Topological nature of multi-weyl semimetals

Abstract

Berry curvature in Weyl semimetals plays a critical role in shaping the topological properties and electronic transport phenomena of these materials. Weyl semimetals, characterized by the presence of Weyl nodes (monopoles of Berry curvature) show unique features such as Fermi arcs on their surface and nontrivial responses to external fields. This report provides a brief overview of the concept of Berry curvature in the context of Weyl semimetals, discussing its emergence from the topology of the electronic band structure and its influence on various physical observables, such as the anomalous Hall effect, chiral anomaly, and magneto-resistance. The role of Berry curvature in mediating the dynamics of charge carriers, particularly its effect on the velocity and current response of electrons near the Weyl nodes, is also explored. Landau quantization comes from charged particles occupying quantized energy levels in presence of magnetic field. It is mainly studied in reference of the two dimensional electron gas. When electron are placed in magnetic field then motion is restricted in plane perpendicular to magnetic field. Energy associated with Landau level is like harmonic oscillator in quantum mechanics. Landau levels help understand Quantum hall effect where conductance in 2d electron gas becomes quantized.