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.

/pdf/berry-phase-effects-on-electronic-properties-53dkbbi2er.pdf

Berry phase effects on electronic properties

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

We present a review of experimental and theoretical studies of the anomalous Hall effect (AHE), focusing on recent developments that have provided a more complete framework for understanding this subtle phenomenon and have, in many instances, replaced controversy by clarity. Synergy between experimental and theoretical work, both playing a crucial role, has been at the heart of these advances. On the theoretical front, the adoption of Berry-phase concepts has established a link between the AHE and the topological nature of the Hall currents which originate from spin-orbit coupling. On the experimental front, new experimental studies of the AHE in transition metals, transition-metal oxides, spinels, pyrochlores, and metallic dilute magnetic semiconductors, have more clearly established systematic trends. These two developments in concert with first-principles electronic structure calculations, strongly favor the dominance of an intrinsic Berry-phase-related AHE mechanism in metallic ferromagnets with moderate conductivity. The intrinsic AHE can be expressed in terms of Berry-phase curvatures and it is therefore an intrinsic quantum mechanical property of a perfect cyrstal. An extrinsic mechanism, skew scattering from disorder, tends to dominate the AHE in highly conductive ferromagnets. We review the full modern semiclassical treatment of the AHE together with the more rigorous quantum-mechanical treatments based on the Kubo and Keldysh formalisms, taking into account multiband effects, and demonstrate the equivalence of all three linear response theories in the metallic regime. Finally we discuss outstanding issues and avenues for future investigation.

/pdf/anomalous-hall-effect-tyeyld308t.pdf

Anomalous hall effect

The term photonic crystals appears because of the analogy between electron waves in crystals and the light waves in artificial periodic dielectric structures. During the recent years the investigation of one-, two-and three-dimensional periodic structures has attracted a widespread attention of the world optics community because of great potentiality of such structures in advanced applied optical fields. The interest in periodic structures has been stimulated by the fast development of semiconductor technology that now allows the fabrication of artificial structures, whose period is comparable with the wavelength of light in the visible and infrared ranges.

http://ieeexplore.ieee.org/iel5/6354/16969/00781867.pdf

Photonic crystals

In solid-state materials with strong relativistic spin-orbit coupling, charge currents generate transverse spin currents. The associated spin Hall and inverse spin Hall effects distinguish between charge and spin current where electron charge is a conserved quantity but its spin direction is not. This review provides a theoretical and experimental treatment of this subfield of spintronics, beginning with distinct microscopic mechanisms seen in ferromagnets and concluding with a discussion of optical-, transport-, and magnetization-dynamics-based experiments closely linked to the microscopic and phenomenological theories presented.

Spin Hall effects

This paper investigates the topological phase transition in honeycomb lattice photonic crystals with and without time-reversal and space-inversion symmetries through extensive analysis on bulk and edge states. In the system with both the symmetries, there appear multiple Dirac cones in the photonic band structure, and the mass gaps are controllable via symmetry breaking. The zigzag and armchair edges of the photonic crystals can support novel edge states that reflect the symmetries of the photonic crystals. The dispersion relation and the field configuration of the edge states are analyzed in detail in comparison to electronic edge states. Leakage of the edge states to free space, which is inherent in photonic systems, is fully taken into account in the analysis. A topological relation between bulk and edge states, which has been discussed in the context of electronic quantum Hall effect, is also examined in the photonic system with leaky edge states.

Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states

The anomalous Hall effect in two-dimensional ferromagnets is discussed to be the physical realization of the parity anomaly in (2+1)D, and the band crossing points behave as the topological singularity in the Brillouin zone. This appears as the sharp peaks and the sign changes of the transverse conductance $\sigma_{xy}$ as a function of the Fermi energy and/or the magnetization. The relevance to the experiments including the three dimensional systems is also discussed.

Topological Nature of Anomalous Hall Effect in Ferromagnet

The anomalous Hall effect (AHE) has been studied for epitaxial films of Eu(1-x)La(x)TiO(3), in which band filling can be controlled by doping x without undesired changes in magnetization. This system has a simple band structure near the conduction band bottom, which makes it possible to design the AHE. As expected, the anomalous Hall resistivity shows a nonmonotonic change as a function of the carrier density accompanied with the sign reversal around n=2.4 x 10(20) cm(-3). This opens a possibility to control the AHE by devising the material, structure, and doping level.

Control of the anomalous hall effect by doping in Eu(1-x)La(x)TiO(3) thin films.

We report an experimental study of generation of photo-induced voltage in nano-porous gold (NPG) thin film under the radiation of obliquely incident nanosecond laser light in visible regions. For s- polarized light, negative voltage is observed along the incident plane for positive incident angles, while for p- polarized light, positive voltage is observed for wavelength longer than 510 nm, while it turns to negative for shorter wavelengths. The transverse voltage for various polarized light is explained in terms of symmetry of configuration and that of microscopically random but macroscopically isotropic NPG.

Masaru Onoda

Papers

Photonic analog of graphene model and its extension: Dirac cone, symmetry, and edge states

Topological Nature of Anomalous Hall Effect in Ferromagnet

Control of the anomalous hall effect by doping in Eu(1-x)La(x)TiO(3) thin films.

Photo-induced voltage in nano-porous gold thin film

Photo-induced voltage in nano-porous gold thin film