The recent discovery of unconventional Mott-like and superconducting phases in twisted bilayer graphene rotated at the magic angle has inspired experimental and theoretical interest in van der Waals heterostructure systems. These vertical heterostructures involve stacks of various two-dimensional layers. It is crucial to develop a systematic and efficient numerical approach to modeling these systems, in order to navigate the extensive parameter space it can give. However, the computations are challenging due to the system size. In our group, we developed an ab initio multi-scale numerical scheme to simulate these systems, which is based on Wannier transformations on top of the density functional theory calculations. We have applied these methods to study the electronic and mechanical properties of many structures such as bilayer graphene, trilayer graphene, transition metal dichalcogenide (TMD) bilayers, and Janus TMDs.

Two-dimensional (2D) Materials

Graphene nanoribbons are few-atom wide strips of hexagonally-bonded carbon atoms which can exhibit semiconducting character. Furthermore, their electronic structure can be engineered via electrical and mechanical stimuli, enabling control over the band gap, the topological quantum phases, and the electrons with linear energy dispersion.

A promising route to improving the thermoelectric performance of devices is to use layered materials such as tin selenide (SnSe) and germanium selenide (GeSe) that have large in-plane anisotropy that can facilitate electron transport while maintaining low lattice thermal conductivity. Accurate calculations of the transport properties of such materials are still computationally intensive, so we have developed a dual-interpolation technique to make calculations feasible with the necessarily dense sampling of momentum space for both the electronic carriers and phonons.

One method of functionalizing nanostructures is by introducing intercalants, such as lithium, between the layers. In addition to direct applications in battery technology, the presence of intercalants can modify the electronic properties through structural changes and electron doping.

Machine Learning Applications

Machine learning tools, in particular neural networks, can be used to tackle scientific problems from new angles. Our group has leveraged these numerical methods to explore the solutions a wide variety of problems, from the exploration of the vast number of novel materials available for nanoscale devices to solutions of the Schrodinger equation for molecular and periodic systems, to the effectiveness of vaccines during the SARS-CoV-2 pandemic.

The entire space of materials - including organic and inorganic crystal structures - is huge. Insight into the behavior of materials can be gained by using data-driven tools to reveal hidden physical relationships which are embedded in a high-dimensional feature space, not readily perceived without statistical tools. The goal of this research is multifaceted and includes both knowledge discovery - gaining new physical insight through data analytics methods - and materials discovery. The Kaxiras group has used machine learning tools to explore two-dimensional magnetic materials, catalysis on metal surfaces and branched electronic flow in graphene. 

The expressiveness of neural networks allows us to simultaneously solve physically relevant differential equations for a variety of parameter choices, or "bundles", eliminating the need to redo the solution for each new set of parameters. Combined with measurements or data, this can yield a solution to the "inverse problem", the determination of the relevant parameters in the equations, such as those governing disease spread.