On the LO‐polaron dispersion in <i>D</i> dimensions

Gerlach, B.; Kalina, F.; Smondyrev, M. A.

doi:10.1002/pssb.200301770

Cited by 10 publications

(21 citation statements)

References 34 publications

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“…28,29 reported that their calculations were "numerically exact" and the error bars were smaller than the size of points at the plot. Previously, 15 we criticized these statements, in particular, because the results obtained give the wrong coefficient even in the second order in α for the polaron ground state energy weak-coupling expansion. As we could see above, the correct second order calculations are crucial for the adequate description of the dispersion near the edge point.…”

Section: The 3d Casementioning

confidence: 96%

See 1 more Smart Citation

Upper and lower bounds for the large polaron dispersion in 1, 2, or 3 dimensions

Gerlach

Smondyrev

2008

Phys. Rev. B

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Numerical results for the polaron dispersion are presented for an arbitrary number of space dimensions. Upper and lower bounds are calculated for the dispersion curves. They are rather close to each other in the cases of small electron-phonon couplings usual for real polar materials. To describe the dispersion in other materials, we suggest a simple fitting formula which can be applied at intermediate values of the Fröhlich electron-phonon coupling constant. Its validity is approved by the comparison with direct calculations and previously obtained results. This makes our results not only reliable and highly accurate but also easy reproducible.

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Section: The 3d Casementioning

confidence: 96%

“…The only problem is that the numerical job becomes time consuming and could be done only for the case D = 1 (see Ref. 15 ). To conclude this section we mention a qualitatively different behavior of the dispersion curves for D = 1, 2 and D = 3.…”

Section: Basic Equationsmentioning

confidence: 99%

Upper and lower bounds for the large polaron dispersion in 1, 2, or 3 dimensions

Gerlach

Smondyrev

2008

Phys. Rev. B

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“…Early work on the behavior of the dispersion curve [16,17] allowed one to conclude that the energy-momentum relation starts off quadratically at low k (thus allowing one to define a polaron mass) but bends over when approaching the continuum edge E c (α) = E 0 (0,α) +hω 0 . Later it was found that in 3D the dispersion hits the continuum edge whereas for 2D it approaches it asymptotically, and upper and lower bounds for the dispersion were obtained [18][19][20]. These bounds, as well as some analytically known limits, constitute good benchmarks for any theory of the polaron dispersion.…”

Section: Introductionmentioning

confidence: 95%

Diagrammatic Monte Carlo study of Fröhlich polaron dispersion in two and three dimensions

et al. 2018

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We present results for the solution of the large polaron Fröhlich Hamiltonian in 3 dimensions (3D) and 2 dimensions (2D) obtained via the diagrammatic Monte Carlo (DMC) method. Our implementation is based on the approach by Mishchenko [A. S. Mishchenko et al., Phys. Rev. B 62, 6317 (2000)]. Polaron ground state energies and effective polaron masses are successfully benchmarked with data obtained using Feynman's path integral formalism. By comparing 3D and 2D data, we verify the analytically exact scaling relations for energies and effective masses from 3D → 2D, which provides a stringent test for the quality of DMC predictions. The accuracy of our results is further proven by providing values for the exactly known coefficients in weakand strong-coupling expansions. Moreover, we compute polaron dispersion curves which are validated with analytically known lower and upper limits in the small-coupling regime and verify the first-order expansion results for larger couplings, thus disproving previous critiques on the apparent incompatibility of DMC with analytical results and furnishing useful reference for a wide range of coupling strengths.

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“…Both large and small polarons have been observed in several experiments, as reported in the next section, and studied by simulations and computational techniques. Historically, large polarons have been investigated mostly via effective Hamiltonians, in particular by means of variational treatments solved by Feynmann's path integral techniques, and by diagrammatic Monte Carlo [27][28][29][40][41][42][43] approaches. First principles techniques are more suitable for the description of the small polaron, but successful attempts to address the large-polaron case have been presented in the last few years [11,44,45].…”

Section: Large Polaron Small Polaronmentioning

confidence: 99%

Handbook of Materials Modeling

Löwe¹

2020

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The formation of polarons is a pervasive phenomenon in transition metal oxide compounds, with a strong impact on the physical properties and functionalities of the hosting materials. In its original formulation the polaron problem considers a single charge carrier in a polar crystal interacting with its surrounding lattice. Depending on the spatial extension of the polaron quasiparticle, originating from the coupling between the excess charge and the phonon field, one speaks of small or large polarons. This chapter discusses the modeling of small polarons in real materials, with a particular focus on the archetypal polaron material TiO 2 . After an introductory part, surveying the fundamental theoretical and experimental aspects of the physics of polarons, the chapter examines how to model small polarons using first principles schemes in order to predict, understand and interpret a variety of polaron properties in bulk phases and surfaces. Following the spirit of this handbook, different types of computational procedures and prescriptions are presented with specific instructions on the setup required to model polaron effects.

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On the LO‐polaron dispersion in D dimensions

Cited by 10 publications

References 34 publications

Upper and lower bounds for the large polaron dispersion in 1, 2, or 3 dimensions

Upper and lower bounds for the large polaron dispersion in 1, 2, or 3 dimensions

Diagrammatic Monte Carlo study of Fröhlich polaron dispersion in two and three dimensions

Handbook of Materials Modeling

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