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.

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Berry phase effects on electronic properties

The linear dispersion relation in graphene gives rise to a surprising prediction: the resistivity due to isotropic scatterers, such as white-noise disorder or phonons, is independent of carrier density, n. Here we show that electron-acoustic phonon scattering is indeed independent of n, and contributes only 30 Omega to graphene's room-temperature resistivity. At a technologically relevant carrier density of 1 x1012 cm-2, we infer a mean free path for electron-acoustic phonon scattering of >2 microm and an intrinsic mobility limit of 2 x 105 cm2 V-1 s-1. If realized, this mobility would exceed that of InSb, the inorganic semiconductor with the highest known mobility ( approximately 7.7 x 104 cm2 V-1 s-1; ref. 9) and that of semiconducting carbon nanotubes ( approximately 1 x 105 cm2 V-1 s-1; ref. 10). A strongly temperature-dependent resistivity contribution is observed above approximately 200 K (ref. 8); its magnitude, temperature dependence and carrier-density dependence are consistent with extrinsic scattering by surface phonons at the SiO2 substrate and limit the room-temperature mobility to approximately 4 x 104 cm2 V-1 s-1, indicating the importance of substrate choice for graphene devices.

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Intrinsic and extrinsic performance limits of graphene devices on SiO2.

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.

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Electronic transport in two-dimensional graphene

Preface Acknowledgements Notation Part I. Overview and Background Topics: 1. Introduction 2. Overview 3. Theoretical background 4. Periodic solids and electron bands 5. Uniform electron gas and simple metals Part II. Density Functional Theory: 6. Density functional theory: foundations 7. The Kohn-Sham ansatz 8. Functionals for exchange and correlation 9. Solving the Kohn-Sham equations Part III. Important Preliminaries on Atoms: 10. Electronic structure of atoms 11. Pseudopotentials Part IV. Determination of Electronic Structure, The Three Basic Methods: 12. Plane waves and grids: basics 13. Plane waves and grids: full calculations 14. Localized orbitals: tight binding 15. Localized orbitals: full calculations 16. Augmented functions: APW, KKR, MTO 17. Augmented functions: linear methods Part V. Predicting Properties of Matter from Electronic Structure - Recent Developments: 18. Quantum molecular dynamics (QMD) 19. Response functions: photons, magnons ... 20. Excitation spectra and optical properties 21. Wannier functions 22. Polarization, localization and Berry's phases 23. Locality and linear scaling O (N) methods 24. Where to find more Appendixes References Index.

Electronic Structure: Basic Theory and Practical Methods

A broad review of recent research work on the preparation and the remarkable properties of intercalation compounds of graphite, covering a wide range of topics from the basic chemistry, physics and materials science to engineering applications.

Intercalation compounds of graphite

The low-lying particlelike excitations of a model linearly conjugated diatomic polymer, ${(A=B)}_{x}$, are found to be pairs of either spin-0 or spin-\textonehalf{} solitons with irrational charge values. The charge values and excitation energies are calculated as functions of the difference of the energy levels of the atomic $p$ orbitals of the two atomic constitutents of the unit cell. The phonon spectrum of the uniform polymer is also calculated.

Elementary Excitations of a Linearly Conjugated Diatomic Polymer

Charged Π-phase kinks in lightly doped polyacetylene

New, nonlinear, charged elementary excitations are predicted to occur for weakly pinned Fr\"ohlich charge-density-wave condensates at low temperatures.

Weakly Pinned Fröhlich Charge-Density-Wave Condensates: A New, Nonlinear, Current-Carrying Elementary Excitation

A model calculation shows that each phonon band which couples to the electron density in an organic linear-chain semiconductor effectively develops an infrared activity along the chain axis. The origin of the effect lies in phase oscillations of additional charge-density-wave distortions which inevitably arise in the presence of electron-phonon interactions. This suggests that organic linear conductors may constitute unique systems for the study of electron-phonon interactions in the organic solid state.

Michael J. Rice

Papers

Elementary Excitations of a Linearly Conjugated Diatomic Polymer

Charged Π-phase kinks in lightly doped polyacetylene

Weakly Pinned Fröhlich Charge-Density-Wave Condensates: A New, Nonlinear, Current-Carrying Elementary Excitation

Organic Linear Conductors as Systems for the Study of Electron-Phonon Interactions in the Organic Solid State

Towards the experimental determination of the fundamental microscopic parameters of organic ion-radical compounds