# Translation-Invariant Excitons in a Phonon Field

## Abstract

**:**

## 1. Introduction

## 2. Hamiltonian of an Exciton in a Polar Crystal

## 3. Exciton Ground State in a Polar Crystal in the Case of Weak and Intermediate Electron-Phonon Interaction

## 4. Exciton Ground State in a Polar Crystal in the Case of Strong Electron-Phonon Interaction

## 5. Spectrum of a TI Exciton

## 6. Peculiarities of Light Absorption and Emission by TI Excitons

## 7. Conclusions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Knox, R.S. Theory of Excitons; Academic Press: New York, NY, USA, 1963; p. 207. [Google Scholar]
- Agranovich, V.M. Theory of Excitons; Nauka: Moscow, Russia, 1968; p. 384. (In Russian) [Google Scholar]
- Davydov, A.S. Theory of Molecular Excitons; Springer Science+Business Media: New York, NY, USA, 1971; p. 313. [Google Scholar] [CrossRef]
- Rashba, E.I.; Sturge, M.D. (Eds.) Excitons; North-Holland: Amsterdam, The Netherlands, 1982; p. 865. [Google Scholar]
- Ueta, M.; Kanzaki, H.; Kobayashi, K.; Toyozawa, Y.; Hanamura, E. Excitonic Processes in Solids; Springer Series in Solid-State Sciences V. 60; Springer: Berlin/Heidelberg, Germany, 1986. [Google Scholar] [CrossRef]
- Kuper, C.G.; Whitfield, G.D. (Eds.) Polarons and Excitons; Oliver and Boyd: Edinburgh, UK, 1963. [Google Scholar]
- Devreese, J.T.; Peeters, F. (Eds.) Polarons and Excitons in Polar Semiconductors and Ionic Crystals; Springer Science+Business Media: New York, NY, USA, 1984; p. 471. [Google Scholar] [CrossRef]
- Kogar, A.; Rak, M.S.; Vig, S.; Husain, A.A.; Flicker, F.; Joe, Y.; Venema, L.; MacDougall, G.J.; Chiang, T.C.; Fradkin, E.; et al. Signatures of exciton condensation in a transition metal dichalcogenide. Science
**2017**, 358, 1314–1317. [Google Scholar] [CrossRef] [Green Version] - Aßmann, M.; Bayer, M. Semiconductor Rydberg Physics. Adv. Quantum Technol.
**2020**, 3, 1900134. [Google Scholar] [CrossRef] - Haken, H. Die Theorie des Exzitons im festen Körper. Fortschr. Phys.
**1958**, 6, 271–334. [Google Scholar] [CrossRef] - Bajaj, K.K. Effect of electron-phonon interaction on the binding energy of a Wannier exciton in a polarizable medium. Solid State Commun.
**1974**, 15, 1221–1224. [Google Scholar] [CrossRef] - Pollmann, J.; Büttner, H. Effective Hamiltonians and bindings energies of Wannier excitons in polar semiconductors. Phys. Rev. B
**1977**, 16, 4480. [Google Scholar] [CrossRef] - Lakhno, V.D.; Balabaev, N.K. Self-consistent solutions in the continuous model of F-centers and the problem of relaxed excited states. Opt. Spectrosc.
**1983**, 55, 308–312. [Google Scholar] - Lakhno, V.D. Energy and Critical Ionic-Bond Parameter of a 3D Large-Radius Bipolaron. JETP
**2010**, 110, 811. [Google Scholar] [CrossRef] - Lakhno, V.D. Translation-invariant bipolarons and the problem of high-temperature superconductivity. Sol. State Commun.
**2012**, 152, 621. [Google Scholar] [CrossRef] [Green Version] - Lakhno, V.D. Translation invariant theory of polaron (bipolaron) and the problem of quantizing near the classical solution. JETP
**2013**, 116, 892. [Google Scholar] [CrossRef] [Green Version] - Kashirina, N.I.; Lakhno, V.D.; Tulub, A.V. The Virial Theorem and the Ground State Problem in Polaron Theory. JETP
**2012**, 114, 867. [Google Scholar] [CrossRef] - Lakhno, V.D. Pekar’s ansatz and the strong coupling problem in polaron theory. Phys. Usp.
**2015**, 58, 295. [Google Scholar] [CrossRef] [Green Version] - Lee, T.D.; Low, F.; Pines, D. The motion of electrons in a polar crystal. Phys. Rev.
**1953**, 90, 297. [Google Scholar] [CrossRef] - Gerlach, B.; Luczak, F. Ground-state energy of an exciton-(LO) phonon system in two and three dimensions: General outline and three-dimensional case. Phys. Rev. B
**1996**, 54, 12841. [Google Scholar] [CrossRef] [PubMed] - Gerlach, B.; Kalina, F. Energy spectrum of the optical polaron at finite total momentum. Phys. Rev. B
**1999**, 60, 10886. [Google Scholar] [CrossRef] - Lakhno, V.D. Superconducting Properties of 3D Low-Density Translation-Invariant Bipolaron Gas. Adv. Condens. Matter Phys.
**2018**, 2018, 1380986. [Google Scholar] [CrossRef] [Green Version] - Snoke, D.; Kavoulakis, G.M. Bose-Einstein condensation of excitons in Cu
_{2}O: Progress over 30 years. Rep. Prog. Phys.**2014**, 77, 116501. [Google Scholar] [CrossRef] [Green Version] - Thouin, F.; Valverde-Chávez, D.A.; Quarti, C.; Cortecchia, D.; Bargigia, I.; Beljonne, D.; Petrozza, A.; Silva, C.; Kandada, A.R.S. Phonon coherences reveal the polaronic character of excitons in two-dimensional lead halide perovskites. Nat. Mater.
**2019**, 18, 349–356. [Google Scholar] [CrossRef] [Green Version] - Keldysh, L.V.; Kopaev, Y.V. Possible Instability of Semimetallic State Toward Coulomb Interaction. Sov. Phys. Solid State
**1965**, 6, 2219. [Google Scholar] - Keldysh, L.V.; Kozlov, A.N. Collective Properties of Excitons in Semiconductors. Sov. Phys. JETP
**1968**, 27, 521. [Google Scholar] - Baranowski, M.; Plochocka, P. Excitons in Metal-Halide Perovskites. Adv. Energy Mater.
**2020**, 10, 1903659. [Google Scholar] [CrossRef] - Camargo, F.; Schmidt, R.; Whalen, J.D.; Ding, R.; Woehl, G., Jr.; Yoshida, S.; Burgdörfer, J.; Dunning, F.B.; Sadeghpour, H.R.; Demler, E.; et al. Creation of Rydberg Polarons in a Bose Gas. Phys. Rev. Lett.
**2018**, 120, 083401. [Google Scholar] [CrossRef] [Green Version] - Dykman, I.M.; Pekar, S.I. Excitons in Ionic Crystals. In S.I. Pekar’s Selected Works; Naukova Dumka: Kiev, Russia, 1988. (In Russian) [Google Scholar]
- Dykman, I.M.; Pekar, S.I. Excitons in Ionic Crystals. Tr. Inst. Fiz. Akad. Nauk Ukr. SSR
**1953**, 4, 92. (In Russian) [Google Scholar] - Dykman, I.M.; Pekar, S.I. Excitons in Ionic Crystals. Dokl. Akad. Nauk SSSR
**1952**, 83, 825. (In Russian) [Google Scholar] - Pekar, S.I.; Rashba, E.I.; Sheka, V.I. Free and self-localized Wannier-Mott excitons in ionic crystals and activation energy of their mutual thermal conversion. Sov. Phys. JETP
**1979**, 49, 129. [Google Scholar] - Sumi, A. Phase Diagram of an Exciton in the Phonon Field. J. Phys. Soc. Jpn.
**1977**, 43, 1286–1294. [Google Scholar] [CrossRef] - Shimamura, S.; Matsuura, M. Self-trapping of a wannier exciton in the optical phonon field. Solid State Commun.
**1983**, 48, 857–860. [Google Scholar] [CrossRef] - Song, K.S.; Williams, R.T. Self-Trapped Excitons, 2nd ed.; Springer: Berlin/Heidelberg, Germany, 1996; p. 410. [Google Scholar] [CrossRef]
- Toyozawa, Y. Optical Processes in Solids; Cambridge University Press: Cambridge, UK, 2003; p. 442. Available online: https://www.cambridge.org/9780521556057 (accessed on 4 June 2021).
- Haken, H. Quantenfeldtheorie des Festkörpers; Springer Fachmedien: Wiesbaden, Germany, 1993; p. 322. [Google Scholar] [CrossRef]
- Adamowski, J. Theory of two-electron systems in polar crystals. In Polarons and Applications; Lakhno, V.D., Ed.; Wiley: Leeds, UK, 1994; pp. 183–204. [Google Scholar]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Lakhno, V.D.
Translation-Invariant Excitons in a Phonon Field. *Condens. Matter* **2021**, *6*, 20.
https://doi.org/10.3390/condmat6020020

**AMA Style**

Lakhno VD.
Translation-Invariant Excitons in a Phonon Field. *Condensed Matter*. 2021; 6(2):20.
https://doi.org/10.3390/condmat6020020

**Chicago/Turabian Style**

Lakhno, Victor D.
2021. "Translation-Invariant Excitons in a Phonon Field" *Condensed Matter* 6, no. 2: 20.
https://doi.org/10.3390/condmat6020020