Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

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Topological insulators and superconductors

Transparent, conductive, and ultrathin graphene films, as an alternative to the ubiquitously employed metal oxides window electrodes for solid-state dye-sensitized solar cells, are demonstrated. These graphene films are fabricated from exfoliated graphite oxide, followed by thermal reduction. The obtained films exhibit a high conductivity of 550 S/cm and a transparency of more than 70% over 1000−3000 nm. Furthermore, they show high chemical and thermal stabilities as well as an ultrasmooth surface with tunable wettability.

Transparent, Conductive Graphene Electrodes for Dye-Sensitized Solar Cells

A quantized Hall plateau of ${\ensuremath{\rho}}_{\mathrm{xy}}=\frac{3h}{{e}^{2}}$, accompanied by a minimum in ${\ensuremath{\rho}}_{\mathrm{xx}}$, was observed at $Tl5$ K in magnetotransport of high-mobility, two-dimensional electrons, when the lowest-energy, spin-polarized Landau level is $\frac{1}{3}$ filled. The formation of a Wigner solid or charge-density-wave state with triangular symmetry is suggested as a possible explanation.

https://link.aps.org/pdf/10.1103/PhysRevLett.48.1559

Two-Dimensional Magnetotransport in the Extreme Quantum Limit

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

Measurements of the Hall voltage of a two-dimensional electron gas, realized with a silicon metal-oxide-semiconductor field-effect transistor, show that the Hall resistance at particular, experimentally well-defined surface carrier concentrations has fixed values which depend only on the fine-structure constant and speed of light, and is insensitive to the geometry of the device. Preliminary data are reported.

https://link.aps.org/pdf/10.1103/PhysRevLett.45.494

New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance

Piezoresistance measurements have been carried out on n‐type inversion layers on (100), (110), and (111) silicon at room temperature as a function of the gate voltage (perpendicular electric field). It has been shown that the values of the piezoresistance coefficients depend not only on the surface orientation but also on the magnitude of the gate voltage. The strongest surface field influence was observed in the (100) plane whereas no gate voltage dependence could be detected on (111) surfaces. The data obtained have been interpreted in terms of the quantization of energy levels in inversion layers. This quantization causes generally an occupation anisotropy of the valleys mostly pronounced for an electric field in the [100] direction and disappearing for a [111] direction of the field. Theoretical expressions for the (100) piezoresistance coefficients π11 and π12 have been derived taking into account the field dependences of the population effect and of the intervally scattering contribution, both affec...

Gerhard Dorda

Papers

New Method for High-Accuracy Determination of the Fine-Structure Constant Based on Quantized Hall Resistance

Piezoresistance in Quantized Conduction Bands in Silicon Inversion Layers

Surface quantum oscillations in (110) and (111) n-type silicon inversion layers

Shubnikov-de Haas oscillations in p-type inversion layers on n-type silicon

Quantum oscillations in p-type inversion layers of (111) and (100) silicon field effect transistors