# Momentum-resolved TDDFT algorithm in atomic basis for real time tracking of electronic excitation

## TL;DR

This paper introduces a momentum-resolved real-time TDDFT algorithm using atomic basis functions, enabling efficient simulation of ultrafast electronic excitations in extended materials like graphene.

## Contribution

The authors develop a novel momentum-resolved rt-TDDFT method with atomic basis and implement electromagnetic field gauges, advancing the simulation of ultrafast dynamics in solids.

## Key findings

- Successfully simulated elementary excitations in graphene
- Observed excitation modes distinguishable in momentum space
- Demonstrated computational efficiency for extended systems

## Abstract

Ultrafast electronic dynamics in solids lies at the core of modern condensed matter and materials physics. To build up a practical ab initio method for studying solids under photoexcitation, we develop a momentum-resolved real-time time dependent density functional theory (rt-TDDFT)algorithm using numerical atomic basis, together with the implementation of both the length and vector gauge of the electromagnetic field. When applied to simulate elementary excitations in two-dimensional materials such as graphene, different excitation modes, only distinguishable in momentum space, are observed. The momentum-resolved rt-TDDFT is important and computationally efficient for the study of ultrafast dynamics in extended systems.