There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

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

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

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 the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

/pdf/science-and-technology-roadmap-for-graphene-related-two-4q9m7czlkc.pdf

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

For a newly discovered iron-based high ${T}_{c}$ superconductor ${\mathrm{LaFeAsO}}_{1\ensuremath{-}x}{\mathrm{F}}_{x}$, we have constructed a minimal model, where inclusion of all five Fe $d$ bands is found to be necessary. The random-phase approximation is applied to the model to investigate the origin of superconductivity. We conclude that the multiple spin-fluctuation modes arising from the nesting across the disconnected Fermi surfaces realize an extended $s$-wave pairing, while $d$-wave pairing can also be another candidate.

Unconventional Pairing Originating from the Disconnected Fermi Surfaces of Superconducting LaFeAsO 1-x F x

Response of electronic systems in intense lights (ac electric fields) to dc source-drain fields is formulated with the Floquet method. We have then applied the formalism to graphene, for which we show that a nonlinear effect of a circularly polarized light can open a gap in the Dirac cone, which is predicted to lead to a photoinduced dc Hall current. This is numerically confirmed for a graphene ribbon attached to electrodes with the Keldysh Green's function.

Photovoltaic Hall effect in graphene

The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of a nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a self-consistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

/pdf/nonequilibrium-dynamical-mean-field-theory-and-its-2hdyavvhi6.pdf

Nonequilibrium dynamical mean-field theory and its applications

We study the effect of the lattice structure on the spin-fluctuation-mediated superconductivity in the iron pnictides adopting the five-band models of several virtual lattice structures of LaFeAsO, as well as actual materials such as NdFeAsO and LaFePO obtained from the maximally localized Wannier orbitals. Random phase approximation is applied to the models to solve the Eliashberg equation. This reveals that the gap function and the strength of the superconducting instability are determined by the cooperation or competition among multiple spin-fluctuation modes arising from several nestings among disconnected pieces of the Fermi surface, which is affected by the lattice structure. Specifically, the appearance of the Fermi surface $\ensuremath{\gamma}$ around $(\ensuremath{\pi},\ensuremath{\pi})$ in the unfolded Brillouin zone is sensitive to the pnictogen height ${h}_{\text{Pn}}$ measured from the Fe plane, where ${h}_{\text{Pn}}$ is shown to act as a switch between high-${T}_{c}$ nodeless and low-${T}_{c}$ nodal pairings. We also find that reduction in the lattice constants generally suppresses superconductivity. We can then combine these to obtain a generic superconducting phase diagram against the pnictogen height and lattice constant. This suggests that NdFeAsO is expected to exhibit a fully gapped, sign-reversing $s$-wave superconductivity with a higher ${T}_{c}$ than in LaFeAsO, while a nodal pairing with a low ${T}_{c}$ is expected for LaFePO, which is consistent with experiments.

Pnictogen height as a possible switch between high- T c nodeless and low- T c nodal pairings in the iron-based superconductors

A new method to provide interatomic pair potentials from ab initio Hartree-Fock self-consistent-field calculations is proposed; potentials are calculated for model clusters of silica (Si${\mathrm{O}}_{2}$). They are tested in the molecular-dynamics simulation of crystalline states, in which four known polymorphs of silica are shown to be dynamically stable.

Hideo Aoki

Papers

Unconventional Pairing Originating from the Disconnected Fermi Surfaces of Superconducting LaFeAsO 1-x F x

Photovoltaic Hall effect in graphene

Nonequilibrium dynamical mean-field theory and its applications

Pnictogen height as a possible switch between high- T c nodeless and low- T c nodal pairings in the iron-based superconductors

First-principles interatomic potential of silica applied to molecular dynamics