<p>Exploring novel two-dimensional (2D) carbon phases with diverse electronic properties, ranging from metallic to semiconducting, is crucial for the development of all-carbon nanodevices. In this study, two new 2D carbon allotropes with buckled geometric features, referred to as twin Irida-α and twin Irida-β sheets, are proposed and theoretically investigated based on the configurations of reported Irida-graphene and twin Irida-graphene. These two developed carbon allotropes can be considered an addition to the derivative structures of Irida-graphene. The calculated cohesive energies, phonon dispersion spectra, and elastic constants, as well as ab initio molecular dynamics simulations, provide solid support for the structural stability of these new 2D carbon phases. Moreover, this work adopts a comparative study within first-principles approaches involving four carbon sheets: the two newly proposed 2D carbon allotropes and the Irida and twin Irida-graphene counterparts. The structural, mechanical, electronic, and optical properties of the Irida-graphene and its derivative structures are comprehensively investigated. Notably, in contrast to the metallic Irida-graphene and twin Irida-graphene sheets, the proposed twin Irida-α sheet is semimetallic, with a Dirac cone located at the K point, while the twin Irida-β sheet is an intrinsic 2D semiconductor with a moderate bandgap. The appealing properties of these novel 2D carbon phases make them promising candidates for use in future all-carbon nanoelectronic and optoelectronic devices and photovoltaic applications.</p>