Negative-Gaussian-Curvature Carbon Monolayer NGC-C40 with Switchable Auxeticity and Ultra-High Potassium Storage

Beyond the geometric planarity of graphene and the outward bulging of fullerenes, a carbon sheet with negative Gaussian curvature (NGC), an “inside-out” saddle world, remains a tantalizing blind spot. A novel 2D carbon allotrope, NGC-C40, is developed through a topological engineering strategy via first-principles calculations. It displays pronounced intrinsic NGC features, lattice dynamical and thermal stability, and rare closed nodal-line semimetal characteristics. Mechanically, NGC-C40 exhibits pronounced anisotropy and a robust auxetic response, with a Poisson’s ratio ranging from −0.254 to +0.041. More importantly, it shows an unusual strain-polarity- and orientation-coupled Poisson’s ratio sign-switching behavior, arising from the cooperative response of the C8C5 skeleton and C4 region. For potassium-ion storage, NGC-C40 has a high theoretical capacity of 1116 mAh g–1, far exceeding the capacity of 223 mAh g–1 obtained for both Li and Na. It also exhibits a low K-ion migration barrier of 0.215 eV, operating voltages ranging from 1.124 to 0.031 V, and a maximum carbon-framework geometric volume expansion of 5.66%, enabled by its NGC architecture. Demonstrating multifunctional capability, NGC-C40 suggests a potential strategy for multifunctional 2D carbon design: negative Gaussian curvature may serve as an underexplored geometric factor.