Coexistence of Electronic and Phononic Dirac Points in TiB₂ Monolayer with Inverse Sandwich Motif

Abstract

Although many Dirac semimetals (DSMs) have been theoretically proposed, the ideal Dirac fermions coexisting with Dirac phonons in a DSM are rare. In this work, we proposed a general strategy to assemble two-dimensional (2D) ideal DSMs using the cluster of transition metal boride with an inverse sandwich configuration. We illustrated this strategy using first-principles calculations, resulting in the creation of a 2D titanium diboride named 2c-TiB2 with a space group of P21/c. This monolayer was found to be thermodynamically, dynamically, and thermally stable. Additionally, it was revealed to be a DSM with an ideal Dirac cone at the Fermi level, and its topology arises from the band inversion between the p z orbitals of B atoms and d x 2–y 2 orbitals of Ti atoms. Furthermore, the monolayer exhibits intersecting Dirac phonons along high-symmetry path Γ–X. The quantized Berry phase, inversed eigenvalues, and apparent electronic and phononic topological edge states all served as further evidence of the topological protection originating from C 2x symmetry. The theoretical investigation into inverse sandwich structured boride monolayer not only predicts the coexistence of Dirac fermions and Dirac phonons in 2D TiB2, but also provides a novel approach to design topological states in 2D nanomaterials.