Threshold phenomena and bound states in the polaron problem

Levinson, I. B.; Rashba, Emmanuel I.

doi:10.1070/pu1974v016n06abeh004097

Cited by 46 publications

(30 citation statements)

References 4 publications

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“…That is because the standard analytical techniques, based, e.g., on variational approaches [3] or on weakcoupling [4] and strong-coupling adiabatic [2] and nonadiabatic [5,6] perturbation expansions, fail to tackle this complicated many-body problem precisely in the physically most important transition region, where the highly non-linear "self-trapping" process from an essentially delocalized quasi-free charge carrier at weak electronphonon (EP) interaction to a "quasi-localized" small polaron at strong coupling takes place. Note that the same problem arises in strongly coupled exciton-phonon systems as well [7].…”

Section: Introductionmentioning

confidence: 99%

Spectral properties of the 2D Holstein polaron

Fehske

Loos

Wellein

1997

Zeitschrift für Physik B Condensed Matter

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The two-dimensional Holstein model is studied by means of direct Lanczos diagonalization preserving the full dynamics and quantum nature of phonons. We present numerical exact results for the single-particle spectral function, the polaronic quasiparticle weight, and the optical conductivity. The polaron band dispersion is derived both from exact diagonalization of small lattices and analytic calculation of the polaron self-energy.

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Section: Introductionmentioning

confidence: 99%

Spectral properties of the 2D Holstein polaron

Fehske

Loos

Wellein

1997

Zeitschrift für Physik B Condensed Matter

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“…The effect of exciton-phonon coupling is especially strong at resonance, with the formation of hybrid EPCs [7,20]. In our case this resonance situation is realized twice in the range of crystal sizes consideredwhen the distance between the 1S and 1P quantum size levels is equal to the energy of one or two optical phonons.…”

Section: Polaron and Exciton-phonon Complexes In Cucl Nanocrystalsmentioning

confidence: 74%

“…Detailed considerations can be found in the review of Ref. [7]. In NCs the possibility of tuning the crystal size dependent energy level spacing to phonon frequencies opens an opportunity for studying resonant exciton-phonon coupling that is not available in the bulk.…”

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confidence: 99%

Polaron and Exciton-Phonon Complexes in CuCl Nanocrystals

et al. 1995

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We report the first evidence of an excitonic polaron and exciton-phonon complexes in nanosize semiconductor crystals. These are observed in CuC1 nanocrystal excitonic luminescence spectra under resonant size-selective excitation. The theory of exciton coupling with spherical phonons through the Frohlich and deformation potentials is developed and describes both the size dependence of the polaron binding energy and the degree of the exciton-phonon hybridization near resonance, when the 1P and 1S exciton level spacing coincides with the oneor two-phonon energy. PACS numbers: 73.20.Dx, 71.35.+z, 71.38.+i, 78.55.m Progress in the study of electronic excitation spectra in semiconductor nanocrystals (NC) for both the strong and weak confinement regimes [1 -5] has opened the door for studies of electron-phonon coupling there. In bulk the phonon interaction lowers the quasiparticle (electron, hole, exciton) ground state energy through the formation of a polaron [6], manifested as a socalled polaron Stokes shift of the resonant luminescence. Another polaron state is a bound state of the quasiparticle and an almost "real" phonon, called an exciton-phonon complex (EPC). Detailed considerations can be found in the review of Ref. [7]. In NCs the possibility of tuning the crystal size dependent energy level spacing to phonon frequencies opens an opportunity for studying resonant exciton-phonon coupling that is not available in the bulk. Most of the attention in NCs has been given to the experimental and theoretical investigation of electronpolar phonon coupling in the strong confined regime [8][9][10][11]. In the weak confinement regime, where absorption and luminescence are determined by the quantization of the exciton center of mass motion, only one excitonphonon coupling study has been reported [12]. This regime is realized in CuC1 NCs where the size dependence of the 1S exciton ground state energy E» = 6 m /2Ma (where M is the exciton effective mass, and a is the NC radius) has been well verified [4,5].In this Letter we report the first observation of excitonic polaron and EPCs in NCs. They are seen in the photoluminescence (PL) fine structure of CuCl NCs undergoing size-selective excitation. This fine structure exhibits a strong resonance behavior when the distance between the 1P and 1S states of the confined exciton equals the energy of one or two optical phonons. A theory of exciton coupling with spherical phonons through the Frohlich and deformation potentials is described for the first time. Quantitative agreement between theory and experiment allows us to attribute the observed fine structure to the formation of EPCs and the Stokes shift of the luminescence to the formation of a polaron, due to the strong exciton-polar phonon coupling in CuCl NCs.Samples of CuC1 NCs in an oxide glass matrix were grown with mean radii a = 15, 21, and 23 A. as measured by small angle x-ray scattering. PL at 2 K is selectively excited by the second harmonic of a tunable dye laser, pumped by a cw mode-locked YAG laser. Figures 1(a) an...

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“…In this case, the light frequency ! can substantially differ from the frequency of transverse optical phonons where the lattice reflection is important [29,30]. This, in turn, will facilitate the experimental observation of the bound states in graphene.…”

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confidence: 95%

“…2 are depicted in a gauge-invariant diagrammatic technique (details about this technique can be found in the Supplemental Material [35] and in Refs. [30,36]). The filled and open squares correspond to the exact, AE n; 0 n 0 ð"jq; q 0 Þ, and the bare, h n; 0 n 0 ð"jq; q 0 Þ, electron-phonon scattering amplitudes, the internal solid and dashed lines to the exact electron and phonon Green functions, G n ð"Þ and Dð!…”

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confidence: 99%

Electron-Phonon Bound States in Graphene in a Perpendicular Magnetic Field

2012

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The spectrum of electron-phonon complexes in monolayer graphene is investigated in the presence of a perpendicular quantizing magnetic field. Despite the small electron-phonon coupling, usual perturbation theory is inapplicable for the calculation of the scattering amplitude near the threshold of optical phonon emission. Our findings, beyond perturbation theory, show that the true spectrum near the phonon-emission threshold is completely governed by new branches, corresponding to bound states of an electron and an optical phonon with a binding energy of the order of αω(0), where α is the electron-phonon coupling and ω(0) the phonon energy.

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Threshold phenomena and bound states in the polaron problem

Cited by 46 publications

References 4 publications

Spectral properties of the 2D Holstein polaron

Spectral properties of the 2D Holstein polaron

Polaron and Exciton-Phonon Complexes in CuCl Nanocrystals

Electron-Phonon Bound States in Graphene in a Perpendicular Magnetic Field

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