Speaker
Description
The crystal structures of transition metal dichalcogenide materials (TMDs) with metal atoms from group 7 of the periodic table (“$d^3$” TMDs), such as ReS$_2$, are known to be distortions of a triangular lattice. Similarly, the crystal structures of some pnictogen solids, such as elemental antimony, are distortions of a simple cubic lattice. The atoms in these materials are known to form covalent bonds. We model covalent bonding by constructing dimer models on the triangular lattice and simple cubic lattice. In these models, a dimer is a line drawn on the lattice to represent a single bond. Dimers are allowed to interact and move, with the lowest-energy arrangement interpreted as yielding the crystal structures of the materials. The energy is written down on physical grounds: bonds that are closer interact stronger. As each atom forms three covalent bonds, there are three dimers that touch at each site – a local “trivalent” constraint. Additionally, no two dimers that touch at a site can be parallel – a local “bending” constraint that arises from intra-orbital repulsion. Due to these constraints, there is no local dynamics. The constraints also cause dimers to form long-ranged patterns across a system. We therefore know the structure of dimers within a bounded system by observing dimers on its surfaces – a holographic principle. We construct phase diagrams of dimer structures on both lattices as energy parameters are varied. We find a phase that resembles the crystal structure of $d^3$ TMDs, while every phase on the cubic lattice resembles both experimentally observed and theoretically stable structures of pnictogen solids. Thus, the holographic principle in our models describes structures of real materials. It might be possible to harness holography for information storage and for understanding and manipulating their mechanical or electronic properties.
| Keyword-1 | Holographic Principle |
|---|---|
| Keyword-2 | Dimer Models |
| Keyword-3 | Crystal Lattices |