. Electric field effect in atomically thin carbon films. Science, 2004, 306: 666 doi: 10.1126/science.1102896
[2]	Apalkov V M, hakraborty T. Fractal butterflies in buckled graphenelike materials. Phys Rev B, 2015, 91: 235447 doi: 10.1103/PhysRevB.91.235447
[3]	Semnani B, Majedi A H, Safavi-Naeini S. Nonlinear quantum optical properties of graphene: the role of chirality and symmetry. Appl Phys Lett, 2015, 85: 115438
[4]	Katsnelson M. Graphene: carbon in two dimensions. Cambridge: Cambridge University Press, 2012
[5]	Bonaccorso F, Sun Z, Hasan T, et al. Graphene photonics and optoelectronics. Nat Photonics, 2010, 4: 611 doi: 10.1038/nphoton.2010.186
[6]	Zheng Y, Ni G X, Toh C T, et al. Graphene field-effect transistors with ferroelectric gating. Phys Rev Lett, 2010, 105: 166602 doi: 10.1103/PhysRevLett.105.166602
[7]	Ferreira A, Peres N M R, Ribeiro R M, et al. Graphene-based photodetector with two cavities. Phys Rev B, 2012, 85: 115438 doi: 10.1103/PhysRevB.85.115438
[8]	Bae S, Kim H, Lee Y B, et al. Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nat Nanotech, 2010, 5: 574 doi: 10.1038/nnano.2010.132
[9]	Britnell L, Gorbachev R V, Geim A K, et al. Resonant tunneling and negative differential conductance in graphene transistors. Nat Commun, 2013, 4: 1794 doi: 10.1038/ncomms2817
[10]	Nguyen V H, Mazzamuto F, Bournel A, et al. Resonant tunneling diodes based on graphene/h-BN heterostructure. J Phys D, 2012, 45: 325104 doi: 10.1088/0022-3727/45/32/325104
[11]	Song Y, Wu H C, Guo Y. Negative differential resistances in graphene double barrier resonant tunneling diodes. Appl Phys Lett, 2013, 102: 093118 doi: 10.1063/1.4794952
[12]	Ferreira G J, Leuenberger M N, Loss D, et al. Low-bias negative differential resistance in graphene nanoribbon superlattices. Phys Rev B, 2011, 84: 125453 doi: 10.1103/PhysRevB.84.125453
[13]	Yamasue K, Fukidome H, Funakubo K, et al. Interfacial charge states in graphene on SiC studied by noncontact scanning nonlinear dielectric potentiometry. Phys Rev Lett, 2015, 114: 226103 doi: 10.1103/PhysRevLett.114.226103
[14]	Kuroda M A, Tersoff J, Martyna G J. Nonlinear screening in multilayer graphene systems. Phys Rev Lett, 2011, 106: 116804 doi: 10.1103/PhysRevLett.106.116804
[15]	Bykov A Y, Murzina T V, Rybin M G, et al. Second harmonic generation in multilayer graphene induced by direct electric current. Phys Rev B, 2012, 85: 121413 doi: 10.1103/PhysRevB.85.121413
[16]	Petrone N, McMillan J F, van der Zande A, et al. Regenerative oscillation and four-wave mixing in graphene optoelectronics. Nat Photonics, 2012, 6: 554 doi: 10.1038/nphoton.2012.147
[17]	Entin M V, Magarill L I, Shepelyansky D L. Theory of resonant photon drag in mono-layer graphene. Phys Rev B, 2010, 81: 165441 doi: 10.1103/PhysRevB.81.165441
[18]	Mai S, Syzranov S V, Efetov K B. Photocurrent in a visible-light graphene photodiode. Phys Rev B, 2011, 83: 033402
[19]	Chu S, Wang S, Gong Q. Ultrafast third-order nonlinear optical properties of graphene in aqueous solution and polyvinyl alcohol film. Chem Phys Lett, 2012, 523: 104 doi: 10.1016/j.cplett.2011.12.024
[20]	Cao J C, Lei X L. Synchronization and chaos in miniband semiconductor superlattices. Phys Rev B, 1999, 60: 1871 doi: 10.1103/PhysRevB.60.1871
[21]	Cao J C, Liu H C, Lei X L, et al. Chaotic dynamics in terahertz-driven semiconductors with negative effective mass. Phys Rev B, 2001, 63: 115308 doi: 10.1103/PhysRevB.63.115308
[22]	Feng W, Cao J C. Nonlinear dynamics in GaAs_1–xN_x diodes under terahertz radiation. J Appl Phys, 2009, 106: 033708 doi: 10.1063/1.3177345
[23]	Cao J C. Interband impact ionization and nonlinear absorption of terahertz radiation in semiconductor heterostructures. Phys Rev Lett, 2003, 91: 237401 doi: 10.1103/PhysRevLett.91.237401

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