# Research

## Quantum Hall effect interferometry

As two indistinguishable particles interchange positions in 3D universe, their many-body wavefunction acquires zero or π phase shift for bosons and fermions, respectively. It has been believed that the dichotomy of the symmetry under an exchange operation is the fundamental property which can classify the all particles in our universe. However, this dichotomy can be broken in the 2D space, where the many-body wave function of excitations, anyons, unlike fermions and bosons, may exhibit a non-trivial exchange phase for Abelian anyons, or even rotate to a new wavefunction for non-Abelian anyons. Among the various two-dimensional charge systems, the fractional quantum Hall effect states are predicted to host these novel quasi-particles.

## Hybrid van der Waals heterostructures

Topological superconductivity is a unique quantum phase of matter, not just characterized by the ability to conduct electrical current with zero resistance, but also involving the presence of special boundary states that behave similar to Majorana fermions, particles that are their own antiparticles. These states are called Majorana zero modes and their presence in a topological superconductor is tied to the material's unique electronic structure and the interaction between superconductivity and spin-orbit coupling. This results in protected states that are robust against external perturbations, making them potentially useful for quantum information storage and manipulation. One way to achieve these properties simultaneously is to assemble together a heterostructure of corresponding atomic layers.

## Paired composite superfluid phases

Many of the phenomena in condensed matter physics are based on correlations between electrons where strong interactions among electrons lead to new entities and new states of matter. One of the most celebrated examples is the fractional quantum Hall effect which is the result of the highly correlated motion of electrons in two-dimensions exposed to a strong out-of-plane magnetic field, moreover, exhibit topological order. Its driving force is the reduction of Coulomb interaction between the like-charged electrons.

## Twistronics

Electronic systems, which have energy bands independent of momentum called flat bands, provide a platform where electrons' coulomb interactions dominate over their kinetic energy. This platform can be used to study strongly correlated phenomena like superconductivity and magnetism. 2D van der Waals materials like graphene, hBN or transition metal dichalcogenides are placed on top of each other in various combinations to make samples to study these phenomena. One interesting combination is to place two or more graphene layers on top of each other at some relative twist angle. The relative rotation of these layers creates moiré superlattices that results in electronic flat bands. Various correlated and topological electronic states have been realized in these flat band systems.