Lattice Study Quantifies Chiral Anomaly at Fermi Surface

The subtle interplay between massless particles and electromagnetic fields, known as the chiral anomaly, presents a long-standing puzzle in physics, with implications for both particle physics and materials science. Huan-Wen Wang from the University of Electronic Science and Technology of China, along with Bo Fu and Shun-Qing Shen from The University of Hong Kong, now offer a fresh perspective on this phenomenon. Their work reinterprets the chiral anomaly as arising not from the behaviour of particles at specific energy levels, but from symmetry-breaking occurring in states far below the usual focus of investigation. This analysis demonstrates that the anomaly is protected by local chiral symmetry and provides a potential theoretical framework for applying the concept of chiral anomaly to a wider range of condensed matter systems, potentially unlocking new avenues for materials design and discovery.

The behaviour of these fermions near their zero-energy point and at high energies receives considerable attention. When exposed to electromagnetic fields, the chiral coefficient, a measure of the anomaly, is found to generally depend on the chemical potential, but is precisely quantised at the Fermi surface where chiral symmetry is preserved. This result provides an alternative interpretation of the chiral anomaly on a lattice; the anomaly arises from symmetry-breaking states at energies below the Fermi surface, and is protected by local chiral symmetry.

Topological Materials and Quantum Hall Effects

This extensive list of references details research related to topological materials, the quantum anomalous Hall effect, and related phenomena. The bibliography covers a broad range of topics, including foundational concepts, specific materials, and theoretical and experimental approaches. It highlights the importance of symmetry in classifying these materials and understanding their unique properties. The references begin with core concepts and foundational work on topological insulators and semimetals, including their classification, surface states, and potential applications. The collection then extends to the quantum anomalous Hall effect, a quantum Hall effect observed without an external magnetic field, arising from intrinsic magnetism and band structure topology.

The role of the Chern number in characterizing this effect and leading to quantized Hall conductance is central to many of the listed works. Further references explore materials combining topological properties with magnetism, crucial for realizing the quantum anomalous Hall effect. The bibliography also includes research on second- and higher-order topological insulators, materials with topological states protected on hinges or corners. Theoretical and computational approaches, such as lattice gauge theory and first-principles calculations, are also well represented, alongside experimental signatures and detection techniques like transport measurements and angle-resolved photoemission spectroscopy. Overall, this bibliography represents a comprehensive overview of the rapidly evolving field of topological materials and related quantum phenomena.

Chiral Symmetry Protects Anomalous Fermion Currents

This research investigates the behaviour of massless Dirac fermions, particularly as they appear on the surfaces of three-dimensional materials known as Chern insulators. The study establishes effective models to describe these fermions in both one and three dimensions, accurately capturing their properties at both low and high energies. A key finding is that the chiral anomaly is linked to the breaking of chiral symmetry at energies away from the point where the fermion’s energy is zero, and is protected by local chiral symmetry. This provides a new perspective on understanding this anomaly within condensed matter systems.

The research demonstrates that, under certain conditions, the chiral current remains conserved even with a non-zero chemical potential. Furthermore, the study explores the magneto-electric effect in these three-dimensional Dirac fermions, finding it to be quarter-quantized under specific circumstances. These results contribute to a deeper understanding of quantum anomalies and may offer insights applicable to particle physics.