Local Bandgap Variations In Moiré Structures - Origin And Parametric Dependence

Abstract

A moiré pattern is a large scale interference pattern formed by the overlap of two small scale patterns with a small twist angle. A moiré structure can be formed by overlapping two 2D materials with similar structures and lattice constants over each other with a small twist angle. Moiré structures made from transition metal dichalcogenide bilayers show interesting properties such as a variation in the local band gap. This low-energy electronic structure can modeled as the properties of a single layer on which a periodic potential energy landscape is imposed. This periodic potential is called the moiré potential. The extent to which the band edges vary in space is a measure of the moiré potential. Theoretical studies of the moiré potential based only on interlayer coupling without taking into account lattice relaxation effects calculate the size of this moiré potential to be of the order of tens of millielectronvolts. Theoretical works that includes lattice relaxation effects calculate the moiré potential to be of the order of a hundred millielectronvolts. Experiments performed on the moiré structure formed by overlaying MoSe2 on WSe2 observed a moiré potential of the order of a hundred millielectronvolts. The moiré potential of this magnitude is called a ‘deep moiré potential’. In this work, we implemented a method to study the moiré potential by using DFT to geometry optimize the structure and obtain the Local Density of States. We then use the LDOS to calculate the valence and conduction band edges and get an estimate of the moiré potential. We find that the extent of variation in the valence and conduction band edges thus obtained is of a similar order of magnitude as the ones obtained in experiments (deep moiré potentials). Furthermore, we use this method to understand the dependence of the moiré potential on the atomic reconstruction of the moiré cell.