Probing the Effective Young's Modulus of ‘Magic Angle’ Inspired Multi-Functional Twisted Nano-Heterostructures

Abstract

Two-dimensional (2D) materials are crucially important nanomaterials because of their exciting multi-functional properties. However, a single layer of 2D materials may not have a certain property adequately, or multiple application-specific properties simultaneously to the desired and optimal level. For mitigating this lacuna, a new trend has emerged recently to develop nano-scale engineered heterostructures by stacking multiple layers of different 2D materials, wherein each of the layers could also be twisted. The vast advantage of combining single layers of different 2D materials with different twisting angles has dramatically expanded this research field well beyond the scope of considering a 2D material mono-layer, leading to a set of multifunctional physical properties corresponding to each possible combination of number of layers, different 2D materials therein, stacking sequence and the twisting angle of each layer. Effective mechanical properties such as Young's moduli are generally of utmost importance for analyzing the viability of such engineered nano-heterostructures in various nanoelectromechanical applications. Efficient closed-form generic formulae are proposed for the effective Young's moduli of twisted multi-layer heterostructures. Based on this physics-based analytical approach, a wide range of insightful new results are presented for twisted heterostructures, covering mono-planar and multi-planar configurations with homogeneous and heterogeneous atomic distributions.