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

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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.

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References

  1. F. J. DiSalvo, Thermoelectric cooling and power generation, Science 285(5428), 703 (1999)

    Article  Google Scholar 

  2. R. Mahajan, Chia-pin Chiu, and G. Chrysler, Cooling a microprocessor chip, Proc. IEEE 94(8), 1476 (2006)

    Article  Google Scholar 

  3. C. B. Vining, An inconvenient truth about thermoelectrics, Nat. Mater. 8(2), 83 (2009)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  7. Y. M. Zuev, W. Chang, and P. Kim, Thermoelectric and magnetothermoelectric transport measurements of graphene, Phys. Rev. Lett. 102(9), 096807 (2009)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  10. D. Dragoman and M. Dragoman, Giant thermoelectric effect in graphene, Appl. Phys. Lett. 91(20), 203116 (2007)

    Article  ADS  Google Scholar 

  11. Y. Ouyang and J. Guo, A theoretical study on thermoelectric properties of graphene nanoribbons, Appl. Phys. Lett. 94(26), 263107 (2009)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  14. M. G. Zeng, W. Huang, and G. C. Liang, Spindependent thermoelectric effects in graphene-based spin valves, Nanoscale 5(1), 200 (2013)

    Article  ADS  Google Scholar 

  15. M. G. Zeng, Y. P. Feng, and G. C. Liang, Graphenebased spin caloritronics, Nano Lett. 11(3), 1369 (2011)

    Article  ADS  Google Scholar 

  16. S. G. Cheng, Spin thermopower and thermoconductance in a ferromagnetic graphene nanoribbon, J. Phys. Condens. Matter 24(38), 385302 (2012)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  21. Y. S. Liu and Y. C. Chen, Seebeck coefficient of thermoelectric molecular junctions: First-principles calculations, Phys. Rev. B 79(19), 193101 (2009)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  37. T. Ohta, A. Bostwick, T. Seyller, K. Horn, and E. Rotenberg, Controlling the electronic structure of bilayer graphene, Science 313(5789), 951 (2006)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  40. R. N. Sajjad and A. W. Ghosh, High efficiency switching using graphene based electron optics, Appl. Phys. Lett. 99(12), 123101 (2011)

    Article  ADS  Google Scholar 

  41. A. F. Young and P. Kim, Quantum interference and Klein tunnelling in graphene heterojunction, Nat. Phys. 5(3), 222 (2009)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  44. T. Low and J. Appenzeller, Electronic transport properties of a tilted graphene p-n junction, Phys. Rev. B 80(15), 155406 (2009)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  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. S. Datta, Quantum Transport-Atom to Transistor, England: Cambridge University Press, 2005

    Book  MATH  Google Scholar 

  51. H. J. W. Haug and A.P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors, Berlin: Springer, 1998

    Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  Google Scholar 

  56. H. Haugen, D. Huertas-Hernando, and A. Brataas, Spin transport in proximity-induced ferromagnetic graphene, Phys. Rev. B 77(11), 115406 (2008)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  58. Q. F. Sun and X. C. Xie, CT-invariant quantum spin hall effect in ferromagnetic graphene, Phys. Rev. Lett. 104(6), 066805 (2010)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  67. 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)

    Article  ADS  Google Scholar 

  68. 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)

    Article  Google Scholar 

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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).

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Authors and Affiliations

  1. Department of Physics, Shaoyang University, Shaoyang, 422001, China

    Ben-Hu Zhou & Yang-Su Zeng

  2. Department of Physics and Key Laboratory for Low-Dimensional Structures and Quantum Manipulation (Ministry of Education), Hunan Normal University, Changsha, 410081, China

    Ben-Liang Zhou & Guang-Hui Zhou

  3. College of Physics and Electronic Engineering, Sichuan Normal University, Chengdu, 610068, China

    Man-Yi Duan

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Correspondence to Ben-Hu Zhou or Guang-Hui Zhou.

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Zhou, BH., Zhou, BL., Zeng, YS. et al. Spin-dependent transport properties and Seebeck effects for a crossed graphene superlattice p-n junction with armchair edge. Front. Phys. 13, 137304 (2018). https://doi.org/10.1007/s11467-018-0770-6

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