Unified Dielectric Nature of Two-Dimensional Materials

Dielectric constant, which defines the polarization of the media, is a key quantity in condensed matter. It describes to a large degree the electron-electron interaction, which has a crucial effect on band gaps, optical excitations, and screening. Here we show that instead of the dielectric constant ε, the 2D polarizabilty α correctly captures the dielectric nature of a 2D material for both in-plane and out-of-plane polarizations. We reveal that the long-sought universal dielectric-scale relationships in the 2D world: the in-plane polarizability α^|| is inversely proportional to the minimal bandgap Eg, while the out-of-plane polarizability α^⊥ is directly related to intrinsic thickness of the 2D material. An analytical quantum-mechanical model is developed which give a sound background to the dielectric-scale relationships, which is supported by a broad high-throughput screening over thousands of materials. Moreover, such relations unify the dielectric properties between the 2D materials and their 3D counterparts in a natural manner, which ultimately pushes the boundary of the understanding of electronic screening in both dimensions.