Research Projects

In this project we shall study the quantum anomalies and transport currents driven purely by these anomalies in unconventional topological semimetals. It will contribute to building connections between topological phases of matter, effective field theories (EFT), and physics of anomalies beyond that addressed so far. Quantum anomalies are non-conservation of classically conserved current due to quantum effects. One of the most famous examples is the chiral anomaly, which is the violation of chiral current conservation, was first predicted for Weyl Fermions in the context of particle physics. Weyl semimetals, which host Weyl Fermions as low energy quasi particles, also realizes this effect and thus becomes test bed for high energy physics. Semimetals are materials where the conduction and valence bands touch at a finite number of discrete points, known as Fermi points or nodes—unlike metals, which have a continuous Fermi surface. These nodes carry quantized topological charges. When the nodes have a unit topological charge and host quasiparticles described by the Weyl equation, the system is called a Weyl semimetal. More recently, this concept has been extended to include nodes with higher topological charges, which give rise to emergent particles that may not follow Lorentz symmetry. These emergent particles possess different anomalous symmetries, which lead to novel charge and thermal transport that can be measured experimentally. Recent developments on spin-1 fermions suggest a generalized EFT description of these higher order topological semimetals in terms of N-flavor Weyl fermions coupled to Lorentz symmetry breakng non-Abelian potential which in general is momentum dependent and couples to electromagnetic potential via minimal coupling. Such an EFT description will allow us to study different quantum anomalies and the corresponding transport current. This project will investigate the following key questions: What is the generalized EFT description for these unconventional semimetals? How the modified Dirac operator in the generalized EFT alters the Index theorem ? How the Lorentz violation in such systems affect charge and thermal transport driven by anomalies? Using the methods of quantum field theories along with Luttinger correspondence between temperature gradient and gravitational potential and linear response theory of transport we shall answer these questions.