We provide a geometrical argument for the emergence of a Wess-Zumino-Witten (WZW) term in a Fermi surface threaded by a Berry curvature. In the presence of external fields, the gauged WZW term yields a chiral (triangle) anomaly for the fermionic current at the edge of the Fermi surface. Fermion number is conserved though since Berry curvatures occur always in pairs with opposite (monopole) char...

Recently, the semiclassical theory of the anomalous Hall effect induced by the Berry curvature in Bloch bands has been introduced. The theory operates only with gauge invariant concepts, that have a simple semiclassical interpretation and provides a clear distinction among various contributions to the Hall current. While the construction of such an approach to the anomalous Hall effect problem ...

We outline a designer approach to endow widely available plain materials with topological properties by stacking them atop other nontopological materials. The approach is illustrated with a model system comprising graphene stacked atop hexagonal boron nitride. In this case, the Berry curvature of the electron Bloch bands is highly sensitive to the stacking configuration. As a result, electron t...

Based on the Keldysh formalism, we derive an effective Boltzmann equation for a quasiparticle constrained within a particular Fermi surface in an interacting Fermi liquid. This provides a many-body derivation of Berry curvatures in electron dynamics with spin-orbit coupling, which has received much attention in recent years in noninteracting models. As is well known, the Berry curvature in mome...

In this paper we have studied a new form of Non-Commutative (NC) phase space with an oper-atorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an " internal " magnetic field, that is singular at a specific position θ −1. By " internal " we mean that the effective magnetic fields depends essentially on the particle properties and modifies the s...

In this paper we have studied a new form of Non-Commutative (NC) phase space with an oper-atorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an " internal " magnetic field, that is singular at a specific position θ −1. By " internal " we mean that the effective magnetic fields depends essentially on the particle properties and modifies the s...

An isolated classical chaotic system, when driven by the slow change in several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations, we show that this holds true also for open quantum systems and provide explicit expressions for those forces in this case. This extends the concept of Berry curvature to th...

Comment on " Berry phase correction to electron density in solids " by Xiao et al. Abstract The main result of Xiao et al. In a recent paper on the semiclassical dynamics of a Bloch electron, Xiao, Shi and Niu [1] claim that, due to a Berry curvature term, Liouville's theorem on the conservation of the phase-space volume element would be violated, a fact which would have been overlooked so far....

In this paper we have studied a new form of Non-Commutative (NC) phase space with an oper-atorial form of noncommutativity. A point particle in this space feels the effect of an interaction with an " internal " magnetic field, that is singular at a specific position θ −1. By " internal " we mean that the effective magnetic fields depends essentially on the particle properties and modifies the s...