Four-band tight-binding model of TiSiCO-family monolayers

TL;DR

This paper develops a minimal four-band tight-binding model for TiSiCO-family monolayers that accurately captures their low-energy electronic structure, valley-layer coupling, and topological properties, facilitating future theoretical studies.

Contribution

The authors introduce a symmetry-allowed four-band tight-binding model fitted to first-principles data, capturing key electronic and topological features of TiSiCO-family monolayers with strong valley-layer coupling.

Findings

The model reproduces the electronic band structure accurately.

It captures the strong valley-layer coupling and high-order topology.

It suggests potential topological phase transitions under electric fields and strain.

Abstract

The TiSiCO-family monolayers have recently been attracting significant attention due to their unique valley-layer coupling (VLC). In this work, we present a minimal, four-band tight-binding (TB) model to capture the low-energy physics of the TiSiCO-family monolayers $X_{2}Y$CO$_{2}$ ($X=$ Ti, Zr, Hf; $Y=$ Si, Ge) with strong VLC. These monolayers comprise two $X$ atom layers separated by approximately $4$ \AA ~in the out-of-plane direction. Around each valley ($X$ or $X'$), the conduction and valence bands are mainly dominated by the $A_{1}\{d_{z^{2}(x^{2}-y^{2})}\}$ and $B_{2}\{d_{yz}\}$ orbitals of the top $X$ atoms,and the $A_{1}\{d_{z^{2}(x^{2}-y^{2})}\}$ and $B_{1}\{d_{xz}\}$ orbitals of the bottom $X$ atoms. Using these four states as a basis, we construct a symmetry-allowed TB model. Through parameter fitting from first-principles calculations, the four-band TB model not only reproduces the electronic band structure, but also captures the strong VLC, high-order topology, and valley-contrasting linear dichroism of the monolayers. Furthermore, the TB model reveals that these monolayers may exhibit various intriguing topological phases under electric fields and biaxial strains. Hence, the TB model established here can serve as the starting point for future research exploring the physics related to VLC and the $X_{2}Y$CO$_{2}$ monolayers.