Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:cond-mat/0603219 · Physical Review Letters

Validity of the Franck-Condon Principle in the Optical Spectroscopy: Optical Conductivity of the Fröhlich Polaron

G. De Filippis, V. Cataudella, Andrei S. Mishchenko, C. A. Perroni, J. T. Devreese

Published Apr 6, 2006• 46 citations
arXivHTMLPDF

Abstract

The optical absorption of the Fröhlich polaron model is obtained by an approximation-free diagrammatic Monte Carlo method and compared with two new approximate approaches that treat lattice relaxation effects in different ways. We show that: (i) a strong coupling expansion, based on the Franck-Condon principle, well describes the optical conductivity for large coupling strengths (alpha > 10); (ii) a memory function formalism with phonon broadened levels reproduces the optical response for weak coupling strengths (alpha < 6) taking the dynamic lattice relaxation into account. In the coupling regime 6 < alpha < 10, the optical conductivity is a rapidly changing superposition of both Franck-Condon and dynamic contributions.

DOI
10.1103/physrevlett.96.136405

Related papers

All-coupling polaron optical response: Analytic approaches beyond the adiabatic approximation

Serghei N. Klimin, Jacques Tempere, J. T. Devreese

In the present work, the problem of an all-coupling analytic description for the optical conductivity of the Fr\"ohlich polaron is treated, with the goal being to bridge the gap in the validity range that exists between two complementary methods: on the one hand, the memory-function formalism and, on the other hand, the strong-coupling expansion based on the Franck-Condon picture for the polaron response. At intermediate coupling, both methods were found to fail as they do not reproduce diagrammatic quantum Monte Carlo results. To resolve this, we modify the memory-function formalism with respect to the Feynman-Hellwarth-Iddings-Platzman approach in order to take into account a nonquadratic interaction in a model system for the polaron. The strong-coupling expansion is extended beyond the adiabatic approximation by including in the treatment nonadiabatic transitions between excited polaron states. The polaron optical conductivity that we obtain at $T=0$ by combining the two extended methods agrees well, both qualitatively and quantitatively, with the diagrammatic quantum Monte Carlo results in the whole available range of the electron-phonon coupling strength.

arXiv:1606.00605•Physical review. B./Physical review. B•Sep 22, 2016•8 citations

Optical conductivity of polarons: Double phonon cloudconcept verified by diagrammatic Monte Carlo simulations

G. De Filippis, V. Cataudella, Andrei S. Mishchenko +1 more

We study theoretically a fundamental issue in solids: the evolution of the optical spectra of polaron as the electron-phonon coupling increases. By comparing the exact results obtained by the diagrammatic Monte Carlo method and the data obtained through exact diagonalization within an appropriate subspace of the phononic wavefunctions, the physical nature of the crossover from weak to strong coupling is revealed. The optical spectra are well understood by the quantum mechanical superposition of states with light and heavy phonon clouds corresponding to large and small polarons, respectively. It is also found that the strong coupling Franck-Condon regime is not accessible at realistic values of the coupling constant.

arXiv:1111.5253•Physical Review B•Mar 9, 2012•27 citations

Optical Conductivity of the Fröhlich Polaron

Andrei S. Mishchenko, Naoto Nagaosa, Nikolay V. Prokof'ev +2 more

We present accurate results for optical conductivity of the three dimensional Fröhlich polaron in all coupling regimes. The systematic-error free diagrammatic quantum Monte Carlo method is employed where the Feynman graphs for the momentum-momentum correlation function in imaginary time are summed up. The real-frequency optical conductivity is obtained by the analytic continuation with stochastic optimization. We compare numerical data with available perturbative and nonperturbative approaches to the optical conductivity and show that the picture of sharp resonances due to relaxed excited states in the strong-coupling regime is "washed out" by large broadening of these states. As a result, the spectrum contains only a single-maximum broad peak with peculiar shape and a shoulder.

arXiv:cond-mat/0312111•Physical Review Letters•Dec 3, 2003•70 citations

Optical Absorption of Polarons in the Feynman-Hellwarth-Iddings-Platzman Approximation

J. T. Devreese, J. DE SITTER, Marc J. Goovaerts

The optical absorption of polarons at rest at zero temperature is calculated starting from the Feynman-Hellwarth-Iddings-Platzman (FHIP) theory of the impedance. The results are compared with the results of theories whose physical interpretation is clearer [weak-coupling theory of Gurevich, Lang, and Firsov (GLF) and product-ansatz strong-coupling theory of Kartheuser, Evrard, and Devreese (KED)] in order to obtain a better understanding of the FHIP approximation. We are particularly interested in the possible role of lattice relaxation [leading to relaxed excited states (RES)] in the optical absorption process. If the FHIP perturbation method were used to expand the conductivity (this would be the normal procedure), essentially Franck-Condon transitions would be found in the spectrum, and lattice relaxation would be absent. In this case the results do not fit with the product ansatz and provide merely the asymptotic limit $\ensuremath{\alpha}\ensuremath{\rightarrow}0$, where $\ensuremath{\alpha}$ is the electron-phonon coupling constant. If, however, the impedance function rather than the conductivity is expanded (as preferred by FHIP for intuitive reasons, without further justification) more reliable results for the optical absorption appear. For $\ensuremath{\alpha}>5$, intense absorption peaks now occur, which presumably correspond to transitions to RES, and the results are in qualitative agreement with the predictions of the product-ansatz treatment in this coupling region. Also in the limit $\ensuremath{\alpha}\ensuremath{\rightarrow}0$ the correct behavior is found. For $3\ensuremath{\lesssim}\ensuremath{\alpha}\ensuremath{\lesssim}5$, the interpretation of the results is somewhat delicate but the possibility that RES contribute to the oscillator strength as soon as $\ensuremath{\alpha}>3$ should be considered. The results so obtained for the optical absorption seem reliable at all $\ensuremath{\alpha}$. This provides an indirect justification for the expansion of $Z(\ensuremath{\Omega})$ rather than $\frac{1}{Z(\ensuremath{\Omega})}$ in FHIP theory and a confirmation of the qualitative strong-coupling predictions of KED. The present study indicates that optical absorption peaks due to free polarons should be observable experimentally in crystals for which $\ensuremath{\alpha}>1$.

Physical review. B, Solid state•Mar 15, 1972•138 citations

Optical conductivity of a strong-coupling Fröhlich polaron

Serghei N. Klimin, J. T. Devreese

The polaron optical conductivity at zero temperature is derived within the strong-coupling approximation accounting for internal nonadiabaticity. The polaron optical conductivity spectrum is provided by the multiphonon optical transitions. The polaron optical conductivity spectra calculated within our analytic strong-coupling approach and the numerically accurate diagrammatic quantum Monte Carlo (DQMC) data are in a good agreement with each other at large $\ensuremath{\alpha}\ensuremath{\gtrsim}9$.

arXiv:1310.4413•Physical Review B•Jan 3, 2014•7 citations

Polaron physics beyond the Holstein model

D. J. J. Marchand

Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.

•Jan 1, 2011•1 citation
The optical absorption of the Fröhlich polaron model is obtained by an approximation-free diagrammatic Monte Carlo method and compared with two new approximate approaches that treat lattice relaxation effects in different ways. We show that: (i) a strong coupling expansion, based on the Franck-Condon principle, well describes the optical conductivity for large coupling strengths (alpha > 10); (ii) a memory function formalism with phonon broadened levels reproduces the optical response for weak coupling strengths (alpha < 6) taking the dynamic lattice relaxation into account. In the coupling regime 6 < alpha < 10, the optical conductivity is a rapidly changing superposition of both Franck-Condon and dynamic contributions.
In the present work, the problem of an all-coupling analytic description for the optical conductivity of the Fr\"ohlich polaron is treated, with the goal being to bridge the gap in the validity range that exists between two complementary methods: on the one hand, the memory-function formalism and, on the other hand, the strong-coupling expansion based on the Franck-Condon picture for the polaron response. At intermediate coupling, both methods were found to fail as they do not reproduce diagrammatic quantum Monte Carlo results. To resolve this, we modify the memory-function formalism with respect to the Feynman-Hellwarth-Iddings-Platzman approach in order to take into account a nonquadratic interaction in a model system for the polaron. The strong-coupling expansion is extended beyond the adiabatic approximation by including in the treatment nonadiabatic transitions between excited polaron states. The polaron optical conductivity that we obtain at T=0T=0T=0 by combining the two extended methods agrees well, both qualitatively and quantitatively, with the diagrammatic quantum Monte Carlo results in the whole available range of the electron-phonon coupling strength.
We study theoretically a fundamental issue in solids: the evolution of the optical spectra of polaron as the electron-phonon coupling increases. By comparing the exact results obtained by the diagrammatic Monte Carlo method and the data obtained through exact diagonalization within an appropriate subspace of the phononic wavefunctions, the physical nature of the crossover from weak to strong coupling is revealed. The optical spectra are well understood by the quantum mechanical superposition of states with light and heavy phonon clouds corresponding to large and small polarons, respectively. It is also found that the strong coupling Franck-Condon regime is not accessible at realistic values of the coupling constant.
We present accurate results for optical conductivity of the three dimensional Fröhlich polaron in all coupling regimes. The systematic-error free diagrammatic quantum Monte Carlo method is employed where the Feynman graphs for the momentum-momentum correlation function in imaginary time are summed up. The real-frequency optical conductivity is obtained by the analytic continuation with stochastic optimization. We compare numerical data with available perturbative and nonperturbative approaches to the optical conductivity and show that the picture of sharp resonances due to relaxed excited states in the strong-coupling regime is "washed out" by large broadening of these states. As a result, the spectrum contains only a single-maximum broad peak with peculiar shape and a shoulder.
The optical absorption of polarons at rest at zero temperature is calculated starting from the Feynman-Hellwarth-Iddings-Platzman (FHIP) theory of the impedance. The results are compared with the results of theories whose physical interpretation is clearer [weak-coupling theory of Gurevich, Lang, and Firsov (GLF) and product-ansatz strong-coupling theory of Kartheuser, Evrard, and Devreese (KED)] in order to obtain a better understanding of the FHIP approximation. We are particularly interested in the possible role of lattice relaxation [leading to relaxed excited states (RES)] in the optical absorption process. If the FHIP perturbation method were used to expand the conductivity (this would be the normal procedure), essentially Franck-Condon transitions would be found in the spectrum, and lattice relaxation would be absent. In this case the results do not fit with the product ansatz and provide merely the asymptotic limit $\ensuremath{\alpha}\ensuremath{\rightarrow}0$, where $\ensuremath{\alpha}$ is the electron-phonon coupling constant. If, however, the impedance function rather than the conductivity is expanded (as preferred by FHIP for intuitive reasons, without further justification) more reliable results for the optical absorption appear. For $\ensuremath{\alpha}>5$, intense absorption peaks now occur, which presumably correspond to transitions to RES, and the results are in qualitative agreement with the predictions of the product-ansatz treatment in this coupling region. Also in the limit $\ensuremath{\alpha}\ensuremath{\rightarrow}0$ the correct behavior is found. For $3\ensuremath{\lesssim}\ensuremath{\alpha}\ensuremath{\lesssim}5$, the interpretation of the results is somewhat delicate but the possibility that RES contribute to the oscillator strength as soon as $\ensuremath{\alpha}>3$ should be considered. The results so obtained for the optical absorption seem reliable at all $\ensuremath{\alpha}$. This provides an indirect justification for the expansion of $Z(\ensuremath{\Omega})$ rather than $\frac{1}{Z(\ensuremath{\Omega})}$ in FHIP theory and a confirmation of the qualitative strong-coupling predictions of KED. The present study indicates that optical absorption peaks due to free polarons should be observable experimentally in crystals for which $\ensuremath{\alpha}>1$.
The polaron optical conductivity at zero temperature is derived within the strong-coupling approximation accounting for internal nonadiabaticity. The polaron optical conductivity spectrum is provided by the multiphonon optical transitions. The polaron optical conductivity spectra calculated within our analytic strong-coupling approach and the numerically accurate diagrammatic quantum Monte Carlo (DQMC) data are in a good agreement with each other at large $\ensuremath{\alpha}\ensuremath{\gtrsim}9$.
Many condensed matter problems involve a particle coupled to its environment. The polaron, originally introduced to describe electrons in a polarizable medium, describes a particle coupled to a bosonic field. The Holstein polaron model, although simple, including only optical Einstein phonons and an interaction that couples them to the electron density, captures almost all of the standard polaronic properties. We herein investigate polarons that differ significantly from this behaviour. We study a model with phonon-modulated hopping, and find a radically different behaviour at strong couplings. We report a sharp transition, not a crossover, with a diverging effective mass at the critical coupling. We also look at a model with acoustic phonons, away from the perturbative limit, and again discover unusual polaron properties. Our work relies on the Bold Diagrammatic Monte Carlo (BDMC) method, which samples Feynman diagrammatic expansions efficiently, even those with weak sign problems. Proposed by Prokof'ev and Svistunov, it is extended to lattice polarons for the first time here. We also use the Momentum Average (MA) approximation, an analytical method proposed by Berciu, and find an excellent agreement with the BDMC results. A novel MA approximation able to treat dispersive phonons is also presented, along with a new exact solution for finite systems, inspired by the same formalism.