Modulating the thermal and structural stability of gallenene via variation of atomistic thickness

Using ab initio molecular dynamics, we show that a recently discovered form of 2D Ga—gallenene—exhibits highly variable thickness dependent properties. Here, 2D Ga of four, five and six atomic layers thick are found to be thermally stable to 457 K, 350 K and 433 K, respectively; all well above that of bulk Ga. Analysis of the liquid structure of 2D Ga shows a thickness dependent ordering both parallel and perpendicular to the Ga/vacuum interface. Furthermore, ground state optimisations of 2D Ga to 12 atomic layers thick shows a return to a bulk-like bonding structure at 10 atoms thick, therefore we anticipate that up to this thickness 2D Ga structures will each exhibit novel properties as discrete 2D materials. Gallenene has exciting potential applications in plasmonics, sensors and electrical contacts however, for the potential of 2D Ga to be fully realised an in depth understanding of its thickness dependent properties is required.


Ground state optimisation
In order to determine the surface termination that should be used for seeding ab initio molecular dynamics (AIMD) simulations at finite temperature, four different quad-layer structures across both α and β phases of bulk Ga were optimised to find the lowest energy ground state structure. Three of the four structures were cut from the α-Ga phase and one was cut from the β-Ga phase. The three α-Ga structures are analogous to those found by Kochat et al. and labelling is kept consistent with their systems. 20 We choose these terminations as they have been found to be experimentally stable, in preference over all other surface terminations thus removing the requirement to test all surface terminations. That being said, we also trial one quad-layer β-phase termination in order to check that we are not missing a lower energy state.
Initial bulk crystals were taken from the Crystallography Open Database α-Ga with unit cell dimensions of 4.527 × 7.645 × 4.511Å was used for α-Ga based systems 11 and β-Ga with unit cell dimensions of 2.791 × 7.890 × 3.286Å was used for β-Ga based structures. ? Three of the four structures were cut from the α-Ga phase and one was cut from the β-Ga phase. The three α-Ga structures are analogous to those found by Kochat et al. and labelling is kept consistent with their systems. 20 Each surface is periodic in x and y dimensions, and separated from the next unit in the z direction by 30Å of vacuum. All surfaces were four atomic layers thick and all unit cells contained 8 atoms. Below details a list of the terminations of the four quad-layer structures. Graphic representations of initial and optimised structures can be found in Table S1.
• Surface 1: α-a 100 : Cut along the (100) plane of bulk α-Ga • Surface 2: α-b 010 a: Cut along the (010) plane of bulk α-Ga, cutting through covalent dimers to generate the surface. This results in a metallic layer, followed by a Ga 2 dimer, followed by a metallic layer.
• Surface 3: α-b 010 b: Cut along the (010) plane of bulk α-Ga, cutting through metallic planes to generate the surface. This results in two layers of stacked Ga 2 dimers.
• Surface 4: β-a 001 : Cut along the (001) plane of bulk β-Ga 1 Electronic Supplementary Material (ESI) for Nanoscale Advances. This journal is © The Royal Society of Chemistry 2020 In all of the α-Ga surfaces, the Ga 2 dimers align with the z dimension upon optimisation. The only structure to display covalency, from the ELF, upon optimisation is α-b 010 a. The α-b 010 a is the lowest energy ground state structure after optimisation. However, the relative energies of all optimised ground-state structures are within 0.1 eV atom -1 making them competitive structures (Table S1).
Profile of average energy as a function of average temperature during annealing Figure S1: Average energy as a function of average temperature for (a) quad-layer, (b) pentalayer and (c) hexa-layer over the course of the annealing simulations.  Figure S2: Radial distribution function of the optimised lowest energy structures of (a) quadlayer, (b) penta-layer and (c) hexa-layer compared to bulk α-and bulk β-Ga. Figure S3: Electron localisation functions for optimised lowest energy structures of (a) bulk α-Ga and resulting from the phase change observed during annealing of (b) quad-layer, (c) the penta-layer and (d) the hexa-layer structure. Isosurface level set to 0.80 and the bond length cut off was set to 2.7Å.

Electron Localisation Function of lowest energy structures
Band structure of lowest energy structures Figure S4: Band structure of optimised lowest energy (a) quad-layer (b) penta-layer and (c) hexa-layer structures.
Electron Localisation Function analysis as a result of increasing the number of layers in the 2D system. Table S3: Increasing the number of layers to examine the convergence to the bulk alpha-Ga structure using electron localisation function. Bonds less than 2.6Å are shown. Isosurface value is set to 0.77. Red atoms denote the quad-layer system, purple represents penta-layer, green represents hexa-layer and blue atoms denote all other optimised systems.    Figure S8: Orientational order correlation function (g 6 (r)) as a function of temperature for (a) quad-layer, (b) penta-layer and (c) hexa-layer. We use the lowest finite temperature simulation as the high temperature "solid" phase and the highest temperature finite temperature simulation as the "liquid" phase. The transitional structure between the solid and liquid comes from the finite temperature in closest proximity to the melting temperature; 450 K for the quad-layer system (T melt : 457 K), 340 K for the penta-layer system (T melt : 350 K) and 440 K for the hexa-layer system (T melt : 430 K).