# Triplet Fermions and Dirac Fermions in Borophene

## TL;DR

This paper derives a Dirac theory for borophene, revealing conditions for gapless cones, emergence of triplet fermions at three-band touching points, and analyzing edge states in nanoribbons.

## Contribution

It provides an explicit Dirac theory for borophene's Dirac cones, introduces effective models for triplet fermions, and studies edge state behaviors based on edge terminations.

## Key findings

- Dirac cones are gapless with inversion symmetry
- Triplet fermions emerge at three-band touching points
- Edge states vary with edge termination methods

## Abstract

Borophene is a monolayer materials made of boron. A perfect planar boropehene called $\beta_{12}$ borophene has Dirac cones and they are well reproduced by a tight-binding model according to recent experimental and first-principles calculation results. We explicitly derive a Dirac theory for them. Dirac cones are gapless when the inversion symmetry exists, while they are gapped when it is broken. In addition, three-band touching points emerge together with pseudospin triplet fermions when all transfer energy is equal and all on-site energy is equal. The three-band touching is slightly resolved otherwise. We construct effective three-band theories for triplet fermions. We also study the edge states of borophene nanoribbons, which show various behaviors depending on the way of edge terminations.