Journal of Computational Electronics

, Volume 16, Issue 3, pp 568–575 | Cite as

Tunable electronic properties of multilayer phosphorene and its nanoribbons



We study the effects of a vertical electric field on the electronic band structure and transport in multilayer phosphorene and its nanoribbons. In phosphorene, at a critical value of the vertical electric field (\(E_\mathrm{c}\)), the band gap closes and the band structure undergoes a massive-to-massless Dirac fermion transition along the armchair direction. This transition is observable in quantum Hall measurements, as the power-law dependence of the Landau-level energy on the magnetic field B goes from \({\sim }(n+1/2)B\) below \(E_\mathrm{c}\), to \({\sim }[(n+1/2)B]^{2/3}\) at \(E_\mathrm{c}\), to \({\sim }[(n+1/2)B]^{1/2}\) above \(E_\mathrm{c}\). In multilayer phosphorene nanoribbons (PNRs), the vertical electric field can be employed to manipulate the midgap energy bands that are associated with edge states, thereby giving rise to new device functionalities. We propose a dual-edge-gate PNR structure that works as a quantum switch.


Phosphorene Edge states NEGF 



The work was primarily supported by the NSF (DMR-1121288) through the University of Wisconsin Materials Research Science and Engineering Center (MRSEC) seed project. After the end of the NSF seed support, funding by the University of Wisconsin-Madison through the Patricia and Michael Splinter Professorship in Electrical and Computer Engineering (awarded to I.K.) enabled successful completion of this work. The work was performed using the resources of the UW-Madison Center for High Throughput Computing (CHTC).


  1. 1.
    Lu, W., et al.: Plasma-assisted fabrication of monolayer phosphorene and its raman characterization. Nano Res. 7(6), 853 (2014)CrossRefGoogle Scholar
  2. 2.
    Liu, H., et al.: Phosphorene: an unexplored 2d semiconductor with a high hole mobility. ACS Nano 8(4), 4033 (2014)CrossRefGoogle Scholar
  3. 3.
    Zhang, S., et al.: Extraordinary photoluminescence and strong temperature/angle-dependent raman responses in few-layer phosphorene. ACS Nano 8(9), 9590 (2014)CrossRefGoogle Scholar
  4. 4.
    Tran, V., et al.: Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Phys. Rev. B 89(23), 235319 (2014)CrossRefGoogle Scholar
  5. 5.
    Jing, Y., et al.: Small molecules make big differences: molecular doping effects on electronic and optical properties of phosphorene. Nanotechnology 26(9), 095201 (2015)CrossRefGoogle Scholar
  6. 6.
    Buscema, M., et al.: Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors. Nano. Lett. 14(6), 3347 (2014)CrossRefGoogle Scholar
  7. 7.
    Koenig, S .P., et al.: Electric field effect in ultrathin black phosphorus. Appl. Phys. Lett. 104(10), 103106 (2014)CrossRefGoogle Scholar
  8. 8.
    Xia, F., Wang, H., Jia, Y.: Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics. Nat. Commun. 5, 4458 (2014)Google Scholar
  9. 9.
    Çakır, D., Sevik, C., Peeters, F.M.: Significant effect of stacking on the electronic and optical properties of few-layer black phosphorus. Phys. Rev. B 92(16), 165406 (2015)CrossRefGoogle Scholar
  10. 10.
    Çakır, D., Sahin, H., Peeters, F.M.: Tuning of the electronic and optical properties of single-layer black phosphorus by strain. Phys. Rev. B 90(20), 205421 (2014)CrossRefGoogle Scholar
  11. 11.
    Fei, R., Yang, L.: Strain-engineering the anisotropic electrical conductance of few-layer black phosphorus. Nano Lett. 14(5), 2884 (2014)CrossRefGoogle Scholar
  12. 12.
    Fei, R., et al.: Enhanced thermoelectric efficiency via orthogonal electrical and thermal conductances in phosphorene. Nano Lett. 14(11), 6393 (2014)CrossRefGoogle Scholar
  13. 13.
    Yuan, S., Rudenko, A., Katsnelson, M.: Transport and optical properties of single-and bilayer black phosphorus with defects. Phys. Rev. B 91(11), 115436 (2015)CrossRefGoogle Scholar
  14. 14.
    Qin, G., et al.: Anisotropic intrinsic lattice thermal conductivity of phosphorene from first principles. Phys. Chem. Chem. Phys. 17(7), 4854 (2015)CrossRefGoogle Scholar
  15. 15.
    Cai, Y., et al.: Giant phononic anisotropy and unusual anharmonicity of phosphorene: interlayer coupling and strain engineering. Adv. Funct. Mater. 25(15), 2230 (2015)CrossRefGoogle Scholar
  16. 16.
    Low, T., et al.: Plasmons and screening in monolayer and multilayer black phosphorus. Phys. Rev. Lett. 113(10), 106802 (2014)CrossRefGoogle Scholar
  17. 17.
    Elahi, M., et al.: Modulation of electronic and mechanical properties of phosphorene through strain. Phys. Rev. B 91(11), 115412 (2015)CrossRefGoogle Scholar
  18. 18.
    Das, S., et al.: Tunable transport gap in phosphorene. Nano Lett. 14(10), 5733 (2014)CrossRefGoogle Scholar
  19. 19.
    Kim, J., et al.: Observation of tunable band gap and anisotropic dirac semimetal state in black phosphorus. Science 349(6249), 723 (2015)CrossRefGoogle Scholar
  20. 20.
    Dutreix, C., Stepanov, E., Katsnelson, M.: Laser-induced topological transitions in phosphorene with inversion symmetry. Phys. Rev. B 93(24), 241404 (2016)CrossRefGoogle Scholar
  21. 21.
    Liu, Q., et al.: Switching a normal insulator into a topological insulator via electric field with application to phosphorene. Nano Lett. 15(2), 1222 (2015)CrossRefGoogle Scholar
  22. 22.
    Low, T., Jiang, Y., Guinea, F.: Topological currents in black phosphorus with broken inversion symmetry. Phys. Rev. B 92(23), 235447 (2015)CrossRefGoogle Scholar
  23. 23.
    Carvalho, A., Rodin, A., Neto, A.C.: Phosphorene nanoribbons. Europhys. Lett. (EPL) 108(4), 47005 (2014)CrossRefGoogle Scholar
  24. 24.
    Guo, H., et al.: Phosphorene nanoribbons, phosphorus nanotubes, and van der waals multilayers. J. Phys. Chem. C 118(25), 14051 (2014)CrossRefGoogle Scholar
  25. 25.
    Ali, M., Keshtan, M., Esmaeilzadeh, M.: Spin filtering in a magnetized zigzag phosphorene nanoribbon. J. Phys. D Appl. Phys. 48(48), 485301 (2015)CrossRefGoogle Scholar
  26. 26.
    Peng, X., Copple, A., Wei, Q.: Edge effects on the electronic properties of phosphorene nanoribbons. J. Appl. Phys. 116(14), 144301 (2014)CrossRefGoogle Scholar
  27. 27.
    Rudenko, A., Yuan, S., Katsnelson, M.: Toward a realistic description of multilayer black phosphorus: from GW approximation to large-scale tight-binding simulations. Phys. Rev. B 92(8), 085419 (2015)CrossRefGoogle Scholar
  28. 28.
    Rudenko, A.N., Katsnelson, M.I.: Quasiparticle band structure and tight-binding model for single-and bilayer black phosphorus. Phys. Rev. B 89(20), 201408 (2014)CrossRefGoogle Scholar
  29. 29.
    Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, vol. 1. Wiley, New York (1972)Google Scholar
  30. 30.
    Zhou, X., et al.: Landau levels and magneto-transport property of monolayer phosphorene. Sci. Rep. 5, 12295 (2015)CrossRefGoogle Scholar
  31. 31.
    Jr Pereira, J., Katsnelson, M.: Landau levels of single-layer and bilayer phosphorene. Phys. Rev. B 92(7), 075437 (2015)CrossRefGoogle Scholar
  32. 32.
    Ghazaryan, A., Chakraborty, T.: Aspects of anisotropic fractional quantum hall effect in phosphorene. Phys. Rev. B 92(16), 165409 (2015)CrossRefGoogle Scholar
  33. 33.
    Harper, P.G.: Single band motion of conduction electrons in a uniform magnetic field. Proc. Phys. Soc. Lond. Sect. A 68(10), 874 (1955)CrossRefMATHGoogle Scholar
  34. 34.
    Thouless, D., et al.: Quantized hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49(6), 405 (1982)CrossRefGoogle Scholar
  35. 35.
    Wakabayashi, K., et al.: Electronic and magnetic properties of nanographite ribbons. Phys. Rev. B 59(12), 8271 (1999)CrossRefGoogle Scholar
  36. 36.
    Wiegmann, P., Zabrodin, A.: Bethe-ansatz for the Bloch electron in magnetic field. Phys. Rev. Lett. 72(12), 1890 (1994)CrossRefMATHGoogle Scholar
  37. 37.
    Jiang, Z., et al.: Infrared spectroscopy of landau levels of graphene. Phys. Rev. Lett. 98, 197403 (2007)CrossRefGoogle Scholar
  38. 38.
    Yuan, S., et al.: Quantum hall effect and semiconductor-to-semimetal transition in biased black phosphorus. Phys. Rev. B 93(24), 245433 (2016)CrossRefGoogle Scholar
  39. 39.
    Hasegawa, Y., et al.: Zero modes of tight-binding electrons on the honeycomb lattice. Phys. Rev. B 74(3), 033413 (2006)CrossRefGoogle Scholar
  40. 40.
    Dietl, P., Piéchon, F., Montambaux, G.: New magnetic field dependence of landau levels in a graphenelike structure. Phys. Rev. Lett. 100(23), 236405 (2008)CrossRefGoogle Scholar
  41. 41.
    Montambaux, G., et al.: Merging of dirac points in a two-dimensional crystal. Phys. Rev. B 80(15), 153412 (2009)CrossRefGoogle Scholar
  42. 42.
    Montambaux, G., et al.: A universal hamiltonian for motion and merging of dirac points in a two-dimensional crystal. Eur. Phys. J. B 72(4), 509 (2009)CrossRefMATHGoogle Scholar
  43. 43.
    Park, C.-H., Marzari, N.: Berry phase and pseudospin winding number in bilayer graphene. Phys. Rev. B 84(20), 205440 (2011)CrossRefGoogle Scholar
  44. 44.
    Resta, R.: Manifestations of Berry’s phase in molecules and condensed matter. J. Phys. Condens. Matter 12(9), R107 (2000)CrossRefGoogle Scholar
  45. 45.
    Zhang, Y., et al.: Experimental observation of the quantum hall effect and berry’s phase in graphene. Nature 438(7065), 201 (2005)CrossRefGoogle Scholar
  46. 46.
    Ramasubramaniam, A., Muniz, A.R.: Ab initio studies of thermodynamic and electronic properties of phosphorene nanoribbons. Phys. Rev. B 90, 085424 (2014)CrossRefGoogle Scholar
  47. 47.
    Grujić, M.M., et al.: Tunable skewed edges in puckered structures. Phys. Rev. B 93(24), 245413 (2016)CrossRefGoogle Scholar
  48. 48.
    Sisakht, E.T., Zare, M.H., Fazileh, F.: Scaling laws of band gaps of phosphorene nanoribbons: a tight-binding calculation. Phys. Rev. B 91(8), 085409 (2015)CrossRefGoogle Scholar
  49. 49.
    Datta, S.: Electronic Transport in Mesoscopic Systems. Cambridge university press, Cambridge (1997)Google Scholar
  50. 50.
    Sancho, M.P.L., et al.: Highly convergent schemes for the calculation of bulk and surface green functions. J. Phys. F Met. Phys. 15(4), 851 (1985)CrossRefGoogle Scholar
  51. 51.
    Craciun, M., et al.: Trilayer graphene is a semimetal with a gate-tunable band overlap. Nature Nanotechnol. 4(6), 383 (2009)CrossRefGoogle Scholar
  52. 52.
    Williams, J., et al.: Gate-controlled guiding of electrons in graphene. Nature Nanotechnol. 6(4), 222 (2011)CrossRefGoogle Scholar
  53. 53.
    Li, L., et al.: Black phosphorus field-effect transistors. Nature Nanotechnol. 9, 372 (2014)CrossRefGoogle Scholar
  54. 54.
    Ezawa, M.: Topological origin of quasi-flat edge band in phosphorene. New J. Phys. 16(11), 115004 (2014)CrossRefGoogle Scholar
  55. 55.
    Choi, W.Y., et al.: Tunneling field-effect transistors (tfets) with subthreshold swing (ss) less than 60 mv/dec. IEEE Electron Device Lett. 28(8), 743 (2007). ISSN 0741-3106CrossRefGoogle Scholar
  56. 56.
    Lifshitz, I., Kosevich, A.: Theory of magnetic susceptibility in metals at low temperatures. Sov. Phys. JETP 2, 636 (1956)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations