Berry Phase Effects on Electronic Properties

Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A common thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.Comment: 48 pages, 16 figures, submitted to RM

Electronic transport in two dimensional graphene

We provide a broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature dependent carrier transport in doped or gated graphene structures. A salient feature of our review is a critical comparison between carrier transport in graphene and in two-dimensional semiconductor systems (e.g. heterostructures, quantum wells, inversion layers) so that the unique features of graphene electronic properties arising from its gap- less, massless, chiral Dirac spectrum are highlighted. Experiment and theory as well as quantum and semi-classical transport are discussed in a synergistic manner in order to provide a unified and comprehensive perspective. Although the emphasis of the review is on those aspects of graphene transport where reasonable consensus exists in the literature, open questions are discussed as well. Various physical mechanisms controlling transport are described in depth including long- range charged impurity scattering, screening, short-range defect scattering, phonon scattering, many-body effects, Klein tunneling, minimum conductivity at the Dirac point, electron-hole puddle formation, p-n junctions, localization, percolation, quantum-classical crossover, midgap states, quantum Hall effects, and other phenomena.Comment: Final version as accepted for publication in Reviews of Modern Physics (in press), 69 pages with 38 figure

Electronic Properties of Graphene in a Strong Magnetic Field

We review the basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field. One of its most salient features is the relativistic quantum Hall effect the observation of which has been the experimental breakthrough in identifying pseudo-relativistic massless charge carriers as the low-energy excitations in graphene. The effect may be understood in terms of Landau quantization for massless Dirac fermions, which is also the theoretical basis for the understanding of more involved phenomena due to electronic interactions. We present the role of electron-electron interactions both in the weak-coupling limit, where the electron-hole excitations are determined by collective modes, and in the strong-coupling regime of partially filled relativistic Landau levels. In the latter limit, exotic ferromagnetic phases and incompressible quantum liquids are expected to be at the origin of recently observed (fractional) quantum Hall states. Furthermore, we discuss briefly the electron-phonon coupling in a strong magnetic field. Although the present review has a dominating theoretical character, a close connection with available experimental observation is intended.Comment: 56 pages, 27 figures; published version with minor corrections and updated reference

Berry phase modification to electron density of states and its applications

textWe 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.Physic