# Interpenetrating Graphene Networks: Three-dimensional Node-line Semimetals with Massive Negative Linear Compressibilities

## TL;DR

This study explores the stability, mechanical, and electronic properties of novel interpenetrating graphene network allotropes, revealing their unusual negative linear compressibility and diverse electronic behaviors, with potential for experimental synthesis.

## Contribution

It introduces and characterizes fifteen metastable IGN carbon allotropes with unique mechanical and electronic properties using density functional theory.

## Key findings

- All IGN allotropes exhibit negative linear compressibility.
- Maximum negative linear compressibility exceeds previous reports at 3.4 GPa.
- Electronic properties vary: zigzag types are node-line semimetals, armchair types are semiconductors or node-line semimetals.

## Abstract

We investigated the stability and mechanical and electronic properties of fifteen metastable mixed $sp^2$-$sp^3$ carbon allotropes in the family of interpenetrating graphene networks (IGNs) using density functional theory (DFT) within the generalized gradient approximation (GGA). IGN allotropes exhibit non-monotonic bulk and linear compressibilities before their structures irreversibly transform into new configurations under large hydrostatic compression. The maximum bulk compressibilities vary widely between structures and range from 3.6 to 306 TPa$^{-1}$. We find all the IGN allotropes have negative linear compressibilities with maximum values varying from -0.74 to -133 TPa$^{-1}$. The maximal negative linear compressibility of Z33 (-133 TPa$^{-1}$ at 3.4 GPa) exceeds previously reported values at pressures higher than 1.0 GPa. IGN allotropes can be classified as either armchair- or zigzag-type, and these two types of IGNs exhibit different electronic properties. Zigzag-type IGNs are node-line semimetals, while armchair-type IGNs are either semiconductors or node-loop or node-line semimetals. Experimental synthesis of these IGN allotropes might be realized since their formation enthalpies relative to graphite are only 0.1 - 0.5 eV/atom (that of C$_{60}$ fullerene is about 0.4 eV/atom), and energetically feasible binary compound pathways are possible.