GRANAD - Simulating GRAphene nanoflakes with ADatoms

Abstract

GRANAD is a program based on the tight-binding approximation to simulate optoelectronic properties of graphene nanoflakes and Su–Schrieffer–Heeger (SSH) chains with possible adatom defects under electromagnetic illumination. Its core feature is the numerical solution of a time-domain master equation for the spin-traced one-particle reduced density matrix. It provides time-resolved evolution of charge distributions, access to induced-field dynamics, and characterization of the plasmonic response. Other computable quantities include energy profiles, electron distribution in real space, and absorption spectra. GRANAD is written in Python and relies on the JAX library for high-performance array computing, just-in-time (JIT) compilation, and differentiability. It is intended to be lightweight, portable, and easy to set up, offering a transparent and efficient way to access the properties of low-dimensional carbon structures from the nanoscale to the mesoscopic regime. GRANAD is open source, with the full code and extensive documentation with usage examples available at https://github.com/GRANADlauncher/granad.git.

Program summary

Program Title: GRANAD

CPC Library link to program files: https://doi.org/10.17632/723d4m4z9x.1

Developer's repository link: https://github.com/GRANADlauncher/granad

Licensing provisions: MIT

Programming language: Python

Supplementary material: Code, documentation and demo files.

Nature of problem: Accessing the dynamical optical properties of graphene nanoflakes and one-dimensional polymer chains up to the mesoscale in the presence of adatoms represents a conceptual and computational challenge. Easily accessible classical methods fail as they do not accommodate relevant quantum effects. At the same time, quantum-mechanical ab initio time-domain approaches are computationally costly, and their implementations are often difficult for the user to set up and extend due to the high complexity of the codebase.

Solution method: A theoretical framework that combines an electronic mean-field approach with a Lindblad-like master equation is implemented to describe these carbon-based systems, where interaction with an external electric field is described semiclassically in the tight-binding approximation. Many-body effects are modeled via a nonlinear interaction term in the Hamiltonian, while dissipative processes are included in the master equation. Simulations are performed in the time domain, providing detailed access to physically relevant quantities. The implementation is lightweight, easily portable, and can be extended to incorporate other materials and nanoflake stacks.

Additional comments including restrictions and unusual features: The program relies on the JAX library, enabling differentiation of its core functions. It is intended to be extendable to, e.g., electric field parameter optimization for desired nanomaterial response and to popularize the differentiable programming technique further.