Simple metal under tensile stress: layer-dependent herringbone reconstruction of thin potassium films on graphite

While understanding the properties of materials under stress is fundamentally important, designing experiments to probe the effects of large tensile stress is difficult. Here tensile stress is created in thin films of potassium (up to 4 atomic layers) by epitaxial growth on a rigid support, graphite. We find that this “simple” metal shows a long-range, periodic “herringbone” reconstruction, observed in 2- and 3- (but not 1- and 4-) layer films by low-temperature scanning tunneling microscopy (STM). Such a pattern has never been observed in a simple metal. Density functional theory (DFT)simulations indicate that the reconstruction consists of self-aligned stripes of enhanced atom density formed to relieve the tensile strain. At the same time marked layer-dependent charging effects lead to substantial variation in the apparent STM layer heights.

The agreement between the hexagonal lattice and the experimental image indicates that the fourth layer of K displays a close-packed surface.

STATISTICS OF THE HEIGHT OF POTASSIUM LAYERS
The apparent height distribution in the red box demarcated on STM image of K/graphite (figure S3a) was counted and displayed in figure S3b. In this figure, we can see five peaks correspondingto the apparent height of the blank graphite surface and the four K films. In order to estimate the apparent height of the four K films, we simulated the five peaks with the Lorentz distribution. The Lorentz fitting peaks agree with the experimental results very well(figure S3b). The parameters of the five Lorentz fitting peaks and the apparent heights of the four K layers are listed in Table S1. Here the FWHM of the Lorentz fitting peaks is used 3 as the error.   Figure S4 shows the STM image of multilayer K film and the zoom-in images from 3rd-layer (figure S4b) and 4th-layer (figure S4c) terraces. We can see the bright stripe pattern in the small 3rd-layer terrace (~30nm).However, such a pattern cannot be seen in the 4th-layer terrace, which has a similar size (~30nm). It indicates that the formation of such bright stripe patternsis independent of the size of the terrace.

SYSTEM
At this point it is worthy remarking that the almost hexagonal (110)   We wish to emphasize that the emergence of the stripe-like pattern occurs spontaneously in this model and is a direct consequence of introducing the density of bulk K in the top layer.
The choice of a unit cell to fit both the bcc (110) surface atoms and hexagonal layer (beneath) enables the emergence of the stripe pattern. However, the theoretical description obtained is not perfect as the diagonal stripes are not continuous, and we believe that this is due to the periodic boundary conditions, as the experiment indicates that the angle between the stripes deviates from 60°. In other words, the orientation of the stripe pattern does not coincide with the hexagonal symmetry, and indeed we can observe a mismatch in the locations of maxima in the periodically repeated images (figure S5). We assume that larger atomic models (unit cells) may well resolve this problem, and that the connection between the herringbone pattern and linearly arranged line defects in the top K layer would appear even more visibly.
However, as noted in figure 1(main text), some undulation along the stripes seems to be apparent in the experimental STM images too. Finally, our calculations for 4-layer systems indicate that the single atom defects, as well as additional "lines", become energetically less favourable, explaining the disappearance of stripes in the STM images. Topology of the slab, 2×2 replicated cell.

SIMULATED LAYER HEIGHTS IN STM IMAGES
The STM layer heights for different number of monolayers were simulated using a surface 6 bias voltage of -2 V and an s-orbital for the tip (main text, figure 4). The reference value of the STM density isosurface, however, was calibrated to the experimental STM height of the second layer. Here an isovalue was chosen so as to obtain the STM height for the second layer as closely as possible to the experimental one. As seen from the layer heights thus obtained, the simulated values have the same trend as the experimental ones (Table S2). The contrast with plain graphite is visible as the first layer is more than 2 Å thicker than any other K layer, and the second and the fourth layers are thicker than the third one. The STM effect is more enhanced than the geometrical effect, where the variations of layer height are between 3.5-4.0 Å for 2-4 ML. The K monolayer separation from the graphite surface is drastically overestimated by STM due to charging effects.
Bader charge analysis for the multilayer systems revealed charging of the surface atoms, and this is visible from the partial charge per surface atom (Table S2). The partial charges are presented in units of elementary charge. The average partial charge per surface atom shows correlation with the simulated layer heights. whereE inters is the total energy of the system with the defect, E ideal is the energy of ideal system and E singleK is the energy of single potassium atom in the same simulation cell. Similarly, we compute the vacancy formation energy as whereE vacancy is the total energy of the system with a single vacancy on the surface.
Cohesive energy E coh was calculated with the equation, whereE tot is the total energy of the system, E graph is the energy of the graphite slab in same calculation cell, N is the number of potassium atoms and E singleK is the energy of single potassium atom in the same calculation cell.

FURTHER INFORMATION OF ATOMIC MODELS
In addition to defect rows, the stack change structure was tested in the same hexagonal unit cell of lateral size 29.47 Å for both two and three layer systems with two graphene layers (see main text, Table 1, system VI). For example, for the bilayer system the second layer was 8 changed from B stacking to C and lines in the stacking change region were placed higher from the surface plane. After geometry optimization the structure had one line in the third layer and second layer had same number of atoms than ideal (2×2) layer (stack change still visible). The starting and optimized geometry are presented in figure S6. The resulting totalenergies of such stack change systems were higher (unfavourable) than for the other systems with the defects (lines). Furthermore, this construction is not a plausible reason for the herringbone pattern because the line in the third layer is more than 3 Å higher than the second layer, which is not comparable to experimental data of the STM heights. The same effect was observed for the optimized 3-layer system with stack change, although the height change had reduced to 2 Å. A laterally larger unit cell was used in order to be able to simulate a potassium bcc (110) layer on a (2×2) commensurate potassium layer and support. At first, the bcc (110) layer and (2×2) layers were placed artificially close to each other, and the system relaxed to a structure resembling the herringbone pattern. The effect was lost and the bcc (110) layer stayed intact (figure S7) when the distance between the layers in the starting structure was increased to a more natural level (no compression). The resulting cohesive energy per K atom was noticeably less favourable (lower) than that for the defected structure.
Next idea was to consider the lateral interplay between different lattices; hexagonal (2×2) vs.

CONSTRUCTION OF GEOMETRIES
The (2×2) potassium layer was based on a previously optimized structure in a smaller hexagonal cell. This was expanded periodically to form a larger slab. The bcc (110) layer was cut out from the bulk structure and put on the (2×2) layer after a suitable rotation along the surface normal. The unit cell size was selected to fulfill periodic boundary conditions for all the layers (graphite, (2×2) potassium and bcc (110) (110) layer. To reduce the simulation load, a single layer of graphene was used as a (fixed) support, and the lower (2×2) potassium layer was kept fixed also.