Broken inversion symmetry in atomic structure can lead to the emergence of specific functionalities at the nanoscale. Therefore, realizing 2D materials in Janus form is a growing field, which offers unique features and opportunities. In this paper, we investigate the structural, vibrational, elastic, piezoelectric, and electronic properties of Janus BiXY (X = S, Se, Te and Y = F, Cl, Br, I) monolayers based on first-principle methods. The structural optimization and vibrational frequency analysis reveal that all of the proposed structures are dynamically stable. Additionally, ab initio molecular dynamics simulations verify the thermal stability of these structures even at elevated temperatures. The mechanical response of the Janus BiXY crystals in the elastic regime is investigated in terms of in-plane stiffness and the Poisson ratio, and the obtained results ascertain their mechanical flexibility. The piezoelectric stress and strain coefficient analysis demonstrates the appearance of strong out-of-plane piezoelectricity, which is comparable with the Janus transition metal dichalcogenide monolayers. The calculated electronic band structures reveal that except for BiTeF, all Janus BiXY monolayers are indirect band gap semiconductors, and their energy band gaps span from the infrared to the visible part of the optical spectrum. Subsequently, large Rashba spin splitting is observed in electronic band structures when the spin-orbit coupling is included. The obtained results point out Janus 2D BiXY structures as promising materials for a wide range of applications in nanoscale piezoelectric and spintronics fields.

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We study the interplay of a random off-diagonal (hopping) disorder with the on-site quasiperiodic potential in a one-dimensional Aubry-André (AA) chain. There is evidence for the absence of delocalized states, at least for a finite lattice, in presence of a weak disorder, thereby removing the possibility of a sharp transition from extended to localized regime. This renders testimony for the presence of a weakly localized phase which we denote as the "critical" phase. We also evaluate whether the random disorder helps or hinders the quasiperiodic term on either side of the "duality" point in inducing a complete localization phenomenon via computing a few relevant quantities, such as the inverse participation ratio (IPR), which estimates the extent of localization, and an extensive multifractal analysis to assess the nature of the disordered states. We observe that a weak random disorder corresponding to the strength of the quasiperiodic term above the critical value (λc = 2) is more efficient in inducing the localization phenomenon as compared to a large disorder below the critical value. We also find that a large disorder is found to compete with the quasiperiodic term beyond its critical value in localizing the eigenstates, while it aids at strengths below the critical value, both of which are intuitively conceivable. Such a differential behavior of the random off-diagonal disorder and its interplay with the quasiperiodic potential albeit expected, have not been reported earlier in the literature. With regard to the multifractal analysis, we ascertain the nature of the critical phase and comment on the fractal dimension, the critical exponents and occurrence of rare events.