Comptes Rendus
Exciton–polarons in two-dimensional semiconductors and the Tavis–Cummings model
Comptes Rendus. Physique, Volume 22 (2021) no. S4, pp. 89-96.

The elementary optical excitations of a two-dimensional electron or hole system have been identified as exciton-Fermi-polarons. Nevertheless, the connection between the bound state of an exciton and an electron, termed trion, and exciton–polarons is subject of ongoing debate. Here, we use an analogy to the Tavis–Cummings model of quantum optics to show that an exciton–polaron can be understood as a hybrid quasiparticle—a coherent superposition of a bare exciton in an unperturbed Fermi sea and a bright collective excitation of many trions. The analogy is valid to the extent that the Chevy Ansatz provides a good description of dynamical screening of excitons and provided the Fermi energy is much smaller than the trion binding energy. We anticipate our results to bring new insight that could help to explain the striking differences between absorption and emission spectra of two-dimensional semiconductors.

Les excitations optiques élémentaires d’un système bidimensionnel d’électrons ou de trous ont été identifiées comme des exciton-Fermi-polarons. Néanmoins, la connexion entre l’état lié d’un exciton et d’un électron, appelé trion, et les exciton–polarons fait l’objet d’un débat permanent. Ici, nous utilisons une analogie avec le modèle de Tavis–Cummings de l’optique quantique pour montrer qu’un exciton–polaron peut être compris comme une quasi-particule hybride — une superposition cohérente d’un exciton nu dans une mer de Fermi non perturbée et une excitation collective brillante de nombreux trions. L’analogie est valable dans la mesure où l’Ansatz de Chevy fournit une bonne description de l’écrantage dynamique des excitons et à condition que l’énergie de Fermi soit beaucoup plus petite que l’énergie de liaison des trions. Nous espérons que nos résultats apporteront de nouvelles connaissances qui pourraient aider à expliquer les différences frappantes entre les spectres d’absorption et d’émission des semi-conducteurs bidimensionnels.

Online First:
Published online:
DOI: 10.5802/crphys.47
Keywords: Exciton–polarons, Two-dimensional semiconductors, Tavis–Cummings model, Quantum optics, Many-body physics
Mot clés : Exciton–polarons, Semi-conducteurs bidimensionnels, Modèle de Tavis–Cummings, Optique quantique, Physique des corps multiples
Atac Imamoglu 1; Ovidiu Cotlet 1; Richard Schmidt 2, 3

1 Institute for Quantum Electronics, ETH Zürich, CH-8093 Zürich, Switzerland
2 Max Planck Institute of Quantum Optics, 85748 Garching, Germany
3 Munich Center for Quantum Science and Technology, Schellingstrasse 4, 80799 Münich, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
     author = {Atac Imamoglu and Ovidiu Cotlet and Richard Schmidt},
     title = {Exciton{\textendash}polarons in two-dimensional semiconductors and the {Tavis{\textendash}Cummings} model},
     journal = {Comptes Rendus. Physique},
     pages = {89--96},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {22},
     number = {S4},
     year = {2021},
     doi = {10.5802/crphys.47},
     language = {en},
AU  - Atac Imamoglu
AU  - Ovidiu Cotlet
AU  - Richard Schmidt
TI  - Exciton–polarons in two-dimensional semiconductors and the Tavis–Cummings model
JO  - Comptes Rendus. Physique
PY  - 2021
SP  - 89
EP  - 96
VL  - 22
IS  - S4
PB  - Académie des sciences, Paris
DO  - 10.5802/crphys.47
LA  - en
ID  - CRPHYS_2021__22_S4_89_0
ER  - 
%0 Journal Article
%A Atac Imamoglu
%A Ovidiu Cotlet
%A Richard Schmidt
%T Exciton–polarons in two-dimensional semiconductors and the Tavis–Cummings model
%J Comptes Rendus. Physique
%D 2021
%P 89-96
%V 22
%N S4
%I Académie des sciences, Paris
%R 10.5802/crphys.47
%G en
%F CRPHYS_2021__22_S4_89_0
Atac Imamoglu; Ovidiu Cotlet; Richard Schmidt. Exciton–polarons in two-dimensional semiconductors and the Tavis–Cummings model. Comptes Rendus. Physique, Volume 22 (2021) no. S4, pp. 89-96. doi : 10.5802/crphys.47.

[1] X. Xu; W. Yao; D. Xiao; T. F. Heinz Spin and pseudospins in layered transition metal dichalcogenides, Nat. Phys., Volume 10 (2014), pp. 343-350 | DOI

[2] J. R. Schaibley; H. Yu; G. Clark; P. Rivera; J. S. Ross; K. L. Seyler; W. Yao; X. Xu Valleytronics in 2d materials, Nat. Rev. Mater., Volume 1 (2016), 16055

[3] G. Wang; A. Chernikov; M. M. Glazov; T. F. Heinz; X. Marie; T. Amand; B. Urbaszek Colloquium: Excitons in atomically thin transition metal dichalcogenides, Rev. Mod. Phys., Volume 90 (2018), 021001 | DOI | MR

[4] P. Back; S. Zeytinoglu; A. Ijaz; M. Kroner; A. Imamoglu Realization of an electrically tunable narrow-bandwidth atomically thin mirror using monolayer MoSe 2 , Phys. Rev. Lett., Volume 120 (2018), 037401 | DOI

[5] G. Scuri; Y. Zhou; A. A. High; D. S. Wild; C. Shu; K. De Greve; L. A. Jauregui; T. Taniguchi; K. Watanabe; P. Kim; M. D. Lukin; H. Park Large excitonic reflectivity of monolayer MoSe 2 encapsulated in hexagonal boron nitride, Phys. Rev. Lett., Volume 120 (2018), 037402 | DOI

[6] R. A Suris Correlation between trion and hole in Fermi distribution in process of trion photo-excitation in doped QWs, Optical Properties of 2D Systems with Interacting Electrons, Springer, 2003, pp. 111-124 | DOI

[7] M. Sidler; P. Back; O. Cotlet; A. Srivastava; T. Fink; M. Kroner; E. Demler; A. Imamoglu Fermi polaron-polaritons in charge-tunable atomically thin semiconductors, Nat. Phys., Volume 13 (2016) no. 10, pp. 255-261

[8] D. K. Efimkin; A. H. MacDonald Many-body theory of trion absorption features in two-dimensional semiconductors, Phys. Rev. B, Volume 95 (2017), 035417

[9] G. V. Astakhov; V. P. Kochereshko; D. R. Yakovlev; W. Ossau; J. Nürnberger; W. Faschinger; G. Landwehr Oscillator strength of trion states in ZnSe-based quantum wells, Phys. Rev. B, Volume 62 (2000), pp. 10345-10352 | DOI

[10] A. Esser; R. Zimmermann; E. Runge Theory of trion spectra in semiconductor nanostructures, Phys. Status Solidi (b), Volume 227 (2001) no. 2, pp. 317-330 | DOI

[11] G. V. Astakhov; V. P. Kochereshko; D. R. Yakovlev; W. Ossau; J. Nürnberger; W. Faschinger; G. Landwehr; T. Wojtowicz; G. Karczewski; J. Kossut Optical method for the determination of carrier density in modulation-doped quantum wells, Phys. Rev. B, Volume 65 (2002), 115310

[12] M. Tavis; F. W. Cummings Exact solution for an n-molecule—radiation-field Hamiltonian, Phys. Rev., Volume 170 (1968), pp. 379-384 | DOI

[13] C. Fey; Peter Schmelcher; A. Imamoglu; R. Schmidt Theory of exciton-electron scattering in atomically thin semiconductors, Phys. Rev. B, Volume 101 (2020), 195417

[14] R. Combescot; S. Giraud Normal state of highly polarized Fermi gases: Full many-body treatment, Phys. Rev. Lett., Volume 101 (2008), 050404 | DOI

[15] C. Trefzger; Y. Castin Impurity in a Fermi sea on a narrow feshbach resonance: A variational study of the polaronic and dimeronic branches, Phys. Rev. A, Volume 85 (2012), 053612 | DOI

[16] F. Chevy Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations, Phys. Rev. A, Volume 74 (2006), 063628 | DOI

[17] R. Schmidt; T. Enss; V. Pietilä; E. Demler Fermi polarons in two dimensions, Phys. Rev. A, Volume 85 (2012), 021602 | DOI

[18] O. Cotleţ; F. Pientka; R. Schmidt; G. Zarand; E. Demler; A. Imamoglu Transport of neutral optical excitations using electric fields, Phys. Rev. X, Volume 9 (2019), 041019

[19] M. Punk; P. T. Dumitrescu; W. Zwerger Polaron-to-molecule transition in a strongly imbalanced Fermi gas, Phys. Rev. A, Volume 80 (2009) no. 5, 053605 | DOI

[20] M. M. Parish Polaron-molecule transitions in a two-dimensional Fermi gas, Phys. Rev. A, Volume 83 (2011), 051603

[21] M. M. Parish; J. Levinsen Highly polarized Fermi gases in two dimensions, Phys. Rev. A, Volume 87 (2013), 033616

[22] P. Kroiss; L. Pollet Diagrammatic Monte Carlo study of quasi-two-dimensional Fermi polarons, Phys. Rev. B, Volume 90 (2014), 104510 | DOI

[23] J. Vlietinck; J. Ryckebusch; K. Van Houcke Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions, Phys. Rev. B, Volume 89 (2014), 085119 | DOI

[24] M. M. Glazov Optical properties of charged excitons in two-dimensional crystals (2020) (

[25] R. Combescot; A. Recati; C. Lobo; F. Chevy Normal state of highly polarized Fermi gases: Simple many-body approaches, Phys. Rev. Lett., Volume 98 (2007), 180402 | DOI

Cited by Sources:

Articles of potential interest

Tuning absorption and emission in monolayer semiconductors: a brief survey

Lei Ren; Cédric Robert; Bernhard Urbaszek; ...

C. R. Phys (2021)

Single- and narrow-line photoluminescence in a boron nitride-supported MoSe 2 /graphene heterostructure

Luis Enrique Parra López; Loïc Moczko; Joanna Wolff; ...

C. R. Phys (2021)

Hyperspectral study of the coupling between trions in WSe 2 monolayers to a circular Bragg grating cavity

Oliver Iff; Marcelo Davanco; Simon Betzold; ...

C. R. Phys (2021)