Strain-engineered diffusive atomic switching in two-dimensional crystals

Strain engineering is an emerging route for tuning the bandgap, carrier mobility, chemical reactivity and diffusivity of materials. Here we show how strain can be used to control atomic diffusion in van der Waals heterostructures of two-dimensional (2D) crystals. We use strain to increase the diffusivity of Ge and Te atoms that are confined to 5 Å thick 2D planes within an Sb2Te3–GeTe van der Waals superlattice. The number of quintuple Sb2Te3 2D crystal layers dictates the strain in the GeTe layers and consequently its diffusive atomic disordering. By identifying four critical rules for the superlattice configuration we lay the foundation for a generalizable approach to the design of switchable van der Waals heterostructures. As Sb2Te3–GeTe is a topological insulator, we envision these rules enabling methods to control spin and topological properties of materials in reversible and energy efficient ways.

Ge-layers in the structure. If the structure is disordered enough to make layers indistinguishable then it is categorised as melting.

SUPPLEMENTARY NOTES
Supplementary Note 1: Sb 2 Te 3 -GeTe superlattice structure measurements Bragg-Brentano symmetric x-ray diffraction scans were taken from the superlattice samples, with a Bruker D8 advance system. Only (00L) peaks are present in the XRD patterns from the superlattices (see Supplementary Figure 1), which indicates that the materials are grown with the desired layer structure.
The hexagonal lattice constants for bulk GeTe given in Table I  We therefore describe the GeTe unit cell using its hexagonal setting, where a = 4.16Å and c = 10.66Å for bulk GeTe.
The superlattices were grown with a fibre-like texture with strong (00L) preferred orientation. The crystallographic domain size was typically 150 nm, which was measured by scanning electron microscopy and atomic force microscopy. Since the superlattice layer thicknesses are much smaller than the crystal domain size, the stresses in the superlattice layers are dominated by the mismatch between the layer thicknesses rather than domain edge effects. Thus it seems that long range in-plane crystallographic order is not absolutely necessary for growing in-domain strained layers, and industrially scalable growth techniques, such as sputtering, are useful for growing strained vdW superlattice heterostructures.

Supplementary Note 2: Premelt disordering
Supplementary Figure 3 shows the crystallinity, of the Sb 2 Te 3 and GeTe layers within the vdW superlattice heterostructure as a function of temperature whilst heating the material from 450 K to 1300 K at a rate of 1.97 K ps −1 . The GeTe layer's crystallinity is lowered to temperatures below that of the melting temperature of Sb 2 Te 3 . This shows that the GeTe layer is substantially less stable than the Sb 2 Te 3 in the superlattice structure. In contrast the bulk melting temperature of GeTe is greater than that of Sb 2 Te 3 . From Table I in the main manuscript we see that the GeTe layer is strained by the Sb 2 Te 3 in the superlattice structure. We also know that the resonant bonds in crystalline GeTe are sensitive to lattice distortions. Here the Sb 2 Te 3 layer is distorting the GeTe crystal structure, which decreases the average overlap of p-orbital bonds in the GeTe and weakens resonant bonding. Thus the strained GeTe layer is more sensitive to distortions caused by phonons and its disordering temperature is lowered.

Supplementary Note 3: Diffusive atomic switching map
The response of Sb 2 Te 3 -GeTe structure to a heat pulse was modelled as a function of in-plane biaxial strain. Isothermal 5 ps runs were used to find the temperature threshold for switching at least one Ge atom into the vdW gap. Supplementary Table 1 Fig. 3b in the main text. Since the atomic switching is stochastic in nature, we drew somewhat blurred boundaries between the different regions.

Supplementary Note 4: Superlattice atom trajectories
When no strain is applied to the superlattice we find that all atoms remain in their initial superlattice layers. See Supplementary Figure 4, which shows the z-axis position of the atoms as a function of time. The lines do not cross, which indicates that the material does not melt or exhibit Ge-Te diffusive atomic disordering. In contrast, at higher temperatures the material melts. Supplementary Figure 5 shows a similar type of plot for the same initial structure where the MD run was conducted at a temperature of 1400 K, which is above the material's melting temperature. The layer structure is quickly lost. After 10 ps there is substantial inter-diffusion of atomic species across the layers. As the material is cooled below 900 K the atoms crystallise but the layers are disordered and not elementally pure.
We see from Fig. 3b in the main manuscript that at least 0.5 % strain is required for atomic switching of Te and Ge. Indeed, Fig. 3d, in the main manuscript, shows Ge-Te diffusive atomic switching when 1.5% strain is applied to the simulation at 950 K.
We find that if the structures melt and the layers inter-diffuse, then the melt tends to crystallise into layers but each layer can contain a mixture of Sb, Te and Ge atoms and the final structure resembles the trigonal phase of a typical Ge 2 Sb 2 Te 5 alloy. The separation of GeTe and Sb 2 Te 3 layers is lost.

Supplementary Note 6: Calculated reflectivity modulation of superlattice
To confirm that the reflectivity modulation measured in Supplementary Figure 8 is reasonable, we used the CASTEP DFT code to compute the optical properties of the Sb 2 Te 3 -GeTe structure with the Ge atoms in the GeTe layer, which is commonly named the Petrov configuration, and the Ge atoms in the vdW gap, which is usually named the Inverted Petrov configuration 4 . The structures were optimised into the ground state using the GGA functional with the PBE exchange. The cut-off energy was 440 eV, whilst the SCF energy tolerance was 5 × 10 −7 eV. The atomic positions and cell geometry were optimised to an energy tolerance better than 5 × 10 −6 eV, and the maximum force was less than 0.1 eV/atom. We used a 7 × 7 × 2 Monkhorst-Pack grid for the k-points. After fully relaxing the structures we calculated the band structure using the HSE03 exchange and a band energy tolerance better than 1 × 10 −5 eV. Then the refractive index of the structures was computed by first calculating the absorption spectra assuming unpolarised light, and then using a Kramers-Kronig transformation to get the refractive index real part.
The structure shows a reflectivity modulation of approximately 10% across the visible spectrum. This change in reflectivity agrees well with the experimentally observed changes shown in Supplementary Figure 8.