Ab initio materials physics and microscopic electrodynamics of media

Starke, R.; Schober, G. A. H.

doi:10.48550/arxiv.1606.00445

Cited by 8 publications

(19 citation statements)

References 142 publications

(177 reference statements)

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“…In this last subsection, we discuss the consistency of the relation (C.71), which we have derived by purely classical considerations, with the quantum field theoretical Kubo formula for the fundamental response tensor given by (see e.g. [8,21,147,166] or [157,Sec. 3.2.4 and App.…”

Section: C3 Kubo Formula For Electromagnetic Response Of the Coresmentioning

confidence: 82%

“…Inter alia, this also leads to a new interpretation of electrodynamics in media, the so-called Functional Approach, which has been expounded by the authors of this article in Refs. [123,157,[161][162][163]. In Sec.…”

Section: C1 Response Function and Kubo Formalismmentioning

confidence: 99%

“…We thus find for the (retarded) density response function in the reference state |Ψ 0 the expression (see [157,Eq. (3.84)])…”

Section: C1 Response Function and Kubo Formalismmentioning

confidence: 99%

“…This shows that within our approximation (C.40)-(C.41) of the four-current, the magnetic field does not couple explicitly to the displacement field (although it does so implicitly, because a transverse electric field is in general also accompanied by a magnetic field). By combining the electromagnetic four-current (C.40)-(C.41) with the formalism of the Functional Approach to electrodynamics of media [123,157,[161][162][163], we are now in a position to express the core electromagnetic response of the solid in terms of the elastic Green function. In fact, from the very definition of the elastic Green function (see Eq.…”

Section: C2 Displacement Field and Electromagnetic Responsementioning

confidence: 99%

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Response Theory of the Electron-Phonon Coupling

Starke¹,

Schober²

2016

Preprint

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This article presents a systematic theoretical enquiry concerning the conceptual foundations and the nature of phonon-mediated electron-electron interactions. Starting from the fundamental many-body Hamiltonian, we propose a simple scheme to decouple the electrons and nuclei of a crystalline solid via effective interactions. These effective interactions, which we express in terms of linear response functions, are completely symmetric under the exchange of electrons and nuclei. Correspondingly, we derive concrete formulae for both the effective electron interaction mediated by phonons and the effective core interaction mediated by electrons. In particular, we rederive from our fundamental ansatz the well-known general expressions of the effective electronelectron interaction in terms of the elastic Green function and the phonon dispersion relation. We further show that the effective core interaction coincides in the instantaneous limit with the dynamical matrix as calculated in electronic structure theory. If combined with the Kubo formalism, our general formulae lend themselves to the calculation of effective interactions from first principles. By showing the compatibility of our approach with the functional integral formalism, this work also paves the way for the derivation of ab initio initial interactions for functional renormalization group applications.

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Section: C3 Kubo Formula For Electromagnetic Response Of the Coresmentioning

confidence: 82%

Section: C1 Response Function and Kubo Formalismmentioning

confidence: 99%

“…We thus find for the (retarded) density response function in the reference state |Ψ 0 the expression (see [157,Eq. (3.84)])…”

Section: C1 Response Function and Kubo Formalismmentioning

confidence: 99%

Section: C2 Displacement Field and Electromagnetic Responsementioning

confidence: 99%

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Response Theory of the Electron-Phonon Coupling

Starke¹,

Schober²

2016

Preprint

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“…The microscopic theory of the refractive index exposed in this article is based on the Functional Approach to electrodynamics of materials [21,[53][54][55][56], which as a microscopic theory encapsulates the common practice in ab initio materials physics. For the convenience of the reader, we first assemble the most important facts as far as they are needed in this article.…”

Section: Functional Approach To Electrodynamics Of Mediamentioning

confidence: 99%

Microscopic theory of the refractive index

Starke

Schober

2017

Optik

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We examine the refractive index from the viewpoint of modern first-principles materials physics. We first argue that the standard formula, n 2 = ε r µ r , is generally in conflict with fundamental principles on the microscopic level. Instead, it turns out that an allegedly approximate relation, n 2 = ε r , which is already being used for most practical purposes, can be justified theoretically at optical wavelengths. More generally, starting from the fundamental, Lorentz-covariant electromagnetic wave equation in materials as used in plasma physics, we rederive a well-known, three-dimensional form of the wave equation in materials and thereby clarify the connection between the covariant fundamental response tensor and the various cartesian tensors used to describe optical properties. Finally, we prove a general theorem by which the fundamental, covariant wave equation can be reformulated concisely in terms of the microscopic dielectric tensor.

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General form of the full electromagnetic Green function in materials physics

Schober

Starke

2019

Chinese Journal of Physics

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In this article, we present the general form of the full electromagnetic Green function which is suitable for the application in bulk materials physics. In particular, we show how the seven adjustable parameter functions of the free Green function translate into seven corresponding parameter functions of the full Green function. Furthermore, for both the fundamental response tensor and the electromagnetic Green function, we discuss the reduction of the Dyson equation on the four-dimensional Minkowski space to an equivalent, three-dimensional Cartesian Dyson equation.

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Ab initio materials physics and microscopic electrodynamics of media

Cited by 8 publications

References 142 publications

Response Theory of the Electron-Phonon Coupling

Response Theory of the Electron-Phonon Coupling

Microscopic theory of the refractive index

General form of the full electromagnetic Green function in materials physics

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