Nano Research

, Volume 11, Issue 3, pp 1541–1553 | Cite as

Tunable electron and phonon properties of folded single-layer molybdenum disulfide

  • Jie Peng
  • Peter W. ChungEmail author
  • Madan Dubey
  • Raju R. Namburu
Research Article


A unique feature of transition metal dichalcogenides is their single-layer form, which enables folding. Although folding has been found to significantly affect the photoluminescence spectrum and some in-plane properties, only limited insight has been gained on how to modulate those properties. In this report, we examine the structure of folds of a single sheet of MoS2 and the dependence of the ground-state electronic and phonon transport properties on the wrapping length. As the folded structure is effectively a bilayer that terminates in a loop, the wrapping length modulates the relative size of the bilayer region to the closed loop along the edge. A combination of computational methods, including approaches based on variational mechanics, classical potentials, and density functional theory, are employed. Highly accurate calculations of the reference folded structure are first carried out to show that the folded structure is largely insensitive to the wrapping length. The folded structures are subsequently used to estimate the electronic band gap, which is found to vary significantly as a function of the wrapping length, and converges from below to the limit value corresponding to an infinite bilayer. The gap values range from 0.43 to 1.09 eV, with a crossover to an indirect gap, which suggests that the transitions must be lattice-assisted, similar to the transitions in the bilayer and bulk forms. However, the phonons, while affected by the formation of the folded structure, are insensitive to the wrapping length. In fact, the overall thermal transport behavior along the folding axis is unchanged. The possibility of modulating the gap value while keeping the thermal properties unchanged opens up new exciting avenues for further applications of this emerging material.


molybdenum disulfide folded structure electronic band structure thermal conductivity phonon 


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J. P. and P. W. C. gratefully acknowledge ARO support under Award W911NF-14-1-0330. Portions of this work were performed through support from the Center for Engineering Concepts Development and the Department of Mechanical Engineering at the University of Maryland, and the Army Research Laboratory Open Campus Initiative through the Oak Ridge Institute for Science and Education supported by the Computational Sciences Division of the Computational and Information Sciences Directorate and hosted by the RF-Division of the Sensors and Electron Devices Directorate. M. D. and R. R. N. acknowledge support of the U.S. Army Research Laboratory Director’s Strategic Initiative program on interfaces in stacked 2D atomic layered materials. Supercomputing resources, made available in part from the University of Maryland (, are gratefully acknowledged.


  1. [1]
    Kadantsev, E. S.; Hawrylak, P. Electronic structure of a single MoS2 monolayer. Solid State Commun. 2012, 152, 909–913.CrossRefGoogle Scholar
  2. [2]
    Radisavljevic, B.; Radenovic, A.; Brivio, J.; Giacometti, I. V.; Kis, A. Single-layer MoS2 transistors. Nat. Nanotechnol. 2011, 6, 147–150.CrossRefGoogle Scholar
  3. [3]
    Jin, Z. L.; Liao, Q. W.; Fang, H. S.; Liu, Z. C.; Liu, W.; Ding, Z. D.; Luo, T. F.; Yang, N. A revisit to high thermoelectric performance of single-layer MoS2. Sci. Rep. 2014, 5, 18342.CrossRefGoogle Scholar
  4. [4]
    Crowne, F. J.; Amani, M.; Birdwell, A. G.; Chin, M. L.; O’Regan, T. P.; Najmaei, S.; Liu, Z.; Ajayan, P. M.; Lou, J.; Dubey, M. Blueshift of the A-exciton peak in folded monolayer 1H-MoS2. Phys. Rev. B 2013, 88, 235302.CrossRefGoogle Scholar
  5. [5]
    Castellanos-Gomez, A.; van der Zant, H. S.; Steele, G. A. Folded MoS2 layers with reduced interlayer coupling. Nano Res. 2014, 7, 572–578.CrossRefGoogle Scholar
  6. [6]
    Jiang, T.; Liu, H. R.; Huang, D.; Zhang, S.; Li, Y. G.; Gong, X. G.; Shen, Y. R.; Liu, W. T.; Wu, S. W. Valley and band structure engineering of folded MoS2 bilayers. Nat Nanotechnol. 2014, 9, 825–829.CrossRefGoogle Scholar
  7. [7]
    Huang, S. X.; Ling, X.; Liang, L. B.; Kong, J.; Terrones, H.; Meunier, V.; Dresselhaus, M. S. Probing the interlayer coupling of twisted bilayer MoS2 using photoluminescence spectroscopy. Nano Lett. 2014, 14, 5500–5508.CrossRefGoogle Scholar
  8. [8]
    Conley, H. J.; Wang, B.; Ziegler, J. I.; Haglund Jr, R. F.; Pantelides, S. T.; Bolotin, K. I. Bandgap engineering of strained monolayer and bilayer MoS2. Nano Lett. 2013, 13, 3626–3630.CrossRefGoogle Scholar
  9. [9]
    Johari, P.; Shenoy, V. B. Tuning the electronic properties of semiconducting transition metal dichalcogenides by applying mechanical strains. ACS Nano. 2012, 6, 5449–5456.CrossRefGoogle Scholar
  10. [10]
    Koskinen, P.; Fampiou, I.; Ramasubramaniam, A. Densityfunctional tight-binding simulations of curvature-controlled layer decoupling and band-gap tuning in bilayer MoS2. Phys. Rev. Lett. 2014, 112, 186802.CrossRefGoogle Scholar
  11. [11]
    Yan, R. S.; Simpson, J. R.; Bertolazzi, S.; Brivio, J.; Watson, M.; Wu, X. F.; Kis, A.; Luo, T. F.; Walker, A. R. H.; Xing, H. G. Thermal conductivity of monolayer molybdenum disulfide obtained from temperature-dependent Raman spectroscopy. ACS Nano. 2014, 8, 986–993.CrossRefGoogle Scholar
  12. [12]
    Peng, B.; Zhang, H.; Shao, H. Z.; Xu, Y. C.; Zhang, X. C.; Zhu, H. Y. Thermal conductivity of monolayer MoS2, MoSe2, and WS2: Interplay of mass effect, interatomic bonding and anharmonicity. RSC Adv. 2016, 6, 5767–5773.CrossRefGoogle Scholar
  13. [13]
    Su, J.; Liu, Z. T.; Feng, L. P.; Li, N. Effect of temperature on thermal properties of monolayer MoS2 sheet. J. Alloy. Compd. 2015, 622, 777–782.CrossRefGoogle Scholar
  14. [14]
    Cai, Y. Q.; Lan, J. H.; Zhang, G.; Zhang, Y. W. Lattice vibrational modes and phonon thermal conductivity of monolayer MoS2. Phys. Rev. B 2014, 89, 035438.CrossRefGoogle Scholar
  15. [15]
    Wei, X. L.; Wang, Y. C.; Shen, Y. L.; Xie, G. F.; Xiao, H. P.; Zhong, J. X.; Zhang, G. Phonon thermal conductivity of monolayer MoS2: A comparison with single layer graphene. Appl. Phys. Lett. 2014, 105, 103902.CrossRefGoogle Scholar
  16. [16]
    Wang, C. X.; Zhang, C.; Jiang, J. W.; Rabczuk, T. A coarsegrained simulation for the folding of molybdenum disulphide. J. Phys. D: Appl. Phys. 2016, 49, 025302.CrossRefGoogle Scholar
  17. [17]
    Ding, Z. W.; Pei, Q. X.; Jiang, J. W.; Zhang, Y. W. Manipulating the thermal conductivity of monolayer MoS2 via lattice defect and strain engineering. J. Phys. Chem. C 2015, 119, 16358–16365.CrossRefGoogle Scholar
  18. [18]
    Mak, K. F.; Lee, C.; Hone, J.; Shan, J.; Heinz, T. F. Atomically thin MoS2: A new direct-gap semiconductor. Phys. Rev. Lett. 2010, 105, 136805.CrossRefGoogle Scholar
  19. [19]
    Lebègue, S.; Eriksson, O. Electronic structure of twodimensional crystals from ab initio theory. Phys. Rev. B 2009, 79, 115409.CrossRefGoogle Scholar
  20. [20]
    Splendiani, A.; Sun, L.; Zhang, Y. B.; Li, T. S.; Kim, J.; Chim, C. Y.; Galli, G.; Wang, F. Emerging photoluminescence in monolayer MoS2. Nano Lett. 2010, 10, 1271–1275.CrossRefGoogle Scholar
  21. [21]
    Gu, X. K.; Li, B. W.; Yang, R. G. Layer thickness-dependent phonon properties and thermal conductivity of MoS2. J. Appl. Phys. 2016, 119, 085106.CrossRefGoogle Scholar
  22. [22]
    Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1–19.CrossRefGoogle Scholar
  23. [23]
    Gale, J. D. GULP: A computer program for the symmetryadapted simulation of solids. J. Chem. Soc. Faraday Trans. 1997, 93, 629–637.CrossRefGoogle Scholar
  24. [24]
    Jiang, J. W.; Park, H. S.; Rabczuk, T. Molecular dynamics simulations of single-layer molybdenum disulphide (MoS2): Stillinger-weber parametrization, mechanical properties, and thermal conductivity. J. Appl. Phys. 2013, 114, 064307.CrossRefGoogle Scholar
  25. [25]
    Liang, T.; Phillpot, S. R.; Sinnott, S. B. Parametrization of a reactive many-body potential for Mo–S systems. Phys. Rev. B 2009, 79, 245110.CrossRefGoogle Scholar
  26. [26]
    Giannozzi, P.; Baroni, S.; Bonini, N.; Calandra, M.; Car, R.; Cavazzoni, C.; Ceresoli, D.; Chiarotti, G. L.; Cococcioni, M.; Dabo, I. et al. QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. J. Phys.: Condens. Matter 2009, 21, 395502.Google Scholar
  27. [27]
    Grimme, S. Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J. Comput. Chem. 2006, 27, 1787–1799.CrossRefGoogle Scholar
  28. [28]
    Cox, B. J.; Baowan, D.; Bacsa, W.; Hill, J. M. Relating elasticity and graphene folding conformation. RSC Adv. 2015, 5, 57515–57520.CrossRefGoogle Scholar
  29. [29]
    Jiang, J. W.; Qi, Z. N.; Park, H. S.; Rabczuk, T. Elastic bending modulus of single-layer molybdenum disulfide (MoS2): Finite thickness effect. Nanotechnology 2013, 24, 435705.CrossRefGoogle Scholar
  30. [30]
    Xiong, S.; Cao, G. X. Bending response of single layer MoS2. Nanotechnology 2016, 27, 105701.CrossRefGoogle Scholar
  31. [31]
    Böker, T.; Severin, R.; Müller, A.; Janowitz, C.; Manzke, R.; Voß, D.; Krüger, P.; Mazur, A.; Pollmann, J. Band structure of MoS2, MoSe2, and α-MoTe2: Angle-resolved photoelectron spectroscopy and ab initio calculations. Phys. Rev. B 2001, 64, 235305.CrossRefGoogle Scholar
  32. [32]
    Shi, H. L.; Pan, H.; Zhang, Y. W.; Yakobson, B. I. Quasiparticle band structures and optical properties of strained monolayer MoS2 and WS2. Phys. Rev. B 2013, 87, 155304.CrossRefGoogle Scholar
  33. [33]
    Ahmad, S.; Mukherjee, S. A comparative study of electronic properties of bulk MoS2 and its monolayer using DFT technique: Application of mechanical strain on MoS2 monolayer. Graphene 2014, 3, 50633.CrossRefGoogle Scholar
  34. [34]
    Liu, Q. H.; Li, L. Z.; Li, Y.; Gao, Z.; Chen, Z.; Lu, J. Tuning electronic structure of bilayer MoS2 by vertical electric field: A first-principles investigation. J. Phys. Chem. C 2012, 116, 21556–21562.CrossRefGoogle Scholar
  35. [35]
    Kuc, A.; Zibouche, N.; Heine, T. Influence of quantum confinement on the electronic structure of the transition metal sulfide TS2. Phys. Rev. B 2011, 83, 245213.CrossRefGoogle Scholar
  36. [36]
    Sahoo, S.; Gaur, A. P. S.; Ahmadi, M.; Guinel, M. J. F.; Katiyar, R. S. Temperature-dependent Raman studies and thermal conductivity of few-layer MoS2. J. Phys.Chem. C 2013, 117, 9042–9047.CrossRefGoogle Scholar
  37. [37]
    McLaren, R. C. Thermal conductivity anisotropy in molybdenum disulfide thin films. Ph.D. Dissertation, University of Illinois at Urbana, Champaign, USA, 2009.Google Scholar
  38. [38]
    Kim, J. Y.; Choi, S. M.; Seo, W. S.; Cho, W. S. Thermal and electronic properties of exfoliated metal chalcogenides. Bull. Korean Chem.Soc. 2010, 31, 3225–3227.CrossRefGoogle Scholar
  39. [39]
    Liu, J.; Choi, G. M.; Cahill, D. G. Measurement of the anisotropic thermal conductivity of molybdenum disulfide by the time-resolved magneto-optic kerr effect. J. Appl. Phys. 2014, 116, 233107.CrossRefGoogle Scholar
  40. [40]
    Muratore, C.; Varshney, V.; Gengler, J. J.; Hu, J. J.; Bultman, J. E.; Roy, A. K.; Farmer, B. L.; Voevodin, A. A. Thermal anisotropy in nano-crystalline MoS2 thin films. Phys. Chem. Chem. Phys. 2014, 16, 1008–1014.CrossRefGoogle Scholar
  41. [41]
    Zhang, X.; Sun, D. Z.; Li, Y. L.; Lee, G. H.; Cui, X.; Chenet, D.; You, Y. M.; Heinz, T. F.; Hone, J. C. Measurement of lateral and interfacial thermal conductivity of single-and bilayer MoS2 and MoSe2 using refined optothermal raman technique. ACS Appl. Mater. Interfaces 2015, 7, 25923–25929.CrossRefGoogle Scholar
  42. [42]
    Gandi, A. N.; Schwingenschlögl, U. Thermal conductivity of bulk and monolayer MoS2. EPL (Europhys. Lett.) 2016, 113, 36002.CrossRefGoogle Scholar
  43. [43]
    Li, W.; Carrete, J.; Mingo, N. Thermal conductivity and phonon linewidths of monolayer MoS2 from first principles. Appl.Phys. Lett. 2013, 103, 253103.CrossRefGoogle Scholar
  44. [44]
    Liu, X. J.; Zhang, G.; Pei, Q. X.; Zhang, Y. W. Phonon thermal conductivity of monolayer MoS2 sheet and nanoribbons. Appl. Phys. Lett. 2013, 103, 133113.CrossRefGoogle Scholar

Copyright information

© Tsinghua University Press and Springer-Verlag GmbH Germany 2018

Authors and Affiliations

  • Jie Peng
    • 1
  • Peter W. Chung
    • 1
    Email author
  • Madan Dubey
    • 2
  • Raju R. Namburu
    • 3
  1. 1.Department of Mechanical EngineeringUniversity of MarylandCollege ParkUSA
  2. 2.Sensors & Electron Devices DirectorateU.S. Army Research LaboratoryAdelphiUSA
  3. 3.Computational & Information Sciences DirectorateU.S. Army Research LaboratoryAberdeen Proving GroundUSA

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