Theory of optically forbidden d-d transitions in strongly correlated crystals

TL;DR

This paper develops a comprehensive theoretical framework for understanding optically forbidden d-d transitions in strongly correlated crystals, emphasizing the role of vertex functions and local interactions.

Contribution

It introduces a unified multiband formulation for linear and nonlinear optical responses in correlated materials, incorporating local vertex functions for practical calculations.

Findings

Derived a general approach for second- and third-order response functions

Applied the theory to a two-orbital model illustrating intraatomic spin-flip contributions

Provided insights into the energy scales of optical transitions in correlated systems

Abstract

A general multiband formulation of linear and non-linear optical response functions for realistic models of correlated crystals is presented. Dipole forbidden d-d optical transitions originate from the vertex functions, which we consider assuming locality of irreducible four-leg vertex. The unified formulation for second- and third-order response functions in terms of the three-leg vertex is suitable for practical calculations in solids. We illustrate the general approach by consideration of intraatomic spin-flip contributions, with the energy of 2J, where J is a Hund exchange, in the simplest two-orbital model.