Basis-independent spectral methods for non-linear optical response in arbitrary tight-binding models.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Physics

Background:

• Calculating the non-linear optical response of materials is crucial for understanding their interaction with light.
• Existing methods often rely on specific system symmetries or basis sets, limiting their applicability.
• Tight-binding models are widely used to describe electronic properties of materials.

Purpose of the Study:

• To develop a versatile and efficient method for calculating the non-linear optical response.
• To apply the method to non-interacting tight-binding models, including those lacking translational invariance.
• To demonstrate the method's capability using gapped graphene with defects.

Main Methods:

• A basis-independent perturbative approach was developed.
• The non-equilibrium Keldysh formalism was employed.
• Efficient numerical implementation using the kernel polynomial method was utilized.

Main Results:

• The method successfully calculates the non-linear optical response for arbitrary non-interacting tight-binding models.
• It is applicable to systems without translational invariance.
• Proof-of-concept results for the second-order optical conductivity of gapped graphene with vacancies and disorder were obtained.

Conclusions:

• The developed method provides a powerful and flexible tool for investigating material optical properties.
• It overcomes limitations of previous approaches by being basis-independent and applicable to disordered systems.
• This work paves the way for more accurate predictions of non-linear optical phenomena in complex materials.