Deformation-induced band gap variation in phosphorene: tight-binding model vs. first-principles simulations

Abstract

We focus on estimating the influences of uniaxial tensile and shear strains on a band gap in the electronic structure of monolayer black phosphorus. To study numerically the dependence of the band gap on the deformation type and strength, we apply two approaches: the tight-binding model (with the exponential and inversely quadratic strain-induced bond-length-dependent hoppings) and the density-functional-theory-based calculations. Both approaches corroborated that phosphorene as a direct semiconductor in the unstrained state can become a semimetal at certain types and strengths of deformations. The critical values of the semiconductor–semimetal transition are different depending on approximations and model parameters.

Keywords:

• Band gap
• density of states
• phosphorene
• strain

Acknowledgments

The first, third, and fourth authors acknowledge the National Academy of Sciences of Ukraine for support within the departmental research for 2022–2026 (state registration number 0122U002396). All authors are obliged to the Armed Forces of Ukraine for providing security making it possible to perform this work.

Authors contributions

A.G.S. and I.Y.S. carried out numerical calculations using the DFT-based QE simulation package and TB-model-based computations, respectively. T.M.R. reviewed the literature, collected data, supervised the findings of this work, and wrote the manuscript with input from all authors. V.A.T. devised the main conceptual ideas, verified analytical approaches, and provided critical feedback. All authors were in charge of the overall direction and planning, analyzed and discussed the results, commented on the manuscript, and contributed to its final version.

Disclosure statement

No potential conflict of interest was reported by the author(s).