In a three-dimensional Fermi liquid, quasiparticles near the the Fermi surface may possess 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.

A kinetic theory can be modified to incorporate triangle anomalies and the chiral magnetic effect by taking into account the Berry curvature flux through the Fermi surface. We show how such a kinetic theory can be derived from underlying quantum field theories. Using the new kinetic theory, we also compute the parity-odd correlation function that is found to be identical to the result in the perturbation theory in the next-to-leading order hard dense loop approximation.

We study the collective modes in relativistic electromagnetic or quark-gluon plasmas with an asymmetry between left-and right-handed chiral fermions, based on the recently formulated kinetic theory with Berry curvature corrections. We find that there exists an unstable mode, signaling the presence of a plasma instability. We argue the fate of this "chiral plasma instability" including the effect of collisions, and briefly discuss its relevance in heavy ion collisions and compact stars.PACS numbers: 12.38. Aw, 11.10.Wx, 12.38.Mh Introduction.-Parity violating effects related to quantum anomalies play an important role in a wide range of physics from quantum Hall systems to cosmology. One example in the transport phenomena is the parity violating current in the presence of a magnetic field and an asymmetry between left and right-handed fermions, parametrized by the chiral chemical potential µ 5 ≡ µ R − µ L . This is called the chiral magnetic effect (CME) [1][2][3][4][5]. Recently hydrodynamics [6] and kinetic theory [7][8][9][10][11] have been appropriately modified to describe quantum anomalies and the CME (see also Refs. [12,13]); in the kinetic theory, essential corrections are the Berry curvature, the concept diversely applied in condensed matter physics [14,15]. These developments enable us to systematically understand the properties and dynamical evolution of various systems with hitherto neglected anomalous effects.