Novel nanomaterials and their heterostructures play a central role in current computational material science research. Recent experimental progress has seen an appearance of several two-dimensional solids with a wide range of electronic properties, ranging from the famous semi-metal graphene to strongly insulating hexagonal boron nitride. Modern synthesis techniques for the creation and manipulation of stable layers of two-dimensional crystals have now become well developed. Likewise, noble metal nanoclusters feature high catalytic reactivity and sharp plasmonic resonances that can be tailored to specific energies. By depositing and subsequent transfers, individual layers may be combined like a sandwich, stacking layers in a predefined sequence. The resulting van der Waals heterostructures exhibit interesting new effects that go beyond the physics accessible only by a single layer. Nanostructure devices composed of such components promise a wide range of applications, from highly efficient catalysts or solar cells to ultra-low-power nanoelectronics.

Simulation of nanodevices

Our research focuses on simulating new nanostructure materials composing realistic nanodevices, including defects and impurities. The term nanodevice in this context refers to the typical device size, up to a few micrometers and containing millions of atoms, but still below mesoscopic dimensions. Consequently, quantum effects play an important role. The theoretical description of these systems thus poses a challenging multi-scale problem, requiring active method development. We simulate transport through nanodevices built by our experimental collaborators (for example at RWTH Aachen or ETH Zürich) as well as the electronic structure and properties of low-dimensional materials and their heterostructures.

Success through imperfection

A small lattice mismatch between adjacent layers, for example for graphene and hexagonal boron nitride, gives rise to regular, periodic moiré patterns. Even in structures composed of layers of the same material, twisting the layers with respect to each other will induce moiré potentials, whose periodicity sensitively depends on the twist angle. The resulting heterostructures feature altered electronic properties such as unconventional superconductivity or Mott-insulating phases. From a broader scope, twist angles allow for modifying the band structure of the heterostructure in surprising ways, promising a pathway towards engineering of desired material properties. Unfortunately, theoretical treatment of the large unit cells of moiré patterns, including a substrate and adjacent functional layers makes a full ab-initio treatment challenging. In an ongoing collaboration with Allan McDonald (Houston, TX, USA), we are developing moiré potentials for twisted trilayer graphene as well as transition metal dichalcogenides. Using an effective moiré potential, we can reproduce the observed fine structures resulting from the moiré. Using a quantum dot induced by an STM tip, our experimental collaborators at RWTH Aachen were also able to directly probe moiré potentials, which compared well to our simulations.

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