Relativistic materials from an alternative viewpoint
- URL: http://arxiv.org/abs/2312.04448v1
- Date: Thu, 7 Dec 2023 17:16:58 GMT
- Title: Relativistic materials from an alternative viewpoint
- Authors: Ann E. Mattsson, Daniel A. Rehn
- Abstract summary: current standard for treatment of electrons in materials containing heavy elements involves density functional theory methods.
We provide a different method for translating between the Dirac and Schr"odinger viewpoints in the context of a Coulomb potential.
We introduce the concepts of densitals and Dirac spherical harmonics that allow us to translate more easily between the Dirac and Schr"odinger solutions.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Electrons in materials containing heavy elements are fundamentally
relativistic and should in principle be described using the Dirac equation.
However, the current standard for treatment of electrons in such materials
involves density functional theory methods originally formulated from the
Schr\"{o}dinger equation. While some extensions of the Schr\"{o}dinger-based
formulation have been explored, such as the scalar relativistic approximation
with or without spin-orbit coupling, these solutions do not provide a way to
fully account for all relativistic effects of electrons, and the language used
to describe such solutions are still based in the language of the
Schr\"{o}dinger equation. In this article, we provide a different method for
translating between the Dirac and Schr\"{o}dinger viewpoints in the context of
a Coulomb potential. By retaining the Dirac four-vector notation and
terminology in taking the non-relativistic limit, we see a much deeper
connection between the Dirac and Schr\"{o}dinger equation solutions that allow
us to more directly compare the effects of relativity in the angular and radial
functions. Through this viewpoint, we introduce the concepts of densitals and
Dirac spherical harmonics that allow us to translate more easily between the
Dirac and Schr\"{o}dinger solutions. These concepts allow us to establish a
useful language for discussing relativistic effects in materials containing
elements throughout the full periodic table and thereby enable a more
fundamental understanding of the effects of relativity on electronic structure.
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