Berry phase modification to electron density of states and its applications

We study the Berry phase correction to the electron density of states and present a number of its applications. It is now well recognized that the Berry phase of the electronic wave function plays an important role in the dynamics of Bloch electrons. For instance, the electron will acquire an anomalous velocity term transverse to the applied electric field, giving rise to an intrinsic contribution to the anomalous Hall effect. On the other hand, we find that the Berry phase also has a fundamental effect on the electron phase space, and leads to a modification of the phase-space density of states. This surprising result has a number of applications, which we shall discuss in detail. We first derive an explicit expression of the orbital magnetization (zero and finite temperature), where it is shown that contributions to the orbital magnetization can be classified into a local rotation of the electron and global centerof-mass motion. Based on this formula, we develop a theory of the Berry-phase effect in anomalous transport in ferromagnets driven by statistical forces such as the gradient of temperature or chemical potential. We also study the Berry phase effect on magnetotransport, showing that a linear (in field) magnetoresistance is possible in ferromagnets. Finally, we propose that in graphene with broken inversion symmetry, a valley Hall effect exists and the finite valley polarization can be detected by measuring the magnetization.