Weyl Semimetals: Discovery of Exotic Electronic States and Topological Phases

Weyl Semimetals: Discovery of Exotic Electronic States and Topological Phases Mehmet Keçeci1 1ORCID : https://orcid.org/0000-0001-9937-9839, İstanbul, Türkiye Received: 17.05.2025 Abstract: Weyl semimetals (WSMs) have emerged as one of the most groundbreaking discoveries in condensed matter physics in recent years, deepening our fundamental scientific understanding and opening new horizons for future technologies. These materials are named after Hermann Weyl, who in 1929 predicted Weyl fermions – massless, chiral relativistic particles. WSMs, as low-energy excitations of these fermions in solid-state systems, possess special points in their electronic band structure where bands cross linearly, known as "Weyl points." These points act as sources or sinks (monopoles) of Berry curvature in momentum space and carry a definite chirality (right- or left-handed). For a material to host a WSM phase, either time-reversal symmetry or inversion symmetry must be broken. One of the most distinctive features of Weyl semimetals is the existence of unique topological surface states known as "Fermi arcs" on their surfaces. These arcs connect Weyl points of opposite chirality within the bulk and form open Fermi surfaces, which are absent in ordinary metals. The presence of Fermi arcs is strong evidence of the topological nature of WSMs and has been experimentally observed using techniques like angle-resolved photoemission spectroscopy (ARPES). Another crucial phenomenon is the "chiral anomaly." This is a quantum field theory effect where chiral charge is not conserved in the presence of parallel electric and magnetic fields, resulting in the pumping of Weyl fermions from one chirality to the other. In solid-state WSMs, the chiral anomaly leads to unusual transport properties, such as a characteristic negative longitudinal magnetoresistance and a giant anomalous Hall effect. These features are important experimental signatures for confirming the existence of Weyl fermions. WSM phases have been theoretically predicted and experimentally realized in various materials, including the TaAs family (TaAs, TaP, NbAs, NbP), WTe₂, MoTe₂, and magnetic WSMs. These materials exhibit a wide range of exotic physical properties, such as anomalous Hall conductivity, giant nonlinear optical responses, thermoelectric effects, and potential catalytic activities. The unique electronic and topological properties of Weyl semimetals make them highly promising candidates for potential applications such as low-energy-consumption electronics, spintronic devices, topological quantum computing, and even high-efficiency catalysts. Intensive research in material synthesis, characterization, and theoretical modeling is ongoing to unlock the full potential of these materials. The discovery of Weyl semimetals has opened up a new and exciting research area in condensed matter physics, highlighting the richness and complexity of topological matter. Keywords: Weyl Semimetals, Topological Phases, Weyl Fermions, Fermi Arcs, Chiral Anomaly, Electronic Band Structure, Berry Curvature, Anomalous Transport, Exotic Electronic States, Condensed Matter Physics.