DOI: 10.5061/dryad.wpzgmsbv3
title: Twisted epitaxy of gold nanodiscs grown between twisted substrate layers of molybdenum disulfide

description: We expand the concept of epitaxy to a regime of “twisted epitaxy” with the
 epilayer crystal orientation between two substrates influenced by their
 relative orientation. We annealed nanometer-thick gold (Au) nanoparticles
 between two substrates of exfoliated hexagonal molybdenum disulfide (MoS2)
 with varying orientation of their basal planes with a mutual twist angle
 from 0° to 60°. Transmission electron microscopy studies show that the Au
 alignment is midway between that of the top and bottom MoS2 when the twist
 angle of the bilayer is small (&lt; ~7°). For larger twist angles, Au
 has only a small misorientation with the bottom MoS2 that varies
 approximately sinusoidally with the twist angle of the bilayer MoS2.
 Four-dimensional scanning transmission electron microscopy analysis
 further reveals a periodic strain variation (&lt; |±0.5%|) in the Au
 nanodiscs associated with the twisted epitaxy, consistent with the Moiré
 registry of the two MoS2 twisted layers.
description: # Twisted Epitaxy of Gold Nanodiscs Grown Between Twisted Substrate Layers
 of Molybdenum Disulfide doi:10.5061/dryad.wpzgmsbv3
 [https://doi.org/10.5061/dryad.wpzgmsbv3](https://doi.org/10.5061/dryad.wpzgmsbv3) These are source structure and codes for density functional theory (DFT) calculations of the interfacial energy of MoS2-Au-MoS2 heterostructure. The DFT simulations were carried out with the code GPAW. The effective core electron wavefunctions of Mo, S, and Au are described by projector augmented wave (PAW) pseudopotentials. The vdw-df-cx exchange-correlation functional is used to account for interlayer van der Waals interaction. The Kohn-Sham wavefunctions are represented in a plane-wave basis with energy cutoff of 600 eV and sampled at Γ point in the Brillouin zone. A Fermi-Dirac smearing of 0.03 eV is used to facilitate self-consistent field (SCF) convergence. The convergence criteria for total energy and atomic forces are, respectively, 5 meV and 10 meV/ Å. The optimized unit cell parameters are 3.18 Å in the xy-plane for MoS<sub>2</sub>, and 4.08 Å for bulk Au. The vacuum is chosen to have a thickness of 15 Å for minimal interlayer interaction between periodic images of the bilayer. The Au-MoS<sub>2</sub> model system consists of an interface between a monolayer MoS<sub>2</sub> (001) (8, 4, 0; 0, 6, 0; 0, 0, 1) slab with a four-layer Au (111) (6x6) slab. The Au slab is trimmed to hexagonal shape for maximal symmetry. The center Au atom is aligned directly above the center S atom. Other configurations were obtained by clockwise rotation of the Au crystal around its center. The distance between the bottom Au layer and top S layer of MoS<sub>2</sub> is set to be 0.26 nm. The file titled "moire\_supercell\_MoS2-3DAu\_30.cif (17.1KB)" is a Au nanoparticle on a monolayer MoS2, where the [111] zone of Au aligns with the [001] zone of MoS2. "30" in the title means the relative orientation of Au {220} planes and MoS2 {110} planes are 30 degree. "merge.py" shows how to merge the Au nanodisc and the monolayer MoS2 to form this heterostructure. "rotate.py" changes the relative orientation of Au and MoS2 from 0 degree to 30 degree with a 2.5 degree interval. "submit.sh" and "job.py" calculates the interfacial energy of the MoS2-Au heterostructure. After getting the interfacial energy of this MoS2-Au heterostructure with different relative orientations, "plot\_E\_interfacial\_\_\_E\_tot.py" plots the total interfacial energy of MoS2-Au-MoS2 trilayer heterostructure.