ETD

• anyon superconductivity
• anyons
• fractional Chern insulators
• moiré materials
• semions
• transition metal dichalcogenides
• unconventional superconductivity

In 2D systems, configuration space topology allows for anyons, quasiparticles that acquire an arbitrary phase factor upon exchange. A recent observation of a fractional Chern insulator (FCI) state near an unconventional superconducting phase in twisted MoTe2 suggests this superconductivity is mediated by FCI anyonic excitations. While current literature focuses on how the moiré potential stabilizes the superconducting anyon type, this thesis addresses a complementary question: how does the moiré potential affect the superconducting phase?

To treat Coulomb repulsion, fractional statistics, and the moiré potential equally, we map anyons to fermions coupled to a statistical gauge field via flux attachment. Because a mean-field approximation yields a non-superconducting state, we use the random phase approximation (RPA) to capture density and current fluctuation interactions. To evaluate the system self-consistently, we develop a single-particle basis that captures both the statistical magnetic field and the discrete translational symmetry. Evaluating the electromagnetic response then allows us to extract the superfluid stiffness.

We numerically apply this framework to semions in a square lattice sinusoidal potential at filling factor 1. Our analysis reveals a potential-driven topological phase transition to a trivial state. RPA calculations demonstrate that superfluid stiffness decreases as the potential strengthens and vanishes at the phase transition, where the system becomes an ordinary diamagnet.