# First principle and tight-binding study of strained SnC

## TL;DR

This study combines DFT and tight-binding models to analyze how strain affects the electronic, optical, and phononic properties of monolayer SnC, revealing strain-induced band gap modulation and transition phenomena.

## Contribution

It introduces a tight-binding Hamiltonian for strained SnC based on DFT results and explores the effects of strain and spin-orbit coupling on its electronic and optical properties.

## Key findings

- Strain induces a transition from indirect to direct band gap in SnC.
- Tensile strain reduces the band gap, leading to a semiconductor to semimetal transition at 7.5%.
- Spin-orbit coupling remains significant even when the band gap closes under strain.

## Abstract

We study the electronic and optical properties of strained single-layer SnC in the density functional theory (DFT) and tight-binding models. We extract the hopping parameters tight-binding Hamiltonian for monolayer SnC by considering the DFT results as a reference point. We also examine the phonon spectra in the scheme of DFT, and analyze the bonding character by using Mulliken bond population. Moreover, we show that the band gap modulation and transition from indirect to direct band gap in the compressive strained SnC. The applied tensile strain reduces the band gap and eventually the semiconductor to semimetal transition occurs for 7.5\% of tensile strain. In the framework of tight-binding model, the effect of spin-orbit coupling on energy spectrum are also discussed. We indicate that while tensile strain closes the band gap, spin-orbit gap is still present which is order of $\sim 40$ meV at the $\Gamma$ point. The substrate effect is modeled through a staggered sub-lattice potential in the tight-binding approximation. The optical properties of pristine and strained SnC are also examined in the DFT scheme. We present the modulation of real and imaginary parts of dielectric function under applied strain.