Moir\xe9 metrology of energy landscapes in van der Waals heterostructures

Dorri Halbertal ,James Hone ,Efthimios Kaxiras ,Kenji Watanabe ,Sara Shabani ,Lei Wang ,S Chen ,Dante M Kennes ,Abhay Pasupathy ,Nathan Finney ,Daniel Rhodes ,Sai Sunku ,Cory Dean ,Carmen Rubio-Verdú ,Lede Xian ,Takashi Taniguchi ,Alexander Kerelsky ,Charles Zhang ,Ángel Rubio ,Derick Gonzalez-Acevedo ,Alexander Mcleod ,Stephen Carr ,D N Basov

doi:10.1038/s41467-020-20428-1

Abstract

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe2/WSe2. Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.

Highlights

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twistangle-induced superlattices offer means to control topology and strong correlations
Moiré metrology, presented here, correlates measurable spatial patterns of the relaxed moiré superlattice with modeling based on the generalized stacking fault energy function (GSFE)
To understand the enhanced sensitivity of moiré metrology under strain, we propose an alternative description of the moiré superlattice in terms of a geometric interference pattern of the lattices of the two layers

Summary

Introduction

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twistangle-induced superlattices offer means to control topology and strong correlations. We introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. We show that the generalized stacking fault energy function (GSFE) is encoded in fine details of the relaxed moiré super-lattice patterns at the low twist-angle limit. SDWs separate two distinct stacking configurations of a moiré superlattice (for instance, ABCA [MM’] and ABAB [MX’] in the TDBG [for twisted H-stacked MoSe2/WSe2, or T-HMoSe2/WSe2 for short] example of Fig. 1a). In cases of inequivalent two lowestenergy configurations (as in Fig. 1), the SDW develops a finite curvature κ, allowing one to extract the domains energy imbalance with an accuracy outperforming the ~3 meV/atom of the gold standard of quantum chemistry[36,37]

Methods

Results

Conclusion