Variational Polaron Equations Applied to the Anisotropic Fröhlich Model

Abstract

Starting from recent advances in the first-principles modeling of polarons, variational polaron equations in the strong-coupling adiabatic approximation are formulated in Bloch space. In this framework, polaron formation energy as well as individual electron, phonon and electron-phonon contributions are obtained. We suggest an efficient gradient-based optimization algorithm and apply these equations to the generalized Fröhlich model with anisotropic non-degenerate electronic bands, both in two- and three-dimensional cases. The effect of the divergence of Fröhlich electron-phonon matrix elements at $\Gamma$-point is treated analytically, improving the convergence with respect to the sampling in reciprocal space. The whole methodology is validated by obtaining the known asymptotic solution of the standard Fröhlich model in isotropic scenario and also by comparing our results with the Gaussian ansatz approach, showing the difference between the numerically exact and Gaussian trial wavefunctions. Additionally, decomposition of the energy into individual terms allows one to recover the Pekar's 1:2:3:4 theorem, which is shown to be valid even in the anisotropic case. We expect that the improvements in the formalism and numerical implementation will be applicable beyond the large polaron hypothesis inherent to Fröhlich model.

14 pages, 5 figures

References in corpus (11)

• Optical Phonons in Methylammonium Lead Halide Perovskites and Implications for Charge Transport
• {\it Ab--initio} finite temperature excitons
• Ab initio theory of polarons: formalism and applications
• Polarons from first principles, without supercells
• Predominance of non-adiabatic effects in zero-point renormalization of the electronic band gap
• Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials
• Band gap renormalization, carrier mobilities, and the electron-phonon self-energy in crystalline naphthalene
• Ab initio dipolar electron-phonon interactions in two-dimensional materials
• Fröhlich polaron effective mass and localization length in cubic materials: degenerate and anisotropic electronic bands
• Facile ab initio approach for self-localized polarons from canonical transformations
• Comparison of the canonical transformation and energy functional formalisms for ab initio calculations of self-localized polarons

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• Comparison between first-principles supercell calculations of polarons and the ab initio polaron equations