# Electronic properties of single-layer antimony: Tight-binding model, spin-orbit coupling and the strength of effective Coulomb interactions

## TL;DR

This study develops a tight-binding model for single-layer antimony incorporating spin-orbit coupling and Coulomb interactions, revealing its strongly correlated electronic nature and providing insights into its electronic properties.

## Contribution

The paper introduces an accurate tight-binding model for single-layer antimony that includes spin-orbit effects and screened Coulomb interactions, advancing understanding of its electronic behavior.

## Key findings

- Spin-orbit coupling significantly affects band structure and hole effective mass.
- Screened Coulomb interactions are mainly due to 5p states, captured within the model.
- Kinetic and Coulomb energies are comparable, indicating strong electron correlations.

## Abstract

The electronic properties of single-layer antimony are studied by a combination of first-principles and tight-binding methods. The band structure obtained from relativistic density functional theory is used to derive an analytic tight-binding model that offers an efficient and accurate description of single-particle electronic states in a wide spectral region up to the mid-UV. The strong ($\lambda=0.34$ eV) intra-atomic spin-orbit interaction plays a fundamental role in the band structure, leading to splitting of the valence band edge and to a significant reduction of the effective mass of the hole carriers. To obtain an effective many-body model of two-dimensional Sb we calculate the screened Coulomb interaction and provide numerical values for the on-site $\bar{V}_{00}$ (Hubbard) and intersite $\bar{V}_{ij}$ interactions. We find that the screening effects originate predominantly from the 5$p$ states, and are thus fully captured within the proposed tight-binding model. The leading kinetic and Coulomb energies are shown to be comparable in magnitude, $|t_{01}|/(\bar{V}_{00}-\bar{V}_{01}) \sim 1.6$, which suggests a strongly correlated character of 5$p$ electrons in Sb. The results presented here provide an essential step toward the understanding and rational description of a variety of electronic properties of this two-dimensional material.