Strain-induced electronic phase transition in phosphorene: A Green’s function study

Straintronics in phosphorene via tensile vs shear strains and their combinations for manipulating the band gap

We study the effects of the uniaxial tensile strain and shear deformation as well as their combinations on the electronic properties of single-layer black phosphorene. The evolutions of the strain-dependent band gap are obtained using the numerical calculations within the tight-binding (TB) model as well as the first-principles (DFT) simulations and compared with previous findings. The TB-model-based findings show that the band gap of the strain-free phosphorene agrees with the experimental value and linearly depends on both stretching and shearing: increases (decreases) as the stretching increases (decreases), whereas gradually decreases with increasing the shear. A linear dependence is less or more similar as compared to that obtained from the ab initio simulations for shear strain, however disagrees with a non-monotonic behaviour from the DFT-based calculations for tensile strain. Possible reasons for the discrepancy are discussed. In case of a combined deformation, when both strain types (tensile/compression + shear) are loaded simultaneously, their mutual influence extends the realizable band gap range: from zero up to the values respective to the wide-band-gap semiconductors. At a switched-on combined strain, the semiconductor-semimetal phase transition in the phosphorene is reachable at a weaker (strictly non-destructive) strain, which contributes to progress in fundamental and breakthroughs.

Optical interband transitions in strained phosphorene

In this paper, we have concentrated on the orbital and hybridization effects induced by applied triaxial strain on the interband optical conductivity (IOC) of phosphorene using a two-band Hamiltonian model, linear response theory and the Kubo formula. In particular, we study the dependence of the electronic band structure and of the IOC of a phosphorene single layer on the modulus and direction of the applied triaxial strain. The triaxial strain is included in a model through the introduction of strain-dependent hopping parameters using the Harrison rule. Among the various configurations for applying the triaxial strain, considerable findings are presented here in three classes: (i) uniform, (ii) in-plane uniform and (iii) non-uniform triaxial strain. The main consequence of applying triaxial strain is that of increasing and decreasing the band gap depending on the considered class of study, resulting in a blue shift and red shift of the interband optical transitions, respectively. Our results show that a pure blue shift independent of the strain modulus as well as strain sign (tensile or compressive) emerges when applying non-uniform triaxial strain. The overall feature of our outcomes is tailoring the edge-dependent optical responses of phosphorene in the presence of triaxial strain, which provides the required conditions of tuning the optical properties of phosphorene for future experimental research.

Strain engineering of optical activity in phosphorene

Optical activity is one of the most fascinating fields in current physics. The strong anisotropic feature in monolayer phosphorene leads to the emergence of non-trivial optoelectronic physics. This paper is devoted to a detailed analysis of strain effects on the optical activity of phosphorene ranging from low-optical-field to high-optical-field. To do so, a numerical study of the two-band tight-binding model is accomplished using the Harrison rule and the linear response theory. Although the transparency of phosphorene confirms at all frequencies independent of the strain modulus and direction, on average, from low- to high-optical-field limit, the polarization of the reflected wave at critical strains becomes circular and the ellipse axis tends to a rotation of 180°. It is found that the maximum absorption takes place at high-energy transitions, which quantitatively depends strongly on the strain modulus and direction. Furthermore, a detailed investigation of compressive and tensile strains results in the dominant contribution of the in-plane compressive and out-of-plane tensile strains to the reflected/transmitted light for low- and intermediate-optical-field ranges, whilst both contribute for the high-optical-field limit. However, overall, in-plane compressive and out-of-plane tensile strains come in to play a role in the absorption spectra. Thereby, the quality of the determined reflection, transmission and absorption waves depends on the regarded regime of the optical field, strain modulus, and strain orientation. These findings if sufficient can be performed and/or tuned experimentally, and a vast number of phosphorene-based optoelectronic devices can be achieved.

This paper is devoted to a detailed analysis of strain effects on the optical activity of phosphorene ranging from low-optical-field to high-optical-field.