Origin of strain tunability in flat valence band and ultrahigh shear piezoelectricity in superflexible non–van der Waals graphitic ScX monolayers ( X=P , As, Sb)

Utilizing the exceptional characteristics of two-dimensional (2D) materials for solid-state electronic devices presents an appealing strategy that could potentially address the need to prolong Moore's law. Evidently, the prevailing fraction of technically viable materials, which have already been successfully scaled up for industrial production, belongs to the category of non--van der Waals (n-vdW) materials. In recent years, research on n-vdW 2D materials has garnered significant growth owing to their potential for diverse applications and the development of synthesis techniques. In this paper, we stabilize 1-atom-thick $\mathrm{Sc}X$ ($X=\mathrm{P}$, As, Sb) monolayers drawn from their n-vdW bulk counterpart in the wurtzite phase by applying a minimal tensile strain of 1--2%. The resulting high flexibility, owing to the extremely small in-plane elastic constants (6--43 N/m) and Young's modulus (6--20 N/m), suits them ideally for extensive strain engineering on a large scale. Complex mixing of acoustic and optic phonon modes for higher strains ensures a large shear-piezoelectric coefficient of up to ${d}_{16}=\ensuremath{-}228.08$, \ensuremath{-}469.87, and \ensuremath{-}397.52 pm/V for ScP, ScAs, and ScSb respectively. This coefficient notably surpasses that in amino acids, making it the highest reported to date, and is accompanied by high in-plane piezoelectric coefficients, $|{d}_{21}|$ and $|{d}_{22}|\phantom{\rule{4pt}{0ex}}>100$ pm/V and highly strain-tunable shear piezoelectric coefficient ${d}_{15}$ ranging from \ensuremath{-}90 to 210 pm/V. The monolayers exhibit rich band structures, including flat bands at the top-most valence band and a large spin splitting of $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$, making them ideal for applications in LED and laser devices and opening exciting avenues for exploration in spintronics. In this paper, we present an in-depth analysis of band flattening caused by tensile strain and demonstrate the strong integrability of ScP monolayer with Si substrate. The ScP monolayer retains its flat band feature when implanted on silicon, which promises significant advancements in various practical applications.