Influence of the velocity barrier on the massive Dirac electron transport in a monolayer MoS₂ quantum structure

Abstract

Using the transfer matrix method, spin- and valley-dependent electron transport properties modulated by the velocity barrier were studied in the normal/ferromagnetic/normal monolayer MoS₂ quantum structure. Based on Snell’s Law in optics, we define the velocity barrier as ξ=v₂/v₁ by changing the Fermi velocity of the intermediate ferromagnetic region to obtain a deflection condition during the electron transport process in the structure. The results show that both the magnitude and the direction of spin- and valley-dependent electron polarization can be regulated by the velocity barrier. –100% polarization of spin- and valley-dependent electron can be achieved for ξ>1, while 100% polarization can be obtained for ξ<1. Furthermore, it is determined that perfect spin and valley transport always occur at a large incident angle. In addition, the spin- and valley-dependent electron transport considerably depends on the length k_FL and the gate voltage U(x) of the intermediate ferromagnetic region. These findings provide an effective method for designing novel spin and valley electronic devices.

Keywords

velocity barrier / monolayer MoS₂ / spin / valley / polarization

References

[1] X. J. Qiu, Z. Z. Cao, J. M. Lei, J. Shen, and C. C. Qin, Optical and Electric Control of Charge and Spin-Valley Transport in Ferromagnetic Silicene Junction, Superlattices Microstruct. 109, 735 (2017)

[2] M. Tahir, Electrical and optical transport properties of single layer WSe₂, Physica E 97, 184 (2017)

[3] K. F. Mak, K. L. He, J. Shan, and T. F. Heinz, Control of valley polarization in monolayer MoS₂ by optical helicity, Nat. Nanotechnol. 7(8), 494 (2012)

[4] H. Li, J. Shao, D. Yao, and G. Yang, Gate-voltagecontrolled spin and valley polarization transport in a normal/ferromagnetic/normal MoS₂ junction, ACS Appl. Mater. Interfaces 6(3), 1759 (2014)

[5] L. F. Sun and Y. Guo, Line-type resonance peaks and their suppression through graphene-based symmetric and asymmetric double barriers, J. Appl. Phys. 109(12), 123719 (2011)

[6] H. P. Huang, D. Liu, H. M. Zhang, and X. J. Kong, Electronic transport and shot noise in Thue-Morse sequence graphene superlattice, J. Appl. Phys. 113(4), 043702 (2013)

[7] P. Ye, R. Y. Yuan, Y. Y. Xia, and X. Zhao, Spin and valley transport in the ferromagnetic MoS₂ junctions subjected by the gate voltage, J. Phys. Conf. Ser. 827, 012011 (2017)

[8] T. Yokoyama, Controllable valley and spin transport in ferromagnetic silicene junctions, Phys. Rev. B 87, 241409(R) (2013)

[9] L. Majidi and R. Asgari, Valley- and spin-switch effects in molybdenum disulfide superconducting spin valve, Phys. Rev. B 90(16), 165440 (2014)

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

[11] P. Stepanov, Y. Barlas, S. Che, K. Myhro, G. Voigt, Z. Pi, K. Watanabe, T. Taniguchi, D. Smirnov, F. Zhang, R. K. Lake, A. H. MacDonald, and C. N. Lau, Quantum parity Hall effect in bernal-stacked trilayer graphene, Proc. Natl. Acad. Sci. USA 116(21), 10286 (2019)

[12] S. Sun, Y. Yu, J. Dang, K. Peng, X. Xie, F. Song, C. Qian, S. Wu, H. Ali, J. Tang, J. Yang, S. Xiao, S. Tian, M. Wang, X. Shan, M. A. Rafiq, C. Wang, and X. Xu, Large gfactor in bilayer WS₂ flakes, Appl. Phys. Lett. 114(11), 113104 (2019)

[13] X. Q. Yu, Z. G. Zhu, J. S. You, T. Low, and G. Su, Topological nonlinear anomalous nernst effect in strained transition metal dichalcogenides, Phys. Rev. B 99(20), 201410 (2019)

[14] E. I. Rashba, Theory of electrical spin injection: tunnel contacts as a solution of the conductivity mismatch problem, Phys. Rev. B 62(24), R16267 (2000)

[15] G. Schmidt, D. Ferrand, L. W. Molenkamp, A. T. Filip, and B. J. van Wees, Fundamental obstacle for electrical spin injection from a ferromagnetic metal into a diffusive semiconductor, Phys. Rev. B 62(8), R4790 (2000)

[16] N. Tombros, C. Jozsa, M. Popinciuc, H. T. Jonkman, and B. J. van Wees, Electronic spin transport and spin precession in single graphene layers at room temperature, Nature 448(7153), 571 (2007)

[17] X. Ma, H. Ai, H. Gao, and X. Zhang, Valley polarization and ferroelectricity in two-dimensional GaAsC₆ monolayer, Phys. Chem. Chem. Phys. 21, 3954 (2019)

[18] K. S. Novoselov, D. V. Andreeva, W. Ren, and G. Shan, Graphene and Other Two-Dimensional Materials, Front. Phys. 14, 13301 (2019)

[19] A. Splendiani, L. Sun, Y. Zhang, T. Li, J. Kim, C.Y. Chim, G. Galli, and F. Wang, Emerging photoluminescence in monolayer MoS₂, Nano Lett. 10(4), 1271 (2010)

[20] K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin MoS₂: A new direct-gap semiconductor, Phys. Rev. Lett. 105(13), 136805 (2010)

[21] G. D. Scholes and G. Rumbles, Excitons in nanoscale systems, Nat. Mater. 5(9), 683 (2006)

[22] M. Law, J. Goldberger, and P. Yang, Semiconductor nanowires and nanotubes, Annu. Rev. Mater. Res. 34(1), 83 (2004)

[23] Y. L. Li, J. Ludwig, T. Low, A. Chernikov, X. Cui, G. Arefe, Y. D. Kim, A. M. van der Zande, A. Rigosi, H. M. Hill, S. H. Kim, J. Hone, Z. Li, D. Smirnov, and T. F. Heinz, Valley splitting and polarization by the Zeeman effect in monolayer MoSe₂, Phys. Rev. Lett. 113(26), 266804 (2014)

[24] D. MacNeil, C. Heikes, K. F. Mak, Z. Anderson, A. Kormanyos, V. Zolymi, J. Park, and D. C. Ralph, Breaking of valley degeneracy by magnetic field in monolayer MoSe₂, Phys. Rev. Lett. 114, 037401 (2015)

[25] G. Aivazian, Z. Gong, A. M. Jones, R. L. Chu, J. Yan, D. G. Mandrus, C. W. Zhang, D. Cobden, W. Yao, and X. Xu, Magnetic control of valley pseudospin in monolayer WSe₂, Nat. Phys. 11, 141 (2015)

[26] A. Srivastava, M. Sidler, A. V. Allain, D. S. Lembke, A. Kis, and A. Imamoğlu, Valley Zeeman effect in elementary optical excitations of monolayer WSe₂, Nat. Phys. 11(2), 141 (2015)

[27] J. S. Qi, X. Li, Q. Niu, and J. Feng, Giant and tunable valley degeneracy splitting in MoTe₂, Phys. Rev. B 92(12), 121403 (2015)

[28] Z. F. Liu, W. X. Feng, H. L. Xin, Y. L. Gao, P. F. Liu, Y. G. Yao, H. M. Weng, and J. J. Zhao, Two-dimensional spin–valley-coupled Dirac semimetals in functionalized SbAs monolayers, Mater. Horiz. 6(4), 781 (2019)

[29] F. V. Tikhonenko, D. W. Horsell, R. V. Gorbachev, and A. K. Savchenko, Weak localization in graphene flakes, Phys. Rev. Lett. 100(5), 056802 (2008)

[30] M. N. Baibich, J. M. Broto, A. Fert, F. N. Van Dau, F. Petroff, P. Etienne, G. Creuzet, A. Friederich, and J. Chazelas, Giant magnetoresistance of (001)Fe/(001)Cr magnetic superlattices, Phys. Rev. Lett. 61(21), 2472 (1988)

[31] S. Datta and B. Das, Electronic analog of the electronoptic modulator, Appl. Phys. Lett. 56(7), 665 (1990)

[32] A. Rycerz, J. Tworzydło, and C. W. J. Beenakker, Valley filter and valley valve in graphene, Nat. Phys. 3(3), 172 (2007)

[33] X. D. Xu, W. Yao, D. Xiao, and T. F. Heinz, Spin and pseudospins in transition metal dichalcogenides, Nat. Phys. 10, 343 (2014)

[34] A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81(1), 109 (2009)

[35] H. M. Dong, S. D. Guo, Y. F. Duan, F. Huang, W. Xu, and J. Zhang, Electronic and optical properties of singlelayer MoS₂, Front. Phys. 13(4), 137307 (2018)

[36] G. Y. Wu, N. Y. Lue, and Y. C. Chen, Quantum manipulation of valleys in bilayer graphene, Phys. Rev. B 88(12), 125422 (2013)

[37] L. Majidi and R. Asgari, Valley- and spin-switch effects in molybdenum disulfide superconducting spin valve, Phys. Rev. B 90(16), 165440 (2014)

[38] P. M. Krstajić, P. Vasilopoulos, and M. Tahir, Spin- and valley-polarized transport through ferromagnetic and antiferromagnetic barriers on monolayer MoS₂, Physica E 75, 317 (2016)

[39] R. P. Arnaud, Velocity-modulation control of electronwave propagation in graphene, Phys. Rev. B 81, 073407 (2010)

[40] A. Concha and Z. Tešanović, Effect of a velocity barrier on the ballistic transport of Dirac fermions, Phys. Rev. B 82(3), 033413 (2010)

[41] P. M. Krstaji and P. Vasilopoulos, Ballistic transport through graphene nanostructures of velocity and potential barriers, J. Phys.: Condes. Matter 23, 135302 (2011)

[42] Y. Wang, Y. Liu, and B. Wang, Resonant tunneling and enhanced Goos–Hänchen shift in a graphene double velocity barrier structure, Physica E 53, 186 (2013)

[43] J. L. Zhang, W. Fu, K.Y. Wang, S.S. Ke, and H.F. Lü, Effect of a velocity barrier on the spin- and valley-dependent transport in ferromagnetic silicene, Physica B 525, 16 (2017)

[44] X. J. Qiu, Q. Lv, and Z. Z. Cao, Velocity barriercontrolled of spin-valley polarized transport in monolayer WSe₂ Junction, Superlattices Microstruct. 449, 117 (2018)

[45] C. H. Park, L. Yang, Y. W. Son, M. L. Cohen, and S. G. Louie, Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials, Nat. Phys. 4(3), 213 (2008)

[46] M. Gibertini, A. Singha, V. Pellegrini, M. Polini, G. Vignale, A. Pinczuk, L. N. Pfeiffer, and K. W. West, Engineering artificial graphene in a two-dimensional electron gas, Phys. Rev. B 79(24), 241406 (2009)

[47] A. Bostwick, T. Ohta, T. Seyller, K. Horn, and E. Rotenberg, Quasiparticle dynamics in graphene, Nat. Phys. 3(1), 36 (2007)

[48] C. Jang, S. Adam, J. H. Chen, E. D. Williams, S. Das Sarma, and M. S. Fuhrer, Tuning the effective fine structure constant in graphene: Opposing effects of dielectric screening on short- and long-range potential scattering, Phys. Rev. Lett. 101(14), 146805 (2008)

[49] X. Li, F. Zhang, and Q. Niu, Unconventional quantum Hall effect and tunable spin Hall effect in MoS₂ trilayers, Phys. Rev. Lett. 110, 066803 (2013)

[50] M. Tahir and U. Schwingenschlögl, Tunable thermoelectricity in monolayers of MoS₂ and other group-VI dichalcogenides, New J. Phys. 16(11), 115003 (2014)

[51] Z. Li and J. P. Carbotte, Longitudinal and spin-valley Hall optical conductivity in single layer MoS₂, Phys. Rev. B 86(20), 205425 (2012)

[52] M. Büttiker, Four-terminal phase-coherent conductance, Phys. Rev. Lett. 57, 1761 (1986)

RIGHTS & PERMISSIONS

2020 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature