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

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

References

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

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

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

[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 Bi_0.96Sb_0.04, Phys. Rev. B 78(16), 161103(R) (2008)

[5] C. Hohn, M. Galffy, and A. Freimuth, Resistivity, Hall effect, Nernst effect, and thermopower in the mixed state of La_1.85Sr_0.15CuO₄, Phys. Rev. B 50(21), 15875 (1994)

[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)

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

[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)

[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)

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

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

[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)

[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)

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

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

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

[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)

[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)

[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)

[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)

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

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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-njunctions in the quantum Hall regime, Phys. Rev. B 92(24), 241301(R) (2015)

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

[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)

[39] B. Őzyilmaz, 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)

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

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

[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)

[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)

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

[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)

[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)

[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)

[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)

[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)

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

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

[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)

[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)

[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)

[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)

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

[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)

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

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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) 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)

[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)

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