Singly ionized oxygen vacancies are produced in $\mathrm{LiAl}{\mathrm{O}}_2$ crystals by direct displacement events during a neutron irradiation. These vacancies, with one trapped electron, are referred to as ${\mathrm{V}}_{\mathrm{O}}^{+}$ centers. They are identified and characterized using electron paramagnetic resonance (EPR) and optical absorption. The EPR spectrum from the ${\mathrm{V}}_{\mathrm{O}}^{+}$ centers is best monitored near 100 K with low microwave power. When the magnetic field is along the [001] direction, this spectrum has a $g$ value of 2.0030 and well-resolved hyperfine interactions of 310 and 240 MHz with the two ${}^{27}\mathrm{Al}$ nuclei that are adjacent to the oxygen vacancy. A second EPR spectrum, also showing hyperfine interactions with two ${}^{27}\mathrm{Al}$ nuclei, is attributed to a metastable state of the ${\mathrm{V}}_{\mathrm{O}}^{+}$ center. An optical absorption band peaking near 238 nm is assigned to ${\mathrm{V}}_{\mathrm{O}}^{+}$ centers. Bleaching light from a Hg lamp converts a portion of the ${\mathrm{V}}_{\mathrm{O}}^{+}$ centers to ${\mathrm{V}}_{\mathrm{O}}^0$ centers (these latter centers are oxygen vacancies with two trapped electrons). The ${\mathrm{V}}_{\mathrm{O}}^0$ centers have an absorption band peaking near 272 nm, a photoluminescence band peaking near 416 nm, and a photoluminescence excitation band peaking near 277 nm. Besides the oxygen-vacancy EPR spectra, a holelike spectrum with a resolved, but smaller, hyperfine interaction with one ${}^{27}\mathrm{Al}$ nucleus is present in $\mathrm{LiAl}{\mathrm{O}}_2$ after the neutron irradiation. This spectrum is tentatively assigned to doubly ionized aluminum vacancies.

We study the ground states and low-energy excitations of a generic Dirac material with spin-orbit coupling and a buckling structure in the presence of a magnetic field. The ground states can be classified into three types under different conditions: SU(2), easy-plane, and Ising quantum Hall ferromagnets. For the SU(2) and the easy-plane quantum Hall ferromagnets there are goldstone modes in the collective excitations, while all the modes are gapped in an Ising-type ground state. We compare the Ising quantum Hall ferromagnet with that of bilayer graphene and present the domain-wall solution at finite temperatures. We then specify the phase transitions and transport gaps in silicene in Landau levels 0 and 1. The phase diagram depends strongly on the magnetic field and the dielectric constant. We note that there exist triple points in the phase diagrams in Landau level $N=1$ that could be observed in experiments.

In a recent experiment, Young et al. [Nature (London) 505, 528 (2014)] observed a metal to insulator transition as well as transport through helical edge states in monolayer graphene under a strong, tilted magnetic field. Under such conditions, the bulk is a magnetic insulator which can exhibit metallic conduction through helical edges. It was found that the two-terminal conductance of the helical channels deviates from the expected quantized value ($=e^2/h$ per edge, at zero temperature). Motivated by this observation, we study the effect of disorder on the conduction through the edge channels. We show that, unlike for helical edges of topological insulators in semiconducting quantum wells, a disorder Rashba spin-orbit coupling does not lead to backscattering, at least to leading order. Instead, we find that the lack of perfect antialignment of the electron spins in the helical channels to be the most likely cause for backscattering arising from scalar (i.e., spin-independent) impurities. The intrinsic spin-orbit coupling and other time-reversal symmetry-breaking and/or sublattice parity-breaking potentials also lead to (subleading) corrections to the channel conductance.

Systems of free fermions are classified by symmetry, space dimensionality, and topological properties described by $K$ homology. Those systems belonging to different classes are inequivalent. In contrast, we show that by taking a many-body/Fock-space viewpoint it becomes possible to establish equivalences of topological insulators and superconductors in terms of duality transformations. These mappings connect topologically inequivalent systems of fermions, jumping across entries in existent classification tables, because of the phenomenon of symmetry transmutation by which a symmetry and its dual partner have identical algebraic properties but very different physical interpretations. To constrain our study to established classification tables, we define and characterize mathematically Gaussian dualities as dualities mapping free fermions to free fermions (and interacting to interacting). By introducing a large, flexible class of Gaussian dualities we show that any insulator is dual to a superconductor, and that fermionic edge modes are dual to Majorana edge modes, that is, the Gaussian dualities of this paper preserve the bulk-boundary correspondence. Transmutation of relevant symmetries, particle number, translation, and time reversal is also investigated in detail. As illustrative examples, we show the duality equivalence of the dimerized Peierls chain and the Majorana chain of Kitaev, and a two-dimensional Kekulé-type topological insulator, including graphene as a special instance in coupling space, dual to a $p$-wave superconductor. Since our analysis extends to interacting fermion systems, we also briefly discuss some such applications.

Strain fields, dislocations, and defects may be used to control electronic properties of graphene. By using advanced imaging techniques with high-resolution transmission electron microscopes, we have measured the strain and rotation fields about dislocations in monolayer graphene with single-atom sensitivity. These fields differ qualitatively from those given by conventional linear elasticity. However, atom positions calculated from two-dimensional (2D) discrete elasticity and three-dimensional discrete periodized Föppl-von Kármán equations (dpFvKEs) yield fields close to experiments when determined by geometric phase analysis. 2D theories produce symmetric fields whereas those from experiments exhibit asymmetries. Numerical solutions of dpFvKEs provide strain and rotation fields of dislocation dipoles and pairs that also exhibit asymmetries and, compared with experiments, may yield information on out-of-plane displacements of atoms. While discrete theories need to be solved numerically, analytical formulas for strains and rotation about dislocations can be obtained from 2D Mindlin's hyperstress theory. These formulas are very useful for fitting experimental data and provide a template to ascertain the importance of nonlinear and nonplanar effects. Measuring the parameters of this theory, we find two characteristic lengths between three and four times the lattice spacings that control dilatation and rotation about a dislocation. At larger distances from the dislocation core, the elastic fields decay to those of conventional elasticity. Our results may be relevant for strain engineering in graphene and other 2D materials of current interest.

We present a theory of Förster energy transfer between arrays of molecules lying on the planar metallic mirror. First, we calculate the complex band structure of the collective Bloch modes of the light-coupled donor molecules. Next, we determine the effective rate of the energy transfer from the donors to the acceptors and reveal its strong modification by the mirror. The rate can be either suppressed or enhanced depending on the relative positions between the acceptor and donor arrays. The strong modification of the transfer rate is a collective effect, mediated by the coupling between the donors; it is absent in the single-donor model.

In the presence of extrinsic Rashba spin-orbit coupling, we find that silicene can host a quantum anomalous Hall state with spin- and valley-polarized edge states, which can be effectively controlled by the exchange field and electric field. In this state, a pair of nontrivial edge states reside in one specific valley and have a strong but opposite spin polarization. A distinctive feature of this state is that both of the spin and valley indexes of the edge states can be switched by reversing the electric field. We also present a microscopic mechanism for the origin of this state. Our findings provide an efficient way to control the topologically protected spin- and valley-polarized edge states, which is crucial for spintronics and valleytronics.

A recent study of a high-mobility two-dimensional hole gas in a strained Ge quantum well revealed strong transport anisotropy in the quantum Hall regime when the magnetic field was tilted away from the sample normal [Q. Shi, M. A. Zudov, C. Morrison, and M. Myronov, Phys. Rev. B 91, 201301(R) (2015)]. In the present study we demonstrate that the anisotropy persists to such high temperatures and filling factors that quantum oscillations are no longer observed. This finding rules out the formation of a stripe phase as a possible origin for the observed anisotropy. However, we also show that the observed anisotropy is not consistent with other known anisotropies, such as those arising from finite-thickness effects or surface roughness.

We introduce an important approach for enhancing the nonlinear response of graphene through its resonant coupling to a plasmonic metasurface via cascaded Fano resonances. Such a hybrid metasurface supports two types of subradiant resonant modes, i.e., asymmetric modes of structured metamaterial elements (“metamolecules”) and graphene plasmons exhibiting strong mutual coupling and avoided dispersion crossing. We demonstrate that the tunability of graphene plasmons facilitates the strong interaction between the subradiant modes, modifying the spectral position and lifetime of the Fano resonances. We reveal that a strong resonant interaction, combined with the subwavelength localization of plasmons, leads to an enhanced nonlinear response and high efficiency of the second-harmonic generation.

The growth and geometric and electronic structures of ${\mathrm{Cr}}_2{\mathrm{O}}_3$ layers on the polar ZnO surfaces were characterized to determine how polar substrates can influence the properties of nonpolar films. X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy (UPS), high resolution transmission electron microscopy (HRTEM), reflection high energy electron diffraction, low energy electron diffraction, x-ray diffraction (XRD), and x-ray reflectivity (XRR) were employed to characterize the growth mode, film quality, and interfacial electronic properties. Chromium oxide growth on ZnO $\left(000\overline{1}\right)$ and $\left(0001\right)$ followed the same trends: two-dimensional growth with initial disorder followed by the formation of epitaxial ${\mathrm{Cr}}_2{\mathrm{O}}_3 \left(0001\right)$. Despite the initial disorder, HRTEM and XRD/XRR measurements on thicker films revealed an abrupt interface with the ${\mathrm{Cr}}_2{\mathrm{O}}_3$ lattice extending all the way to the interface. This indicates that above a critical thickness of 10–15 $\mathrm{Cr}-{\mathrm{O}}_3-\mathrm{Cr}$ repeat units, the entire film reorganizes into an ordered structure. It is postulated that the oxygen remained ordered throughout the growth but that the chromium initially filled interstices randomly in the oxygen sublattice, which allowed the film to eventually grow with a well-defined epitaxial relationship with the substrate. The polar interfaces showed a small band offset that decayed with increasing film thickness, suggesting that the compensating charges at the interface may partially migrate to the film surface. No evidence of formal changes in the Cr oxidation state at the interfaces was seen. On the other hand, statistical analyses of UPS valence band spectra revealed an enhanced density of states near the valence band edge for ${\mathrm{Cr}}_2{\mathrm{O}}_3$ on ZnO $\left(0001\right)$, consistent with stabilization of the positive interface by filling surface electronic states. In contrast, no significant valence band differences were observed between bulk ${\mathrm{Cr}}_2{\mathrm{O}}_3$ and thin ${\mathrm{Cr}}_2{\mathrm{O}}_3$ layers on ZnO $\left(000\overline{1}\right)$, suggesting a different charge compensation mechanism on the negative surface. The potential impact of these findings on the surface properties of chromium oxide thin films is discussed.

We study the quantum correction to conductivity on the surface of cubic topological Kondo insulators with multiple Dirac bands. We consider the model of time-reversal invariant disorder which induces the scattering of the electrons within the Dirac bands as well as between the bands. When only intraband scattering is present we find three long-range diffusion modes leading to weak antilocalization correction to conductivity which remains independent of the microscopic details such as Fermi velocities and relaxation times. Interband scattering gaps out two diffusion modes leaving only one long-range mode. We find that depending on the value of the phase coherence time, either three or only one long-range diffusion modes contribute to weak localization correction rendering the quantum correction to conductivity nonuniversal. We provide an interpretation for the results of the recent transport experiments on samarium hexaboride where weak antilocalization has been observed.

We analyze the low-energy properties of a device with $N+1$ quantum dots in a star configuration. A central quantum dot is tunnel-coupled to source and drain electrodes and to $N$ quantum dots. Extending previous results for the $N=2$ case, we show that, in the appropriate parameter regime, the low-energy Hamiltonian of the system is a ferromagnetic Kondo model for an $S=(N-1)/2$ impurity spin. For small enough interdot tunnel coupling, however, a two-stage Kondo effect takes place as the temperature is decreased. The spin $1/2$ in the central quantum dot is Kondo-screened first, and at lower temperatures the antiferromagnetic coupling to the side-coupled quantum dots leads to an underscreened $S=N/2$ Kondo effect. We present numerical results for the thermodynamic and spectral properties of the system, which show a singular behavior at low temperatures and allow us to characterize the different strongly correlated regimes of the device.

Experimental and theoretical studies of the coherent spin dynamics of two-dimensional GaAs/AlGaAs electron gas were performed. The system in the quantum Hall ferromagnet state exhibits a spin relaxation mechanism that is determined by many-particle Coulomb interactions. In addition to the spin exciton with changes in the spin quantum numbers of $\delta S=\delta S_z=-1$, the quantum Hall ferromagnet supports a Goldstone spin exciton that changes the spin quantum numbers to $\delta S=0$ and $\delta S_z=-1$, which corresponds to a coherent spin rotation of the entire electron system to a certain angle. The Goldstone spin exciton decays through a specific relaxation mechanism that is unlike any other collective spin state.

The quantum anomalous Hall (QAH) effect is a novel quantum state characterized by edge states which are topologically protected from backscattering and hold great potential for applications in low-power-consumption electronics. The experimental observation of QAH effects in magnetic topological insulators of Cr- or V-doped (Bi,${\mathrm{Sb})}_2{\mathrm{Te}}_3$ films is, however, full of challenges, hindering seriously the development of this field. Here a robust QAH effect is predicted in a van der Waals (vdW) heterostructure consisting of graphene and a layered ferromagnetic (FM) insulator ${\mathrm{Cr}}_2{\mathrm{Ge}}_2{\mathrm{Te}}_6$, from ab initio calculations. The achieved QAH effect is found to be independent of the stacking patterns between graphene and the FM substrate. This robustness makes the experimental observation highly flexible. The Fermi level is found to be located exactly inside the nontrivial bulk band gap which can be tuned effectively by varying the vdW gap. The mechanism is analyzed through tight-binding models. A high Chern number QAH device prototype is proposed, which can dramatically increase the conductance of the device.

The transport quantities of a classical spin chain with quenched disorder in antiferromagnetic coupling $J_i$ are evaluated using a dynamical simulation at finite temperatures $T>0$. Since the classical model is nonintegrable, spin and thermal conductivities remain finite even in the pure case. On the other hand, the role of disorder becomes crucial at low $T$, leading to a vanishing transport due to Anderson localization within the linearized regime. The crossover from the insulator to the conductor appears both for spin and thermal transport at quite low $T^{*}\ll J$. Still the many-body localization regime at $T>0$ evidenced by extremely short mean free paths can be strongly enhanced by introducing into the model an additional staggered field.

We have studied the superconducting state of $2H-{\mathrm{NbSe}}_2$ by scanning tunneling spectroscopy along two different crystal orientations, the $c$ and the $a/b$ axes. Along the $c$ axis a large gap is dominant in the spectra, while a smaller gap is measured along the $a/b$ axis. We show that these spectra are accurately described by the McMillan model where the small gap is induced through the coupling to the band associated with the large gap. In order to assign the small and large gaps to specific parts of the $2H-{\mathrm{NbSe}}_2$ Fermi surface, the electronic structure was studied using first-principles calculations. While we cannot exclude the possibility of intrinsic anisotropy of the gaps, we propose that the large gap opens in the Fermi surface cylinders located around the corner $K$ points while the sheets located around $\mathrm{\Gamma }$ are associated with the small gap. An additional component of the Fermi surface, a selenium based pocket, plays an essential role in the tunneling process. The role of the charge density wave occurring in this material is also discussed. Finally, we are able to give a coherent description of the observed characteristics of the tunneling spectra of $2H-{\mathrm{NbSe}}_2$ as well as the differences with $2H-{\mathrm{NbS}}_2$ where no charge density wave state is present. Further experimental work, such as high-resolution ARPES, would be very useful to confirm our interpretation. The approach and modeling developed here could also be relevant for other compounds of the dichalcogenide family.

Exciton annihilation dynamics in a disordered organic model system is investigated by ultrafast absorption spectroscopy. We show that the temporal evolution of the exciton density can be quantitatively understood by applying Förster energy transfer theory to describe the diffusion of the excitons as well as the annihilation step itself. To this end, previous formulations of Förster theory are extended to account for the inhomogeneous distribution of the $S_0-S_1$ transition energies resulting in an effective exciton diffusion constant. Two annihilation pathways are considered, the direct transfer of an exciton between two excited molecules and diffusive motion by multiple transfer steps towards a second exciton preceding the annihilation event. One pathway can be emphasized with respect to the other by tuning the exciton diffusion constant via the chromophore concentration. The investigated system allows one to extract all relevant parameters for the description and provides in this way a proof that the annihilation dynamics can be entirely understood and modeled by Förster energy transfer.

The main focus of this paper is to introduce, in a thermodynamically consistent manner, an anisotropic interface energy into a phase field theory for phase transformations. Here we use a small strain formulation for simplicity, but we retain some geometric nonlinearities, which are necessary for introducing correct interface stresses. Previous theories have assumed the free energy density (i.e., gradient energy) is an anisotropic function of the gradient of the order parameters in the current (deformed) state, which yields a nonsymmetric Cauchy stress tensor. This violates two fundamental principles: the angular momentum equation and the principle of material objectivity. Here, it is justified that for a noncontradictory theory the gradient energy must be an isotropic function of the gradient of the order parameters in the current state, which also depends anisotropically on the direction of the gradient of the order parameters in the reference state. A complete system of thermodynamically consistent equations is presented. We find that the main contribution to the Ginzburg-Landau equation resulting from small strains arises from the anisotropy of the interface energy, which was neglected before. The explicit expression for the free energy is justified. An analytical solution for the nonequilibrium interface and critical nucleus has been found and a parametric study is performed for orientation dependence of the interface energy and width as well as the distribution of interface stresses.