Quantum Penomena in low-dimensional Nanostructures

One of the discoveries that have been made with graphene, a two-dimensional (2D) crystal that has led to the Nobel prize of physics, is that functionality can be introduced by the crystal lattice: as monolayer, its honeycomb lattice raises Dirac points in the electronic structure, which makes it theorist's simplest 2D topological insulator. A 2D topological insulater is a material where the symmetry of the crystal lattice imposes protected electronic state at the edges, yielding dissipation-free spin and charge currents independent on the edge termination and environment. As bilayer, a slight twisting generates flat electronic bands which make it superconducting. The concept of lattice-imposed functionality is not deeply known at present.
We are currently investigating the twisting effects in twister bilayers beyond graphene, e.g. bilayers of MoS2. In these cases, our calculations show a strong restructuring effect, giving raise to large, ordered bilayer crystal domains and domain walls with intriguing structural and electronic effects, including solitonic states, which allow structural information transfer through the crystal (Figure 1).

Besides the well-known honeycomb lattice, there are many more 2D lattices possible [1]. 2D polymers, new synthetic 2D materials, can in principle reflect any mathematically possible lattice topology. One of the most interesting ones is the Lieb lattice (Figure 2), a simple square lattice composed of building blocks with 4 and 2 connections. Due to the lattice topology, it features a flat band and a Dirac cone. This combination offers a rich physics, as it incorporates high-mobility charge carriers, very large densities of states with the potential emergence of Landau levels and superconductivity. 

A further topologically interesting network is the kagome lattice, which is closely related to the honeycomb lattice and can be obtained when triangular molecular building blocks are polymerized [2]. These 2D polymers also feature Dirac cones and flat bands. They have been realized recently in experiment and proof, for the first time, that the electronic structure inherent to the lattice is also reflected in a 2D polymer where the high-symmetry lattice points are represented by rather large molecular units rather than individual atoms (Figure 3) [3].

Besides the intriguing electronic properties that call for further investigations as topological materials, superconductors or quantum computers, these materials may have the potential to act as metal-free catalysts in chemistry applications.
One of the big obstacles in the transition to a green energy production is to convert solar to chemical energy, e.g. to produce hydrogen by water splitting. Such photocatalysts heavily rely on platinum as catalyst, which prevents wide-range application, in particular in decentralized facilities. The catalyst needs to drive the two half-reactions of the water splitting process, namely the oxygen and hydrogen evolution. In a detailed analysis, we have shown that the above-mentioned honeycomb-kagome 2D polymers can be tailored by a rational choice of the center atom: if it is boron, then the overall chemical potential is lowered, while it is high if a nitrogen resides at the center. If combined in a tandem cell and electrically coupled, these materials show the possibility to become highly efficient photocatalysts capable of splitting water molecules by absorbing visible light, without any additional sacrificial agent, catalyst, or external potential (Figure 4) [4].  

References
[1] Topological two-dimensional polymers, M. A. Springer, T.-J. Liu, A. Kuc, T. Heine, Chem. Soc. Rev. 49 (2020) 2007-2019
[2] Two-dimensional Kagome Lattices Made of Hetero Triangulenes are Dirac Semimetals or Single-Band Semiconductors, Y. Jing, T. Heine, J. Am. Chem. Soc. 141 (2019) 743-747
[3] Making 2D topological polymers a reality, Y. Jing, T. Heine, Nat. Mater. 19 (2020) 823-824
[4] 2D Honeycomb-Kagome Polymer Tandem as Effective Metal-Free Photocatalysts for Water Splitting, Y. Jing, Z. Zhou, W. Geng, X. Zhu, T. Heine, Adv. Mater. 33 (2021) 2008645