Frontiers of Physics

, 13:137304 | Cite as

Spin-dependent transport properties and Seebeck effects for a crossed graphene superlattice p-n junction with armchair edge

Research article
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Abstract

Using the nonequilibrium Green’s function method combined with the tight-binding Hamiltonian, we theoretically investigate the spin-dependent transmission probability and spin Seebeck coefficient of a crossed armchair-edge graphene nanoribbon (AGNR) superlattice p-n junction under a perpendicular magnetic field with a ferromagnetic insulator, where junction widths W1 of 40 and 41 are considered to exemplify the effect of semiconducting and metallic AGNRs, respectively. A pristine AGNR system is metallic when the transverse layer m = 3j + 2 with a positive integer j and an insulator otherwise. When stubs are present, a semiconducting AGNR junction with width W1 = 40 always shows metallic behavior regardless of the potential drop magnitude, magnetization strength, stub length, and perpendicular magnetic field strength. However, metallic or semiconducting behavior can be obtained from a metallic AGNR junction with W1 = 41 by adjusting these physical parameters. Furthermore, a metal-to-semiconductor transition can be obtained for both superlattice p-n junctions by adjusting the number of periods of the superlattice. In addition, the spin-dependent Seebeck coefficient and spin Seebeck coefficient of the two systems are of the same order of magnitude owing to the appearance of a transmission gap, and the maximum absolute value of the spin Seebeck coefficient reaches 370 µV/K when the optimized parameters are used. The calculated results offer new possibilities for designing electronic or heat-spintronic nanodevices based on the graphene superlattice p-n junction.

Keywords

crossed graphene superlattice p-n junction spin-dependent transport properties Seebeck coefficient nonequilibrium Green’s function 

PACS numbers

73.22.-f 73.63.-b 72.25.Dc 79.10.-n 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11704118, 11774085, and 11404230), the Scientific Research Fund of Hunan Provincial Education Department (Grant Nos. 17A193 and 17C0946), the Hunan Provincial Natural Science Foundation of China (Grant No. 2017JJ3210), and the Foundation of Science and Technology Bureau of Sichuan Province (No. 2013JY0085).

References

  1. 1.
    F. J. DiSalvo, Thermoelectric cooling and power generation, Science 285(5428), 703 (1999)CrossRefGoogle Scholar
  2. 2.
    R. Mahajan, Chia-pin Chiu, and G. Chrysler, Cooling a microprocessor chip, Proc. IEEE 94(8), 1476 (2006)CrossRefGoogle Scholar
  3. 3.
    C. B. Vining, An inconvenient truth about thermoelectrics, Nat. Mater. 8(2), 83 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    A. Banerjee, B. Fauque, K. Izawa, A. Miyake, I. Sheikin, J. Flouquet, B. Lenoir, and K. Behnia, Transport anomalies across the quantum limit in semimetallic Bi0.96Sb0.04, Phys. Rev. B 78(16), 161103(R) (2008)ADSCrossRefGoogle Scholar
  5. 5.
    C. Hohn, M. Galffy, and A. Freimuth, Resistivity, Hall effect, Nernst effect, and thermopower in the mixed state of La1.85Sr0.15CuO4, Phys. Rev. B 50(21), 15875 (1994)ADSCrossRefGoogle Scholar
  6. 6.
    J. P. Small, K. M. Perez, and P. Kim, Modulation of thermoelectric power of individual carbon nanotubes, Phys. Rev. Lett. 91(25), 256801 (2003)ADSCrossRefGoogle Scholar
  7. 7.
    Y. M. Zuev, W. Chang, and P. Kim, Thermoelectric and magnetothermoelectric transport measurements of graphene, Phys. Rev. Lett. 102(9), 096807 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    P. Wei, W. Bao, Y. Pu, C. N. Lau, and J. Shi, Anomalous thermoelectric transport of Dirac particles in graphene, Phys. Rev. Lett. 102(16), 166808 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    J. G. Checkelsky and N. P. Ong, Thermopower and Nernst effect in graphene in a magnetic field, Phys. Rev. B 80(8), 081413(R) (2009)ADSCrossRefGoogle Scholar
  10. 10.
    D. Dragoman and M. Dragoman, Giant thermoelectric effect in graphene, Appl. Phys. Lett. 91(20), 203116 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    Y. Ouyang and J. Guo, A theoretical study on thermoelectric properties of graphene nanoribbons, Appl. Phys. Lett. 94(26), 263107 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    Y. X. Xing, Q. F. Sun, and J. Wang, Nernst and Seebeck effects in a graphene nanoribbon, Phys. Rev. B 80(23), 235411 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, and E. Saitoh, Observation of the spin Seebeck effect, Nature 455(7214), 778 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    M. G. Zeng, W. Huang, and G. C. Liang, Spindependent thermoelectric effects in graphene-based spin valves, Nanoscale 5(1), 200 (2013)ADSCrossRefGoogle Scholar
  15. 15.
    M. G. Zeng, Y. P. Feng, and G. C. Liang, Graphenebased spin caloritronics, Nano Lett. 11(3), 1369 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    S. G. Cheng, Spin thermopower and thermoconductance in a ferromagnetic graphene nanoribbon, J. Phys. Condens. Matter 24(38), 385302 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    Y. S. Liu, X. F. Wang, and F. Chi, Non-magnetic doping induced a high spin-filter efficiency and large spin Seebeck eFFect in zigzag graphene nanoribbons, J. Mater. Chem. C Mater. Opt. Electron. Devices 1(48), 8046 (2013)CrossRefGoogle Scholar
  18. 18.
    X. B. Chen, Y. Z. Liu, B.-L. Gu, W. H. Duan, and F. Liu, Giant room-temperature spin caloritronics in spinsemiconducting graphene nanoribbons, Phys. Rev. B 90(12), 121403(R) (2014)ADSCrossRefGoogle Scholar
  19. 19.
    R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O’Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit, Nature 413(6856), 597 (2001)ADSCrossRefGoogle Scholar
  20. 20.
    A. I. Hochbaum, R. K. Chen, R. D. Delgado, W. J. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. D. Yang, Enhanced thermoelectric performance of rough silicon nanowires, Nature 451, 163 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    Y. S. Liu and Y. C. Chen, Seebeck coefficient of thermoelectric molecular junctions: First-principles calculations, Phys. Rev. B 79(19), 193101 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    Y. S. Liu, Y. R. Chen, and Y. C. Chen, Thermoelectric efficiency in nanojunctions: A comparison between atomic junctions and molecular junctions, ASC Nano 3(11), 3497 (2009)CrossRefGoogle Scholar
  23. 23.
    Y. S. Liu, X. F. Yang, X. H. Fan, and Y. J. Xia, Transport properties of a Kondo dot with a larger side-coupled noninteracting quantum dot, J. Phys. Condens. Matter 20(13), 135226 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    Z. X. Xie, L. M. Tang, C. N. Pan, K. M. Li, K. Q. Chen, and W. H. Duan, Enhancement of thermoelectric properties in graphene nanoribbons modulated with stub structures, Appl. Phys. Lett. 100(7), 073105 (2012)ADSCrossRefGoogle Scholar
  25. 25.
    F. Mazzamuto, V. Hung Nguyen, Y. Apertet, C. Caër, C. Chassat, J. Saint-Martin, and P. Dollfus, Enhanced thermoelectric properties in graphene nanoribbons by resonant tunneling of electrons, Phys. Rev. B 83(23), 235426 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    V. T. Tran, J. Saint-Martin, and P. Dollfus, High thermoelectric performance in graphene nanoribbons by graphene/BN interface engineering, Nanotechnology 26(49), 495202 (2015)CrossRefGoogle Scholar
  27. 27.
    J. W. Li, B. Wang, Y. J. Yu, Y. D. Wei, Z. Z. Yu, and Y. Wang, Spin-resolved quantum transport in graphenebased nanojunctions, Front. Phys. 12(4), 126501 (2017)CrossRefGoogle Scholar
  28. 28.
    T. Gunst, T. Markussen, A. P. Jauho, and M. Brandbyge, Thermoelectric properties of finite graphene antidot lattices, Phys. Rev. B 84(15), 155449 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    H. Karamitaheri, M. Pourfath, R. Faez, and H. Kosina, Geometrical effects on the thermoelectric properties of ballistic graphene antidot lattices, J. Appl. Phys. 110(5), 054506 (2011)ADSCrossRefGoogle Scholar
  30. 30.
    Y. H. Yan, Q. F. Liang, H. Zhao, C. Q. Wu, and B. W. Li, Thermoelectric properties of one-dimensional graphene antidot arrays, Phys. Lett. A 376(35), 2425 (2012)ADSCrossRefGoogle Scholar
  31. 31.
    P.-H. Chang and B. K. Nikolić, Edge currents and nanopore arrays in zigzag and chiral graphene nanoribbons as a route toward high-ZT thermoelectrics, Phys. Rev. B 86(4), 041406(R) (2012)ADSCrossRefGoogle Scholar
  32. 32.
    M. Wierzbicki, R. Swirkowicz, and J. Barnaś, Giant spin thermoelectric efficiency in ferromagnetic graphene nanoribbons with antidots, Phys. Rev. B 88(23), 235434 (2013)ADSCrossRefGoogle Scholar
  33. 33.
    J. R. Williams, L. DiCarlo, and C. M. Marcus, Quantum hall effect in a gate-controlled p-n junction of graphene, Science 317(5838), 638 (2007)ADSCrossRefGoogle Scholar
  34. 34.
    T. Lohmann, K. von Klitzing, and J. H. Smet, Four terminal magneto-transport in graphene p-n junctions created by spatially selective doping, Nano Lett. 9(5), 1973 (2009)ADSCrossRefGoogle Scholar
  35. 35.
    L. DiCarlo, J. R. Williams, Y. M. Zhang, D. T. Mc-Clure, and C. M. Marcus, Shot noise in graphene, Phys. Rev. Lett. 100(15), 156801 (2008)ADSCrossRefGoogle Scholar
  36. 36.
    N. N. Klimov, S. T. Le, J. Yan, P.Agnihotri, E. Comfort, J. U. Lee, D. B. Newell, and C. A. Richter, Edge-state transport in graphene p-n junctions in the quantum Hall regime, Phys. Rev. B 92(24), 241301(R) (2015)ADSCrossRefGoogle Scholar
  37. 37.
    T. Ohta, A. Bostwick, T. Seyller, K. Horn, and E. Rotenberg, Controlling the electronic structure of bilayer graphene, Science 313(5789), 951 (2006)ADSCrossRefGoogle Scholar
  38. 38.
    E. D. Herbschleb, R. K. Puddy, P. Marconcini, J. P. Griffiths, G. A. C. Jones, M. Macucci, C. G. Smith, and M. R. Connolly, Direct imaging of coherent quantum transport in graphene p-n-p junctions, Phys. Rev. B 92(12), 125414 (2015)ADSCrossRefGoogle Scholar
  39. 39.
    B. Özyilmaz, P. Jarillo-Herrero, D. Efetov, D. A. Abanin, L. S. Levitov, and P. Kim, Electronic transport and quantum hall effect in bipolar graphene p-n-p junctions, Phys. Rev. Lett. 99(16), 166804 (2007)ADSCrossRefGoogle Scholar
  40. 40.
    R. N. Sajjad and A. W. Ghosh, High efficiency switching using graphene based electron optics, Appl. Phys. Lett. 99(12), 123101 (2011)ADSCrossRefGoogle Scholar
  41. 41.
    A. F. Young and P. Kim, Quantum interference and Klein tunnelling in graphene heterojunction, Nat. Phys. 5(3), 222 (2009)CrossRefGoogle Scholar
  42. 42.
    C. H. Park, Y. W. Son, L. Yang, M. L. Cohen, and S. G. Louie, Electron beam supercollimation in graphene superlattices, Nano Lett. 8(9), 2920 (2008)ADSCrossRefGoogle Scholar
  43. 43.
    M. Woszczyna, M. Friedemann, T. Dziomba, T. Weimann, and F. J. Ahlers, Graphene p-n junction arrays as quantum-Hall resistance standards, Appl. Phys. Lett. 99(2), 022112 (2011)ADSCrossRefGoogle Scholar
  44. 44.
    T. Low and J. Appenzeller, Electronic transport properties of a tilted graphene p-n junction, Phys. Rev. B 80(15), 155406 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    Y. X. Xing, J. Wang, and Q. F. Sun, Focusing of electron flow in a bipolar graphene ribbon with different chiralities, Phys. Rev. B 81(16), 165425 (2010)ADSCrossRefGoogle Scholar
  46. 46.
    N. Dai and Q. F. Sun, Mode mixing induced by disorder in a graphene pnp junction in a magnetic field, Phys. Rev. B 95(6), 064205 (2017)ADSCrossRefGoogle Scholar
  47. 47.
    H. Y. Tian, K. S. Chan, and J. Wang, Efficient spin injection in graphene using electron optics, Phys. Rev. B 86(24), 245413 (2012)ADSCrossRefGoogle Scholar
  48. 48.
    F. M. Xu, Z. Z. Yu, Z. R. Gong, and H. Jin, Firstprinciples study on the electronic and transport properties of periodically nitrogen-doped graphene and carbon nanotube superlattices, Front. Phys. 12(4), 127306 (2017)CrossRefGoogle Scholar
  49. 49.
    B. H. Zhou, B. L. Zhou, Y. G. Yao, G. H. Zhou, and M. Hu, Spin-dependent Seebeck effects in a graphene superlattice p-n junction with different shapes, J. Phys.: Condens. Matter 29(40), 405303 (2017)Google Scholar
  50. 50.
    S. Datta, Quantum Transport-Atom to Transistor, England: Cambridge University Press, 2005CrossRefMATHGoogle Scholar
  51. 51.
    H. J. W. Haug and A.P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Berlin: Springer, 1998Google Scholar
  52. 52.
    A. P. Jauho, N. S. Wingreen, and Y. Meir, Timedependent transport in interacting and noninteracting resonanttunneling systems, Phys. Rev. B 50(8), 5528 (1994)ADSCrossRefGoogle Scholar
  53. 53.
    K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric field effect in atomically thin carbon films, Science 306(5696), 666 (2004)ADSCrossRefGoogle Scholar
  54. 54.
    Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature 438(7065), 201 (2005)ADSCrossRefGoogle Scholar
  55. 55.
    L. Ci, L. Song, D. Jariwala, A. L. ElÃas, W. Gao, M. Terrones, and P. M. Ajayan, Graphene shape control by multistage cutting and transfer, Adv. Mater. 21(44), 4487 (2009)CrossRefGoogle Scholar
  56. 56.
    H. Haugen, D. Huertas-Hernando, and A. Brataas, Spin transport in proximity-induced ferromagnetic graphene, Phys. Rev. B 77(11), 115406 (2008)ADSCrossRefGoogle Scholar
  57. 57.
    K. H. Ding, Z. G. Zhu, and G. Su, Spin-dependent transport and current-induced spin transfer torque in a strained graphene spin valve, Phys. Rev. B 89(19), 195443 (2014)ADSCrossRefGoogle Scholar
  58. 58.
    Q. F. Sun and X. C. Xie, CT-invariant quantum spin hall effect in ferromagnetic graphene, Phys. Rev. Lett. 104(6), 066805 (2010)ADSCrossRefGoogle Scholar
  59. 59.
    M. P. L. Sancho, J. M. L. Sancho, J. M. L. Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface Green functions, J. Phys. F Met. Phys. 15(4), 851 (1985)ADSCrossRefGoogle Scholar
  60. 60.
    D. H. Lee and J. D. Joannopoulos, Simple scheme for surfaceband calculations (II): The Green’s function, Phys. Rev. B 23(10), 4997 (1981)ADSCrossRefGoogle Scholar
  61. 61.
    R. Świrkowicz, M. Wierzbicki, and J. Barnaś, Thermoelectric effects in transport through quantum dots attached to ferromagnetic leads with noncollinear magnetic moments, Phys. Rev. B 80(19), 195409 (2009)ADSCrossRefGoogle Scholar
  62. 62.
    P. Trocha and J. Barnaś, Large enhancement of thermoelectric effects in a double quantum dot system due to interference and Coulomb correlation phenomena, Phys. Rev. B 85(8), 085408 (2012)ADSCrossRefGoogle Scholar
  63. 63.
    X. B. Chen, D. P. Liu, W. H. Duan, and H. Guo, Photon-assisted thermoelectric properties of noncollinear spin valves, Phys. Rev. B 87(8), 085427 (2013)ADSCrossRefGoogle Scholar
  64. 64.
    S. H. Lv, S. B. Feng, and Y. X. Li, Thermopower and conductance for a graphene p-n junction, J. Phys. Condens. Matter 24(14), 145801 (2012)ADSCrossRefGoogle Scholar
  65. 65.
    T. Rejec, A. Ramšak, and J. H. Jefferson, Spindependent thermoelectric transport coe_cients in near perfect quantum wires, Phys. Rev. B 65(23), 235301 (2002)ADSCrossRefGoogle Scholar
  66. 66.
    B. H. Zhou, B. L. Zhou, Y. S. Zeng, G. H. Zhou, and T. Ouyang, Seebeck effects in a graphene nanoribbon coupled to two ferromagnetic leads, J. Appl. Phys. 115(11), 114305 (2014)ADSCrossRefGoogle Scholar
  67. 66a.
    B. H. Zhou, B. L. Zhou, Y. S. Zeng, G. H. Zhou, and T. Ouyang, Spin-dependent Seebeck effects in a graphene nanoribbon coupled to two square lattice ferromagnetic leads, J. Appl. Phys. 117(10), 104305 (2015)ADSCrossRefGoogle Scholar
  68. 67.
    L. J. Yin, K. K. Bai, W. X. Wang, S. Y. Li, Y. Zhang, and L. He, Landau quantization of Dirac fermions in graphene and its multilayers, Front. Phys. 12(4), 127208 (2017)CrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhysicsShaoyang UniversityShaoyangChina
  2. 2.Department of Physics and Key Laboratory for Low-Dimensional Structures and Quantum Manipulation (Ministry of Education)Hunan Normal UniversityChangshaChina
  3. 3.College of Physics and Electronic EngineeringSichuan Normal UniversityChengduChina

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