Colloquium with Jacob Gayles, Assistant Professor, University of South Florida, Department of Physics.

The advent of quantum materials has penetrated nearly every aspect of human society, from fundamental research to practical applications, due to the ability to engineer them from the quantum constituents. The materials take advantage of the momentum space electronic structure and real space magnetic structure and have come to the forefront of condensed matter research due to their exotic transport properties inherently tied to their symmetry and echoes of relativity in real materials. The advent of such materials comes from the Nobel prize winning experimental discovery of graphene, a 2D carbon allotrope which host Dirac Fermions in the low energy limit. Nearly simultaneously, the Nobel Prize experiments on giant magnetoresistance led to research on novel magnetic phases. Since these two groundbreaking Nobel prizes experiments the Weyl semimetal and the Skyrmion phase have been discovered. The Weyl semimetal and the magnetic Skyrmion phase are two quantum phenomena that have recently become of great interest, both of which display unique topological phases. Weyl materials have a topological crossing of the bands with high mobilities, which lead to efficient charge to spin conversion. The skyrmion, a topological magnetic texture, can be manipulated efficiently by external fields, as an advantageous route for next-generation devices. We begin discussing the historic view of how understand the electronic and magnetic behavior in materials. We then will introduce the minimal crystal symmetries and Hamiltonians that determine these quantum materials. We will show how to compute and observe such phenomena and detail the success of combined experimental and theory methods. We will focus on materials in which these phenomena have been experimentally observed and predicted. These phenomena show emergent electromagnetic fields where the language of Berry curvature simplifies the understanding.  Lastly, we will discuss the combination of these quantum phenomena in heterostructure Weyl/Skyrmion and the coexistence of both in a single bulk material. The connection these seemingly dissimilar quantum phenomena may give rise to new device applications and novel implications for fundamental physics.