Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids (1203.2697v2)

Abstract: In a three-dimensional Fermi liquid, quasiparticles near the Fermi surface may possess a Berry curvature. We show that if the Berry curvature has a nonvanishing flux through the Fermi surface, the particle number associated with this Fermi surface has a triangle anomaly in external electromagnetic fields. We show how Landau's Fermi liquid theory should be modified to take into account the Berry curvature. We show that the "chiral magnetic effect" also emerges from the Berry curvature flux.

• The paper introduces a modified Fermi liquid framework by incorporating nonzero Berry curvature flux to bridge topological effects with traditional quasiparticle theory.
• It derives altered commutation relations that produce the chiral magnetic effect, revealing a dissipationless current response under applied magnetic fields.
• The study extends kinetic equations with topological corrections, paving the way for experimental insights in materials like Weyl semimetals and quark matter phases.

Berry Curvature, Triangle Anomalies, and the Chiral Magnetic Effect in Fermi Liquids

The paper authored by Dam Thanh Son and Naoki Yamamoto substantially advances the understanding of Berry curvature and its implications within the context of Fermi liquids. Traditionally, the Landau Fermi liquid theory has described the low-energy excitations in terms of quasiparticles without including topological effects such as Berry curvature. This paper proposes necessary modifications to account for these effects, particularly when Berry curvature flux does not vanish through the Fermi surface.

The authors derive that the inclusion of Berry curvature in a Fermi liquid leads to a modification in the commutation relations of the quasiparticle density operators. This modified structure results in the emergence of the chiral magnetic effect (CME) within a Fermi liquid, which had previously been recognized in relativistic quantum field theories. The CME describes a phenomenological response where an external magnetic field combined with a non-zero Berry curvature flux induces a dissipationless current along the field direction.

The theoretical framework presented innovatively extends the kinetic equation of the Landau Fermi liquid theory to a Hamiltonian system accommodating Berry curvature. The Poisson brackets of classical mechanics are thus modified in the presence of Berry curvature, leading to new formulations for the dynamics of quasiparticles. This adaptation is especially relevant for exotic materials such as Weyl semimetals, where nontrivial band topology and Berry curvature are known to play essential roles.

Key results are embodied by the equation:

$$\frac{\partial n}{\partial t} + \nabla \cdot j = \frac{k}{4\pi^2} \mathbf{E} \cdot \mathbf{B},$$

where $E$ and $B$ represent the electric and magnetic fields, respectively, and $k$ stands for the monopole charge associated with the Berry curvature flux through the Fermi surface. This equation is akin to the triangle anomaly equation in quantum field theory, formulated here in the context of Fermi liquids enriched with Berry curvature.

The implications of this work are multifold. Practically, it suggests that strongly interacting electronic systems, previously describable only without topological considerations, may exhibit novel electromagnetic responses when Berry curvature is incorporated. Theoretically, this work proposes a deeper connection between topological effects and traditional many-body physics, expanding the landscape for analyzing Fermi surface-related phenomena beyond conventional approaches.

Future directions motivated by this research could explore the inclusion of collision terms in the kinetic equations to probe the hydrodynamic regime, where Berry curvature effects manifest in collective modes of the Fermi liquid. Secondly, given the fundamental connection between topology and anomalies outlined here, further studies could focus on applying these principles to quark matter phases, a topic of interest in high-energy physics.

In conclusion, Son and Yamamoto's work presents a refined understanding of how topological constructs like Berry curvature impact Fermi liquid theory. This could potentially lead to novel experimental predictions and observations in materials exhibiting strong correlations and topological excitations. This formulation also paves the way for further theoretical advancements in understanding anomalies in condensed matter systems, suggesting a rich domain for future exploration.