The $F^{+}$ center consisting of an electron trapped at an oxygen vacancy ($V_{\mathrm{O}}$) was investigated in oxygen deficient ${\mathrm{Y}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$ (YAG) garnet crystals by electron paramagnetic resonance (EPR) techniques. The measurements were performed in the wide temperature interval 5–450 K and the frequency range 9.4–350 GHz using both the conventional continuous-wave and pulse EPR experiments. Pulse electron-nuclear double resonance was applied to resolve the hyperfine interaction of the trapped electron with surrounding nuclei. The measurements show that at low temperatures, $T<50$ K, the EPR spectrum of the $F^{+}$ center is anisotropic with $g$ factors in the range 1.999–1.988 and originates from three magnetically inequivalent positions of the center in a garnet lattice. As the temperature increases, the EPR spectrum becomes isotropic suggesting a motional averaging of the anisotropy due to motion of the $F^{+}$-center electron between neighboring oxygen vacancies. With further increase of temperature up to $T$ > 200 K, we observed delocalization of the $F^{+}$-center electron into the conduction band with the activation energy about 0.4–0.5 eV that resulted in substantial narrowing of the EPR spectral line with simultaneous change of its shape from Gaussian to Lorentzian due to disappearance of the Fermi contact hyperfine field at ${}^{27}\mathrm{Al}$ and ${}^{89}\mathrm{Y}$ nuclei. Such temperature behavior of the $F^{+}$-center electron in YAG is completely similar to behavior of a donor electron in a semiconductor. Our findings are further supported by measurements of the conductivity and dielectric properties. In particular, these data show that the electrons in the conduction band are not homogeneously distributed in the crystal: There are highly conductive regions separated by poorly conductive dielectric layers. This leads to the so-called Maxwell-Wagner dielectric relaxation with huge apparent dielectric constant at low frequencies. This paper reports an observation of a donorlike behavior of an $F^{+}$ center in wide band-gap insulating crystals.

The $S=\frac{1}{2}$ quasi-one-dimensional antiferromagnet ${\mathrm{K}}_2{\mathrm{CuSO}}_4{X}_2(X=\mathrm{Cl}$, Br) exhibits peculiar Dzyaloshinskii-Moriya (DM) interactions that are uniform along its spin chains and antiparallel with respect to neighboring chains. This feature has received much attention recently because it leads to spin frustration, however, the spin dynamics around $T_{\mathrm{N}}$ and magnetic structure have not been reported. Here we report magnetic behaviors of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$. The orthorhombic crystal structure of ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$, which is identical to $\mathrm{K}{}_2{\mathrm{CuSO}}_4{X}_2$, was verified. The results of the thermodynamic measurements suggest that this compound has moderately strong intra- and interchain interaction for investigation of the spin state around $T_{\mathrm{N}}$. The inelastic neutron scattering and muon spin relaxation and rotation measurements reveal the presence of a two-spinon continuum, and below $T_{\mathrm{N}}$, the long-range order develops. However, the obtained critical exponent is $\beta =0.18$, which is not indicative of a three-dimensional magnetic system; instead, one-dimensional (1D) spin correlation likely affects the formation of magnetic ordering in ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$. There is a possibility that ${\mathrm{Na}}_2{\mathrm{CuSO}}_4{\mathrm{Cl}}_2$ is a model compound for investigation of DM-induced frustration effects in a 1D quantum spin system.

Magnetic van der Waals materials with intrinsic magnetic properties provide the ideal platform for exploring magnetism in the low-dimensional limit. In this work, we investigate the electronic and magnetic properties of the ${\mathrm{VI}}_3$ material, a new member of the ferromagnetic van der Waals materials. First-principles results confirm the Mott-insulator state as its electronic ground state. The half-metallic state as reported in the literature is a metastable state, with a total energy 0.2–0.3 eV per ${\mathrm{VI}}_3$ higher than the Mott-insulator state. Magnetocrystalline anisotropy calculations confirm an out-of-plane magnetic easy axis of the ${\mathrm{VI}}_3$ monolayer. We predict the interlayer exchange coupling of the ${\mathrm{VI}}_3$ bilayer to be determined by the interlayer stacking order, ferromagnetic at the most stable and antiferromagnetic at the metastable stacking orders, respectively, reminiscent of the ${\mathrm{CrI}}_3$ material.

By using the first-principles calculations and model analyses, we found that the combination of defected tungsten disulfide monolayer and manganese adsorption may give a $K{K}^{\prime }$ valley spin splitting up to 210 meV. This system also has a tunable magnetic anisotropy energy and its Fermi level sits right in a large band gap. Therefore it can be used for the realization of the valley-polarized anomalous Hall effect and for the exploration of other valley related physics without using optical methods. A protective environment can be formed by covering it with a hexagonal BN layer, without much disturbance to the benign properties of $\mathrm{Mn}/\mathrm{W}{\mathrm{S}}_2$.

We consider magnon excitations in the spin-glass phase of geometrically frustrated antiferromagnets with weak exchange disorder, focusing on the nearest-neighbor pyrochlore-lattice Heisenberg model at large spin. The low-energy degrees of freedom in this system are represented by three copies of a $\mathrm{U}\left(1\right)$ emergent gauge field, related by global spin-rotation symmetry. We show that the Goldstone modes associated with spin-glass order are excitations of these gauge fields, and that the standard theory of Goldstone modes in Heisenberg spin glasses (due to Halperin and Saslow) must be modified in this setting.

In this paper, we investigate the relation between odd-frequency pairing and proximity effect in nonuniform Kitaev chain systems with a particular interest in the topological critical point. First, we correlate the odd-frequency pairing and Majorana fermion in a semi-infinite Kitaev chain, where we find that the spatial dependence of the odd-frequency pair amplitude coincides with that of the local density of states at low frequencies. Second, we demonstrate that, contrary to the standard view, the odd-frequency pair amplitude spreads into the bulk of a semi-infinite Kitaev chain at the topological critical point. Finally, we show that odd-frequency Cooper pairs cause the proximity effect in a normal metal/diffusive normal metal/Kitaev chain junction even at the topological critical point. Our results hold relevance to the investigation of odd-frequency pairing and topological superconductivity in more complicated systems that involve Rashba nanowires with magnetic fields.

Many recent studies show that the hole-doped monolayer transition metal dichalcogenides (TMDs) exhibit Ising superconductivity. The Ising-type spin-orbit coupling (SOC) results in spin-momentum locking perpendicular to the two-dimensional crystal near the $K$ and $-K$ valleys, strongly protecting the superconducting state against in-plane magnetic fields. In this work, we theoretically study the Kondo effect of a magnetic impurity doped in monolayer TMDs with the Ising SOC protected superconducting state. Based on behaviors of spin-induced Yu-Shiba-Rusinov bound states and localized magnetic susceptibility, we show that the Ising SOC plays an important role in enhancing or suppressing the Kondo screening of the magnetic impurity, depending on the relative position of the Fermi level with respect to the Ising splitting. More importantly, the Ising SOC exhibits opposite influences on the quantum phase transition between magnetic doublet and Kondo singlet ground states in electron- and hole-doped cases. These features in Kondo screening can be tuned by ionic liquid-gating in experiments.

New refractory hard materials with a favorable band gap are in high demand for the next-generation semiconductors capable of withstanding high temperature and other hostile environments. Boron phosphide (BP) is such an attractive candidate with exceptional properties; however, it has mainly been studied theoretically because of the difficulty in sample preparation. In this work, we report successful synthesis of large millimeter-sized single-crystal BP. The final product has a zinc-blende structure with a unique electronic structure and is optically transparent with a moderate band gap of ∼2.1 eV. Our experiments, in conjunction with ab initio simulations, reveal that the compound exhibits extraordinary strain stiffening and unusually high load-invariant hardness of ∼38 (3) GPa, which is close to the 40-GPa threshold for superhard materials, making BP the hardest among all known semiconductors. Based on the first-principles calculations, the fracture mechanisms in BP under tensile and shear deformations can be attributed to the formation of a metastable hexagonal phase. Further spectroscopic measurements indicate that an unusual electronic transition occurs at high pressures of ∼13 GPa, resulting in an asymptotically enhanced covalent bonding state. The pressure dependence of multiphonon processes is also determined by Raman measurement. In addition, our studies suggest a phonon-assisted photoluminescence process and evidence for the photon-pumped étalon effect at 707 nm.

Controlled adiabatic transfer of a single electron through a chain of quantum dots has been recently achieved in GaAs and Si/SiGe based quantum dots, opening prospects for turning stationary spin qubits into mobile ones and solving in this way the problem of long-distance communication between quantum registers in a scalable quantum computing architecture based on quantum dots. We consider theoretically the process of such an electron transfer between two tunnel-coupled quantum dots, focusing on control by slowly varying the detuning of energy levels in the dots. We take into account the fluctuations in detuning caused by $1/f$-type noise that is ubiquitous in semiconductor nanostructures and analyze their influence on probability of successful transfer of an electron in a spin eigenstate. With numerical and analytical calculations we show that probability of electron not being transferred due to $1/f^{\beta }$ noise in detuning is $\propto {\sigma }^2{t}^{\beta -1}/v$, where $\sigma$ characterizes the noise amplitude, $t$ is the interdot tunnel coupling, and $v$ is the detuning sweep rate. Interestingly, this means that the noise-induced errors in charge transfer are independent of $t$ for $1/f$ noise. For realistic parameters taken from experiments on silicon-based quantum dots, we obtain the minimal probability of charge transfer failure between a pair of dots is limited by $1/f$ noise in detuning to be the on the order of 0.01. This means that in order to reliably transfer charges across many quantum dots, charge noise in the devices should be further suppressed, or tunnel couplings should be increased, in order to allow for faster transfer (and less exposure to noise), while not triggering the deterministic Landau-Zener excitation.

We study the interplay of electron and photon spin in nonreciprocal materials. Traditionally, the primary mechanism to design nonreciprocal photonic devices has been magnetic fields in conjunction with magnetic oxides, such as iron garnets. In this work, we present an alternative paradigm that allows tunability and reconfigurability of the nonreciprocity through spintronic approaches. The proposed design uses the high spin-orbit coupling (SOC) of a narrow-band-gap semiconductor (InSb) with ferromagnetic dopants. A combination of the intrinsic SOC and a gate-applied electric field gives rise to a strong external Rashba spin-orbit coupling (RSOC) in a magnetically doped InSb film. The RSOC which is gate alterable is shown to adjust the magnetic permeability tensor via the electron $g$ factor of the medium. We use electronic band structure calculations $(\mathrm{k}·\mathrm{p}$ theory) to show that the gate-adjustable RSOC manifest itself in the nonreciprocal coefficient of photon fields via shifts in the Kerr and Faraday rotations. In addition, we show that photon spin properties of dipolar emitters placed in the vicinity of a nonreciprocal electromagnetic environment are distinct from reciprocal counterparts. The Purcell factor $\left(F_p\right)$ of a spin-polarized emitter (right-handed circular dipole) is significantly enhanced due to a larger $g$ factor while a left-handed dipole remains essentially unaffected. Our search for novel nonreciprocal material platforms can lead to electron-spin-controlled reconfigurable photonic devices.

A strong low-temperature enhancement of the tunneling conductance between graphene bilayers has been reported recently and interpreted as a signature of equilibrium electron-hole pairing, first predicted in bilayers more than 40 years ago but previously unobserved. Here we provide a detailed theory of conductance enhanced by fluctuating electron-hole Cooper pairs, which are a precursor to equilibrium pairing, that accounts for specific details of the multiband double graphene bilayer system which supports several different pairing channels. Above the equilibrium condensation temperature, pairs have finite temporal coherence and do not support dissipationless tunneling. Instead they strongly boost the tunneling conductivity via a fluctuational internal Josephson effect. Our theory makes predictions for the dependence of the zero bias peak in the differential tunneling conductance on temperature and electron-hole density imbalance that capture important aspects of the experimental observations. In our interpretation of the observations, cleaner samples with longer disorder scattering times would condense at temperatures $T_c$ up to $\sim 50\mathrm{K}$, compared to the record $T_c\sim 1.5\mathrm{K}$ achieved to date in experiment.

Space-group symmetries dictate the energy degeneracy of quasiparticles (e.g., electronic, photonic) in crystalline structures. For spinless systems, there can only be double or triple degeneracies protected by these symmetries, while other degeneracies are usually taken as accidental. In this Rapid Communication we show that it is possible to design higher degeneracies exploring site permutation symmetries. These design principles are shown to be satisfied in previously studied lattices, and new structures are proposed with three, four, and five degeneracy points for spinless systems. The results are general and apply to different quasiparticle models. Here, we focus on a tight-binding approach for the electronic case as a proof of principle. The resulting high-degeneracy points are protected by the site-permutation symmetries, yielding pseudospin-1 and -2 Dirac fermions. The strategy proposed here can be used to design lattices with high-degeneracy points in electronic (e.g., metal-organic frameworks), photonic, phononic, magnonic, and cold-atom systems.

We investigate the inverse Faraday effect (IFE) by surface plasmon traveling modes in an ultracompact magnetoplasmonic disk resonator side-coupled to a plasmonic waveguide. The magnetic field by the IFE reacts to the traveling modes and leads to a nonlinear shift of the resonance in the disk resonator. Describing those nonlinear phenomena analytically by using the temporal coupled mode theory and the Lorentz reciprocity theorem, we propose a conception of hysteretic optomagnetic bistability that the system has two stable states of optically induced magnetic field to switch on and off, depending upon the history of the incident optical power. The numerical simulations agree well with the analytical prediction. The proposed conception may find potential applications in all-optical magnetic recording and switching with nanometer resolution.

We present an infinite-dimensional lattice of two-by-two plaquettes, the quadruple Bethe lattice, with Hubbard interaction and solve it exactly by means of the cluster dynamical mean-field theory. It exhibits a $d$-wave superconducting phase that is related to a highly degenerate point in the phase diagram of the isolated plaquette at that the ground states of the particle number sectors $N=2,3,\text{and}4$ cross. The superconducting gap is formed by the renormalized lower Slater peak of the correlated, hole-doped Mott insulator. We engineer parts of the interaction and find that pair hoppings between $X/Y$ momenta are the main two-particle correlations of the superconducting phase. The suppression of the superconductivity is caused by the diminishing of pair hopping correlations in the overdoped regime and by the charge blocking in the underdoped one. The optimal doping is $\sim 0.15$ at which the underlying normal state shows a Lifshitz transition. Tuning intra- and interplaquette hoppings allows to disentangle superconductivity from antiferromagnetism as the latter requires larger interplaquette hoppings. We expect our results to provide additional insight into the nature of the superconductivity in cuprates.

We study the mass fluctuations in gapped Dirac materials by treating the mass term as both a continuous and discrete random variable. Gapped Dirac materials were proposed to be used as materials for dark-matter sensors. One thus would need to estimate the role of disorder and fluctuations on the interband absorption of dark matter. We find that both continuous and discrete fluctuations across the sample introduce tails (e.g., Dirac-Lifshitz tails) in the density of states and the interband absorption rate. We estimate the strength of the gap filling and discuss implications of these fluctuations on the performance as sensors for dark matter detection. The approach used in this work provides a basic framework to model the disorder by any arbitrary mechanism on the interband absorption of Dirac material sensors.

The free-exciton photoluminescence (PL) spectrum of $4H$-SiC exhibits a detailed fine structure due to the different phonons involved in the indirect gap transition. Here a first-principles calculation of these phonons, their symmetry labeling and their contribution to the photoluminescence spectrum is presented. The calculation uses phonons and electron-phonon coupling matrix elements computed via density functional perturbation theory and energy bands and optical phonon matrix elements calculated in density functional theory. The results are in excellent agreement with the experiment for the phonon energies and the polarization dependence of the spectrum. The relative intensities are also in fair agreement if we allow for some phonons within a few meV to be interchanged. There is however a remarkable discrepancy that the experimental spectrum shows a distinct behavior for phonons with energy below $\sim 55$ meV and above that energy, which is absent in the theory. The experimental PL lines corresponding to phonon energies below 55 meV are about a factor 5–10 smaller in intensity. This is not found in our calculations. The calculations show a similar peak distribution as the experiment in this range but with intensities comparable to those above 55 meV. This indicates that another mechanism outside the scope of the electron-phonon mediated transitions is operative for photon energies of the PL lines closer to the indirect exciton gap than this 55 meV cutoff, which reduces the overall intensity of these lines. We propose that this may result from competition between the phonon-assisted PL and trapping of the electron in the available unoccupied hexagonal site N-donor shallow level at 53-meV binding energy. As part of this study, we also present the phonon dispersions and density of states in $4H$-SiC and the electronic band structure including quasiparticle corrections.

The fundamental mechanisms of strengthening/hardening and toughening that may be modified by various nanometer-spaced planar defects in the ultrahard nanostructured diamond and boron nitride (BN), e.g., nanotwins, stacking faults, and coherent heterophase interfaces, are still far from understood. In the present work, by means of first-principles approaches to derive ideal strength and Peierls stress, we performed a comprehensive investigation on the effect of the nanometer-spaced planar defects on the strength and plasticity of nanostructured diamond and BN under both uniform and localized deformations. A profound strengthening under uniform strain is revealed to be closely dependent on the spacing of planar defects, yet differing from the disappearing dependence under localized strain. It is further shown that the breakage and reconstruction of covalent bonds occurs only for very small spacing of planar defects under uniform deformations, being inconsistent with the average spacing found in the experimentally prepared nanotwinned diamond and BN, thus casting a doubt on the feasibility of the previously proposed strengthening mechanism. Under localized deformations, only the planar defects of twin in c-diamond or c-BN and coherent heterophase interface in c-/h-diamond or c-/w-BN are found to increase the barrier for the parallel slip of both $1/2\langle 110\rangle$ shuffle-set full dislocation and $1/6\langle 112\rangle$ glide-set partial dislocation, resulting in the strengthening of nanostructured diamond and BN, which agrees to the experimental observation. These findings not only yield a physical insight in strengthening/toughening nanostructured diamond and BN, but highlight the importance to understand the synergetic effect of length scale and interface between planar defects in designing superhard nanostructured materials.

Ferroelectric tunnel junctions (FTJs) have been intensively studied in recent years due to the great potential in nonvolatile memory devices and two-dimensional (2D) FTJs have started to catch attention lately because of their atomic thickness and their significance in miniaturizing FTJ device sizes. In this work, we propose a mechanism for building 2D FTJs based on the large difference between the two work functions of a 2D ferroelectric polar material with out-of-plane polarization. When it forms a van der Waals (vdW) vertical heterostructure with another 2D material there will be two kinds of interfaces, according to which surface of the 2D polar material is contacted. Depending on the relative work functions of the contacted surfaces of the two materials, charge transfer may or may not occur between them, thus the 2D polar material may become conducting or be still insulating, resulting in two distinct conducting states (“ON” and “OFF”). We demonstrate the feasibility of this proposal by the example of a vdW heterostructure FTJ constructed with graphene and 2D ferroelectric ${\mathrm{In}}_2{\mathrm{Se}}_3$ with out-of-plane polarization. Specifically, based on density functional calculations, we show that excellent tunnel electroresistance (TER) effect with TER ratio $\sim 1\times {10}^8\%$ is achieved, suggesting a promising route for applying 2D ferroelectric materials with out-of-plane polarization in ferroelectric memory devices.