Journal of Materials Science

, Volume 53, Issue 22, pp 15541–15548 | Cite as

Energy-loss function for monolayer phosphorene

  • Hieu T. Nguyen-Truong


We calculate the energy-loss function for monolayer phosphorene in the framework of time-dependent density functional theory. The calculations are performed in the adiabatic local density approximation with local field effects. We study the origin of the features in the absorption spectra and the energy dispersion of the features in the excitation spectra. The energy dispersions show a strong directional dependence. At vanishing momentum transfer, the excitation spectra are dominated by a plasmon peak at 10.5 eV. At finite momentum transfer, the plasmon dispersion can be described by the layer electron gas model.



This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 103.01-2015.02.


  1. 1.
    Li L, Yu Y, Ye GJ, Ge Q, Ou X, Wu H, Feng D, Chen XH, Zhang Y (2014) Black phosphorus field-effect transistors. Nat Nano 9(5):372–377CrossRefGoogle Scholar
  2. 2.
    Liu H, Neal AT, Zhu Z, Luo Z, Xu X, Tománek D, Ye PD (2014) Phosphorene: an unexplored 2D semiconductor with a high hole mobility. ACS Nano 8(4):4033–4041CrossRefGoogle Scholar
  3. 3.
    Qiao J, Kong X, Hu ZX, Yang F, Ji W (2014) High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus. Nat Commun 5:4475CrossRefGoogle Scholar
  4. 4.
    Liu Q, Zhang X, Abdalla LB, Fazzio A, Zunger A (2015) Switching a normal insulator into a topological insulator via electric field with application to phosphorene. Nano Lett 15(2):1222–1228CrossRefGoogle Scholar
  5. 5.
    Fei R, Faghaninia A, Soklaski R, Yan JA, Lo C, Yang L (2014) Enhanced thermoelectric efficiency via orthogonal electrical and thermal conductances in phosphorene. Nano Lett 14(11):6393–6399CrossRefGoogle Scholar
  6. 6.
    Lu W, Nan H, Hong J, Chen Y, Zhu C, Liang Z, Ma X, Ni Z, Jin C, Zhang Z (2014) Plasma-assisted fabrication of monolayer phosphorene and its Raman characterization. Nano Res 7(6):853–859CrossRefGoogle Scholar
  7. 7.
    Pei J, Gai X, Yang J, Wang X, Yu Z, Choi DY, Luther-Davies B, Lu Y (2016) Producing air-stable monolayers of phosphorene and their defect engineering. Nat Commun 7:10450CrossRefGoogle Scholar
  8. 8.
    Guan J, Zhu Z, Tománek D (2014) Phase coexistence and metal-insulator transition in few-layer phosphorene: a computational study. Phys Rev Lett 113(4):046804CrossRefGoogle Scholar
  9. 9.
    Zhu Z, Tománek D (2014) Semiconducting layered blue phosphorus: a computational study. Phys Rev Lett 112(17):176802CrossRefGoogle Scholar
  10. 10.
    Wu M, Fu H, Zhou L, Yao K, Zeng XC (2015) Nine new phosphorene polymorphs with non-honeycomb structures: a much extended family. Nano Lett 15(5):3557–3562CrossRefGoogle Scholar
  11. 11.
    Schuster R, Trinckauf J, Habenicht C, Knupfer M, Büchner B (2015) Anisotropic particle-hole excitations in black phosphorus. Phys Rev Lett 115(2):026404CrossRefGoogle Scholar
  12. 12.
    Yang J, Xu R, Pei J, Myint YW, Wang F, Wang Z, Zhang S, Yu Z, Lu Y (2015) Optical tuning of exciton and trion emissions in monolayer phosphorene. Light Sci Appl 4:e312CrossRefGoogle Scholar
  13. 13.
    Li L, Kim J, Jin C, Ye GJ, Qiu DY, da Jornada FH, Shi Z, Chen L, Zhang Z, Yang F, Watanabe K, Taniguchi T, Ren W, Louie SG, Chen XH, Zhang Y, Wang F (2016) Direct observation of the layer-dependent electronic structure in phosphorene. Nat Nanotechnol 12:21–25CrossRefGoogle Scholar
  14. 14.
    Akhtar M, Anderson G, Zhao R, Alruqi A, Mroczkowska JE, Sumanasekera G, Jasinski JB (2017) Recent advances in synthesis, properties, and applications of phosphorene, npj 2D Mater Appl 1(1):5CrossRefGoogle Scholar
  15. 15.
    Zare M, Rameshti BZ, Ghamsari FG, Asgari R (2017) Thermoelectric transport in monolayer phosphorene. Phys Rev B 95(4):045422CrossRefGoogle Scholar
  16. 16.
    Ong ZY, Cai Y, Zhang G, Zhang YW (2014) Strong thermal transport anisotropy and strain modulation in single-layer phosphorene. J Phys Chem C 118(43):25272–25277CrossRefGoogle Scholar
  17. 17.
    Tran V, Soklaski R, Liang Y, Yang L (2014) Layer-controlled band gap and anisotropic excitons in few-layer black phosphorus. Phys Rev B 89(23):235319CrossRefGoogle Scholar
  18. 18.
    Wei Q, Peng X (2014) Superior mechanical flexibility of phosphorene and few-layer black phosphorus. Appl Phys Lett 104(25):251915CrossRefGoogle Scholar
  19. 19.
    Wang X, Jones AM, Seyler KL, Tran V, Jia Y, Zhao H, Wang H, Yang L, Xu X, Xia F (2015) Highly anisotropic and robust excitons in monolayer black phosphorus. Nat Nano 10(6):517–521CrossRefGoogle Scholar
  20. 20.
    Ghosh B, Kumar P, Thakur A, Chauhan YS, Bhowmick S, Agarwal A (2017) Anisotropic plasmons, excitons, and electron energy loss spectroscopy of phosphorene. Phys Rev B 96(3):035422CrossRefGoogle Scholar
  21. 21.
    Cocchi C, Draxl C (2015) Optical spectra from molecules to crystals: Insight from many-body perturbation theory. Phys Rev B 92(20):205126CrossRefGoogle Scholar
  22. 22.
    Nguyen-Truong HT (2016) Low-energy electron inelastic mean free path in materials. Appl Phys Lett 108(17):172901CrossRefGoogle Scholar
  23. 23.
    Nguyen-Truong HT (2017) Electron inelastic mean free path at energies below 100 eV. J Phys Condens Matter 29(21):215501CrossRefGoogle Scholar
  24. 24.
    Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I, Dal Corso A, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen AP, Smogunov A, Umari P, Wentzcovitch RM (2009) QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J Phys Condens Matter 21(39):395502CrossRefGoogle Scholar
  25. 25.
    Giannozzi P, Andreussi O, Brumme T, Bunau O, Nardelli MB, Calandra M, Car R, Cavazzoni C, Ceresoli D, Cococcioni M, Colonna N, Carnimeo I, Corso AD, de Gironcoli S, Delugas P, Jr RAD, Ferretti A, Floris A, Fratesi G, Fugallo G, Gebauer R, Gerstmann U, Giustino F, Gorni T, Jia J, Kawamura M, Ko HY, Kokalj A, Küçükbenli E, Lazzeri M, Marsili M, Marzari N, Mauri F, Nguyen NL, Nguyen HV, Otero-de-la Roza A, Paulatto L, Poncé S, Rocca D, Sabatini R, Santra B, Schlipf M, Seitsonen AP, Smogunov A, Timrov I, Thonhauser T, Umari P, Vast N, Wu X, Baroni S (2017) Advanced capabilities for materials modelling with QUANTUM ESPRESSO. J Phys Condens Matter 29(46):465901CrossRefGoogle Scholar
  26. 26.
    Perdew JP, Ruzsinszky A, Csonka GI, Vydrov OA, Scuseria GE, Constantin LA, Zhou X, Burke K (2008) Restoring the density-gradient expansion for exchange in solids and surfaces. Phys Rev Lett 100(13):136406CrossRefGoogle Scholar
  27. 27.
    Rappe AM, Rabe KM, Kaxiras E, Joannopoulos JD (1990) Optimized pseudopotentials. Phys Rev B 41(2):1227–1230CrossRefGoogle Scholar
  28. 28.
    Hultgren R, Gingrich NS, Warren BE (1935) The atomic distribution in red and black phosphorus and the crystal structure of black phosphorus. J Chem Phys 3(6):351–355CrossRefGoogle Scholar
  29. 29.
    Gulans A, Kontur S, Meisenbichler C, Nabok D, Pavone P, Rigamonti S, Sagmeister S, Werner U, Draxl C (2014) EXCITING: a full-potential all-electron package implementing density-functional theory and many-body perturbation theory. J Phys Condens Matter 26(36):363202CrossRefGoogle Scholar
  30. 30.
    Mahabal MS, Deshpande MD, Hussain T, Ahuja R (2016) Sensing characteristics of phosphorene monolayers toward PH3 and AsH3 gases upon the introduction of vacancy defects. J Phys Chem C 120(36):20428–20436CrossRefGoogle Scholar
  31. 31.
    Vienna ab initio simulation package (VASP) (1999) Technische Universitat WienGoogle Scholar
  32. 32.
    Ferreira F, Ribeiro RM (2017) Improvements in the \(GW\) and Bethe–Salpeter-equation calculations on phosphorene. Phys Rev B 96(11):115431CrossRefGoogle Scholar
  33. 33.
    Mohan B, Thakur R, Ahluwalia PK (2016) Electronic energy loss spectra from mono-layer to few layers of phosphorene. In: AIP Conf Proc, vol 731, no 1. p 50026Google Scholar
  34. 34.
    Soler JM, Artacho E, Gale JD, García A, Junquera J, Ordejón P, Sánchez-Portal D (2002) The SIESTA method for ab initio order-\(N\) materials simulation. J Phys Condens Matter 14(11):2745–2779CrossRefGoogle Scholar
  35. 35.
    Shiles E, Sasaki T, Inokuti M, Smith DY (1980) Self-consistency and sum-rule tests in the Kramers-Kronig analysis of optical data: applications to aluminum. Phys Rev B 22(4):1612–1628CrossRefGoogle Scholar
  36. 36.
    Fetter AL (1974) Electrodynamics of a layered electron gas. II. Periodic array. Ann Phys (NY) 88(1):1–25CrossRefGoogle Scholar
  37. 37.
    Olego D, Pinczuk A, Gossard AC, Wiegmann W (1982) Plasma dispersion in a layered electron gas: a determination in GaAs-(AlGa) As heterostructures. Phys Rev B 25(12):7867–7870CrossRefGoogle Scholar
  38. 38.
    Allen SJ, Tsui DC, Logan RA (1977) Observation of the two-dimensional plasmon in silicon inversion layers. Phys Rev Lett 38(17):980–983CrossRefGoogle Scholar
  39. 39.
    Nagao T, Hildebrandt T, Henzler M, Hasegawa S (2001) Dispersion and damping of a two-dimensional plasmon in a metallic surface-state band. Phys Rev Lett 86(25):5747–5750CrossRefGoogle Scholar
  40. 40.
    Raether H (1980) Excitation of plasmons and interband transitions by electrons. Springer, BerlinGoogle Scholar
  41. 41.
    Wang YY, Cheng SC, Dravid VP, Zhang FC (1995) Momentum-transfer resolved electron energy loss spectroscopy of solids: problems, solutions and applications. Ultramicroscopy 59(1):109–119CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Theoretical Physics Research Group, Advanced Institute of Materials ScienceTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Applied SciencesTon Duc Thang UniversityHo Chi Minh CityVietnam

Personalised recommendations