Twelve Inequivalent Dirac Cones in Two-Dimensional ZrB2

TL;DR

This paper predicts 12 unique Dirac cones in monolayer ZrB2, revealing complex electronic properties and the effects of symmetry and external stimuli on these cones, with implications for 2D material design.

Contribution

It provides the first theoretical evidence of multiple inequivalent Dirac cones in 2D ZrB2 and explains their origin and tunability.

Findings

12 inequivalent Dirac cones near Fermi energy

One cone insensitive to lattice expansion

Second cone vanishes with Zr vertical displacement

Abstract

Theoretical evidence of the existence of 12 inequivalent Dirac cones at the vicinity of the Fermi energy in monolayered ZrB$_2$ is presented. Two-dimensional ZrB$_2$ is a mechanically stable d- and p-orbital compound exhibiting a unique electronic structure with two Dirac cones out of high-symmetry points in the irreducible Brillouin zone with a small electron-pocket compensation. First-principles calculations demonstrate that while one of the cones is insensitive to lattice expansion, the second cone vanishes for small perturbation of the vertical Zr position. Internal symmetry breaking with external physical stimuli, along with the relativistic effect of SOC, is able to remove selectively the Dirac cones. A rational explanation in terms of d- and p-orbital mixing is provided to elucidate the origin of the infrequent amount of Dirac cones in a flat structure. The versatility of transition metal d-orbitals combined with the honeycomb lattice provided by the B atoms yields novel features never observed in a two-dimensional material.