# Lattice deformation on flat-band modulation in 3D Hopf-linked carbon allotrope: Hopfene

## TL;DR

This study investigates how lattice deformation affects flat-band levels in the 3D Hopfene carbon allotrope using DFT and TB analyses, aiming to control electronic properties for magnetic and electronic applications.

## Contribution

It introduces a detailed DFT and TB analysis of lattice deformation effects on flat bands in Hopfene, proposing a structure for flat-band tuning.

## Key findings

- Flat-band levels shift linearly with lattice deformation.
- Qualitative agreement between DFT and TB band analyses.
- Proposed double-hetero-like structure for flat-band level control.

## Abstract

Flat bands form in a 3D Hopf-linked graphene crystal or a 3D carbon allotrope named Hopfene, which qualitatively differ from bands of only graphenes. This paper discusses carbon-hexagon deformation on the level shift of a flat band via density-functional-theoretical (DFT) analysis to set the flat-band level to the Fermi level, viz., to utilize its large density of states for magnetic- and electronic-property researches. Tight-binding (TB) analysis is also performed for a comparison with the DFT analysis; here, a qualitative agreement between TB and DFT bands is obtained. The DFT analysis shows an almost linear flat-band level shift to the lattice-deformation rate, where electron-interaction effects are included within the Kohn-Sham method. To tune the flat-band level so that it fits the Fermi level, a double-hetero-like structure is also proposed as a way of hexagon-deformation control.