Frenkel-like Wannier-Mott excitons in few-layer PbI2

Toulouse, Alexis S.; Isaacoff, Benjamin P.; Shi, Guangsha; Matuchová, Marie; Kioupakis, Emmanouil; Merlin, Roberto

doi:10.1103/PhysRevB.91.165308

Frenkel-like Wannier-Mott excitons in few-layer $Pb I_{2}$

Journal Article · Wed Apr 15 00:00:00 EDT 2015 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PhysRevB.91.165308· OSTI ID:1370080

Toulouse, Alexis S. ^[1]; Isaacoff, Benjamin P. ^[1]; Shi, Guangsha ^[1]; Matuchová, Marie ^[2]; Kioupakis, Emmanouil ^[1]; Merlin, Roberto ^[1]

Univ. of Michigan, Ann Arbor, MI (United States)
Inst. of Chemical Technology Prague (Czech Republic)

Optical measurements and first-principles calculations of the band structure and exciton states in direct-gap bulk and few-layer PbI₂ indicate that the n = 1 exciton is Frenkel-like in nature in that its energy exhibits a weak dependence on thickness down to atomic-length scales. Results reveal large increases in the gap and exciton binding energy with a decreasing number of layers and a transition of the fundamental gap, which becomes indirect for one and two monolayers. Calculated values are in reasonable agreement with a particle-in-a-box model relying on the Wannier-Mott theory of exciton formation. In conclusion, general arguments and existing data suggest that the Frenkel-like character of the lowest exciton is a universal feature of wide-gap layered semiconductors whose effective masses and dielectric constants give bulk Bohr radii that are on the order of the layer spacing.

View Accepted Manuscript (DOE)

Research Organization:: Energy Frontier Research Centers (EFRC) (United States). Center for Solar and Thermal Energy Conversion (CSTEC)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); NSF

Grant/Contract Number:: SC0000957; AC02-05CH11231

OSTI ID:: 1370080

Alternate ID(s):: OSTI ID: 1178611

Journal Information:: Physical Review. B, Condensed Matter and Materials Physics, Journal Name: Physical Review. B, Condensed Matter and Materials Physics Journal Issue: 16 Vol. 91; ISSN 1098-0121; ISSN PRBMDO

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (37)

Polytypism and Lattice Vibrations of PbI2 Grisel, A.; Schmid, Ph. physica status solidi (b), Vol. 73, Issue 2 https://doi.org/10.1002/pssb.2220730225	journal	February 1976
Electrical, optical and structural properties of lead iodide Matuchova, Marie; Zdansky, Karel; Zavadil, Jiri Journal of Materials Science: Materials in Electronics, Vol. 20, Issue 3 https://doi.org/10.1007/s10854-008-9831-x	journal	December 2008
The exciton spectrum of lead iodide Tubbs, M. R.; Forty, A. J. Journal of Physics and Chemistry of Solids, Vol. 26, Issue 4 https://doi.org/10.1016/0022-3697(65)90023-5	journal	April 1965
The exciton spectrum of lead iodide Tubbs, M. R.; Forty, A. J. Solid State Communications, Vol. 3, Issue 2 https://doi.org/10.1016/0038-1098(65)90081-5	journal	February 1965
Band-edge photoluminescence of PbI2 Lévy, F.; Mercier, A.; Voitchovsky, J. -P. Solid State Communications, Vol. 15, Issue 5 https://doi.org/10.1016/0038-1098(74)90671-1	journal	September 1974
BerkeleyGW: A massively parallel computer package for the calculation of the quasiparticle and optical properties of materials and nanostructures Deslippe, Jack; Samsonidze, Georgy; Strubbe, David A. Computer Physics Communications, Vol. 183, Issue 6 https://doi.org/10.1016/j.cpc.2011.12.006	journal	June 2012
Synthesis of Few-Layer GaSe Nanosheets for High Performance Photodetectors Hu, PingAn; Wen, Zhenzhong; Wang, Lifeng ACS Nano, Vol. 6, Issue 7 https://doi.org/10.1021/nn300889c	journal	June 2012
Evolution of Electronic Structure in Atomically Thin Sheets of WS ₂ and WSe ₂ Zhao, Weijie; Ghorannevis, Zohreh; Chu, Leiqiang ACS Nano, Vol. 7, Issue 1 https://doi.org/10.1021/nn305275h	journal	December 2012
Monolayer behaviour in bulk ReS2 due to electronic and vibrational decoupling Tongay, Sefaattin; Sahin, Hasan; Ko, Changhyun Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms4252	journal	February 2014
The rise of graphene Geim, A. K.; Novoselov, K. S. Nature Materials, Vol. 6, Issue 3, p. 183-191 https://doi.org/10.1038/nmat1849	journal	March 2007
Two-dimensional atomic crystals Novoselov, K. S.; Jiang, D.; Schedin, F. Proceedings of the National Academy of Sciences, Vol. 102, Issue 30, p. 10451-10453 https://doi.org/10.1073/pnas.0502848102	journal	July 2005
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502 https://doi.org/10.1088/0953-8984/21/39/395502	journal	September 2009
Excitonic Effects in the Electroreflectance of Lead Iodide Gähwiller, Ch.; Harbeke, G. Physical Review, Vol. 185, Issue 3 https://doi.org/10.1103/PhysRev.185.1141	journal	September 1969
Excitons in molybdenum disulphide Fortin, Emery; Raga, Francesco Physical Review B, Vol. 11, Issue 2 https://doi.org/10.1103/PhysRevB.11.905	journal	January 1975
Multiphonon processes in YbS Merlin, R.; Güntherodt, G.; Humphreys, R. Physical Review B, Vol. 17, Issue 12 https://doi.org/10.1103/PhysRevB.17.4951	journal	June 1978
Self-interaction correction to density-functional approximations for many-electron systems Perdew, J. P.; Zunger, Alex Physical Review B, Vol. 23, Issue 10, p. 5048-5079 https://doi.org/10.1103/PhysRevB.23.5048	journal	May 1981
Exciton binding energy in quantum wells Bastard, G.; Mendez, E. E.; Chang, L. L. Physical Review B, Vol. 26, Issue 4 https://doi.org/10.1103/PhysRevB.26.1974	journal	August 1982
Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies Hybertsen, Mark S.; Louie, Steven G. Physical Review B, Vol. 34, Issue 8, p. 5390-5413 https://doi.org/10.1103/PhysRevB.34.5390	journal	October 1986
Magnetoabsorption spectra of band-edge excitons in 2 H - PbI 2 at high magnetic fields up to 40 T Nagamune, Y.; Takeyama, S.; Miura, N. Physical Review B, Vol. 40, Issue 11 https://doi.org/10.1103/PhysRevB.40.8099	journal	October 1989
Electron-hole excitations and optical spectra from first principles Rohlfing, Michael; Louie, Steven G. Physical Review B, Vol. 62, Issue 8 https://doi.org/10.1103/PhysRevB.62.4927	journal	August 2000
Quasiparticle electronic structure of bismuth telluride in the G W approximation Kioupakis, Emmanouil; Tiago, Murilo L.; Louie, Steven G. Physical Review B, Vol. 82, Issue 24 https://doi.org/10.1103/PhysRevB.82.245203	journal	December 2010
Exciton character in picene molecular solids Roth, Friedrich; Mahns, Benjamin; Büchner, Bernd Physical Review B, Vol. 83, Issue 16 https://doi.org/10.1103/PhysRevB.83.165436	journal	April 2011
Effects of confinement and environment on the electronic structure and exciton binding energy of MoS 2 from first principles Komsa, Hannu-Pekka; Krasheninnikov, Arkady V. Physical Review B, Vol. 86, Issue 24 https://doi.org/10.1103/PhysRevB.86.241201	journal	December 2012
Electronic structure and optical properties of Pb I 2 Schlüter, I. Ch.; Schlüter, M. Physical Review B, Vol. 9, Issue 4 https://doi.org/10.1103/PhysRevB.9.1652	journal	February 1974
Atomically Thin MoS2 A New Direct-Gap Semiconductor Mak, Kin Fai; Lee, Changgu; Hone, James Physical Review Letters, Vol. 105, Issue 13, Article No.136805 https://doi.org/10.1103/PhysRevLett.105.136805	journal	September 2010
Phonon-Assisted Optical Absorption in Silicon from First Principles Noffsinger, Jesse; Kioupakis, Emmanouil; Van de Walle, Chris G. Physical Review Letters, Vol. 108, Issue 16 https://doi.org/10.1103/PhysRevLett.108.167402	journal	April 2012
Exciton Binding Energy and Nonhydrogenic Rydberg Series in Monolayer WS 2 Chernikov, Alexey; Berkelbach, Timothy C.; Hill, Heather M. Physical Review Letters, Vol. 113, Issue 7 https://doi.org/10.1103/PhysRevLett.113.076802	journal	August 2014
Band-Edge Excitons in Pb I 2 : A Puzzle? Harbeke, G.; Tosatti, E. Physical Review Letters, Vol. 28, Issue 24 https://doi.org/10.1103/PhysRevLett.28.1567	journal	June 1972
Electronic excitations: density-functional versus many-body Green’s-function approaches Onida, Giovanni; Reining, Lucia; Rubio, Angel Reviews of Modern Physics, Vol. 74, Issue 2 https://doi.org/10.1103/RevModPhys.74.601	journal	June 2002
Maximally localized Wannier functions: Theory and applications Marzari, Nicola; Mostofi, Arash A.; Yates, Jonathan R. Reviews of Modern Physics, Vol. 84, Issue 4 https://doi.org/10.1103/RevModPhys.84.1419	journal	October 2012
Two-Dimensional Analog to the Hydrogen Atom Zaslow, B.; Zandler, Melvin E. American Journal of Physics, Vol. 35, Issue 12 https://doi.org/10.1119/1.1973790	journal	December 1967
The rise of graphene Rodgers, Peter; Geim, A. K.; Novoselov, K. S. Nanoscience and Technology: A Collection of Reviews from Nature Journals, p. 11-19 https://doi.org/10.1142/9789814287005_0002	book	August 2009
Exciton character in picene molecular solids Roth, Friedrich; Mahns, Benjamin; Büchner, Bernd arXiv https://doi.org/10.48550/arxiv.1103.3935	text	January 2011
Maximally localized Wannier functions: Theory and applications Marzari, Nicola; Mostofi, Arash A.; Yates, Jonathan R. arXiv https://doi.org/10.48550/arxiv.1112.5411	text	January 2011
Phonon-assisted optical absorption in silicon from first principles Noffsinger, Jesse; Kioupakis, Emmanouil; Van de Walle, Chris G. arXiv https://doi.org/10.48550/arxiv.1202.3454	text	January 2012
Evolution of Electronic Structure in Atomically Thin Sheets of WS2 and WSe2 Zhao, Weijie; Ghorannevis, Zohreh; Chua, Leiqiang arXiv https://doi.org/10.48550/arxiv.1212.5415	text	January 2012
Two Dimensional Atomic Crystals Novoselov, K. S.; Jiang, D.; Booth, T. arXiv https://doi.org/10.48550/arxiv.cond-mat/0503533	text	January 2005

Cited By (10)

Near-Infrared Photoresponse of One-Sided Abrupt MAPbI ₃ /TiO ₂ Heterojunction through a Tunneling Process Yan, Keyou; Wei, Zhanhua; Zhang, Tiankai Advanced Functional Materials, Vol. 26, Issue 46 https://doi.org/10.1002/adfm.201602736	journal	October 2016
Band Structure Engineering of Interfacial Semiconductors Based on Atomically Thin Lead Iodide Crystals Sun, Yan; Zhou, Zishu; Huang, Zhen Advanced Materials, Vol. 31, Issue 17 https://doi.org/10.1002/adma.201806562	journal	March 2019
Anisotropic temperature-dependence of optical phonons in layered PbI ₂ Zhang, Zhaojun; Zheng, Wei; Wang, Weiliang Journal of Raman Spectroscopy, Vol. 49, Issue 4 https://doi.org/10.1002/jrs.5341	journal	February 2018
Low Threshold Fabry-Pérot Mode Lasing from Lead Iodide Trapezoidal Nanoplatelets Zhong, Yangguang; Wei, Qi; Liu, Zhen Small, Vol. 14, Issue 35 https://doi.org/10.1002/smll.201801938	journal	July 2018
Large-scale 2D PbI ₂ monolayers: experimental realization and their indirect band-gap related properties Zhong, Mianzeng; Zhang, Shuai; Huang, Le Nanoscale, Vol. 9, Issue 11 https://doi.org/10.1039/c6nr07924e	journal	January 2017
Single layer PbI ₂ : hydrogenation-driven reconstructions Bacaksiz, C.; Sahin, H. RSC Advances, Vol. 6, Issue 92 https://doi.org/10.1039/c6ra15020a	journal	January 2016
Single-layer metal halides MX ₂ (X = Cl, Br, I): stability and tunable magnetism from first principles and Monte Carlo simulations Kulish, Vadym V.; Huang, Wei Journal of Materials Chemistry C, Vol. 5, Issue 34 https://doi.org/10.1039/c7tc02664a	journal	January 2017
Monitoring the electronic, thermal and optical properties of two-dimensional MoO ₂ under strain via vibrational spectroscopies: a first-principles investigation Ersan, Fatih; Sarikurt, Sevil Physical Chemistry Chemical Physics, Vol. 21, Issue 36 https://doi.org/10.1039/c9cp04183d	journal	January 2019
Perseverance of direct bandgap in multilayer 2D PbI ₂ under an experimental strain up to 7.69% Du, Lena; Wang, Cong; Xiong, Wenqi 2D Materials, Vol. 6, Issue 2 https://doi.org/10.1088/2053-1583/ab01eb	journal	February 2019
Electronic and vibrational properties of PbI 2 : From bulk to monolayer Yagmurcukardes, M.; Peeters, F. M.; Sahin, H. Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/physrevb.98.085431	journal	August 2018