The energy spectrum of the three-dimensional (3D) velocity field, induced by collapsing vortex filaments, is studied. One of the aims of this work is to clarify the appearance of the Kolmogorov-type energy spectrum $E\left(k\right)\propto k^{-5/3}$, observed in many numerical works on discrete vortex tubes and quantized vortex filaments in quantum fluids at zero temperature. Usually when explaining classical turbulent properties of quantum turbulence the model of vortex bundles is used. This model is necessary to mimic the vortex stretching, which is responsible for the energy transfer in classical turbulence. In my consideration I do not appeal to the possible “bundle arrangement” but instead explore the alternative idea that the turbulent spectra appear from a singular solution, which describes the collapsing line at moments of reconnection. One more aim is related to an important and intensively discussed topic—the role of hydrodynamic collapse in the formation of turbulent spectra. I demonstrated that the specific vortex filament configuration generated the spectrum $E\left(k\right)$ close to the Kolmogorov dependence and discussed the reason for this as well as the reason for deviation. I also discuss the obtained results from the points of view of both classical and quantum turbulence.

We report on ${}^{139}\mathrm{La}$ and ${}^{13}\mathrm{C}$ nuclear magnetic resonance (NMR) study of noncentrosymmetric superconductor ${\mathrm{La}}_2{\mathrm{C}}_3$ with superconducting critical temperature $T_{\mathrm{c}}=11.8$ K. In the normal state ${}^{139}\mathrm{La}$ NMR spectra show a characteristic quadrupole polycrystalline broadening yielding a quadrupole frequency ${\nu }_{\mathrm{Q}}=3.1$ MHz and a very large shift of $\sim 3000$ ppm. A significant part of this shift arises from the Van Vleck-like susceptibility as a result of a sizable spin-orbit coupling. In the superconducting phase ${\mathrm{La}}_2{\mathrm{C}}_3$ shows abnormal behavior that dramatically deviates from the conventional $s$-wave superconductors. Namely, (i) ${}^{139}\mathrm{La}$ and ${}^{13}\mathrm{C}$ NMR shifts in the superconducting state do not change from their normal-state values, and (ii) the ${}^{139}\mathrm{La}$ spin-lattice relaxation rate is strongly enhanced below $T_{\mathrm{c}}$. Such unconventional response in the local static and dynamic spin susceptibilities is discussed in terms of possible mixture of spin-singlet and spin-triplet Cooper pairs, which is promoted by the asymmetric spin-orbit coupling in the system without the center of inversion.

Hund's rule is one of the fundamentals of the correlation physics at the atomic level, determining the ground state multiplet of the electrons. It consists of three laws: (i) maximum $S$ (total spin), (ii) maximum $L$ (total orbital angular momentum) under the constraint of (i), and (iii) the total angular momentum $J$ is $|L-S|$ for electron number less than half, while $J=L+S$ for more than half due to the relativistic spin-orbit interaction (SOI). In real systems, the electrons hop between the atoms and gain the itinerancy, which is usually described by the band theory. The whole content of theories on correlation is to provide a reliable way to describe the intermediate situation between the two limits. Here we propose an approach toward this goal, i.e., we study the two-atom systems of three $t_{2g}$ orbitals and see how the Hund's rule is modified by the transfer integral $t$ between them. It is found that the competition between $t$ and the Hund's coupling $J$ at each atom determines the crossover from the molecular orbital limit to the strong correlation limit. Especially, the focus is on the generalization of the third rule, i.e., the inter- and intra-atomic SOI's in the presence of the correlation. We have found that there are cases where the effective SOI's are appreciably enhanced by the Hund's coupling. The conditions for the enhancement are the intermediate Hund's coupling and the filling of four or five electrons.

We discuss the rich phase diagram of doped $A{B}_{2}t\text{−}J$ chains by using data from density matrix renormalization group and exact diagonalization techniques. The $J$ vs $\delta$ (hole doping) phase diagram exhibits regions of itinerant ferrimagnetism, incommensurate, resonating valence bond and Nagaoka states, phase separation, and Luttinger liquid (LL) physics. Several features are highlighted, such as the modulated ferrimagnetic structure, the occurrence of Nagaoka spin polarons in the underdoped regime and small values of $J=4t^2/U$, where $t$ is the first-neighbor hopping amplitude and $U$ is the on-site repulsive Coulomb interaction, incommensurate structures with nonzero magnetization, and strong-coupling LL physics in the high-doped regime. We also verify that relevant findings are in agreement with the corresponding findings in square and $n$-leg ladder lattices. In particular, we mention the instability of Nagaoka ferromagnetism against $J$ and $\delta$.

We compute the spectral functions for the two-site dynamical cluster theory and for the two-orbital dynamical mean-field theory in the density-matrix renormalization group (DMRG) framework using Chebyshev expansions represented with matrix product states (MPS). We obtain quantitatively precise results at modest computational effort through technical improvements regarding the truncation scheme and the Chebyshev rescaling procedure. We furthermore establish the relation of the Chebyshev iteration to real-time evolution and discuss technical aspects as computation time and implementation in detail.

We present calculations of the electronic and magnetic structures of vanadium-benzene (Bz) multidecker clusters ${\mathrm{V}}_n{\mathrm{Bz}}_{n+1} \left(n=1–3\right)$ using advanced quantum Monte Carlo methods. These and related systems have been identified as prospective spin filters in spintronic applications, assuming that their ground states are half-metallic ferromagnets. Although we find that magnetic properties of these multidecker clusters are consistent with ferromagnetic coupling, their electronic structures do not appear to be half metallic as previously assumed. In fact, they are ferromagnetic insulators with large and broadly similar $\uparrow \text{−}/\downarrow$-spin gaps. This makes the potential of these and related materials as spin filtering devices very limited, unless they are further modified or functionalized.

We demonstrate the generation of circularly polarized light induced current of bulk Dirac electrons at room temperature by exploiting a giant Rashba effect in a bulk semiconductor. The photocurrent is spin polarized due to the spin-momentum locking of the electronic states, which is manifested by a sign reversal upon flipping either the photon helicity or the sign of the Rashba parameter, without any stray current. The action spectra revealed the photon energy range, where the photocurrent is carried by the Dirac electrons at the inner Fermi surface. This photogalvanic control is enabled by the sizable spin splittings both at the valence and conduction bands with the same helicity, and also by a number of optical transition pathways compared to those in the two-dimensional Rashba systems. An efficient coupling between the photon field and large spin-orbit interaction is accordingly proposed to allow the universal control of Dirac electrons.

While each atom species in PbSe corresponds to a single crystallographic site and transport measurements reveal a single carrier density, ${}^{207}\mathrm{Pb}$ NMR reveals a more complicated picture than previously thought comprising three discrete homogeneous carrier components, each associated with $n$- or $p$-type carrier fractions. The origins of these fractions are discussed in terms of electronic heterogeneity of the native semiconductor. The interaction mechanism between nuclear spins and lattice vibrations via fluctuating spin-rotation interaction, applicable to heavy spin-1/2 nuclei [Phys. Rev. B 74, 214420 (2006)], does not hold. Instead, a higher-order temperature dependence dominates the relaxation pathway. Shallow acceptor states and deep level defects in the midgap explain the complex temperature dependence of the direct band gap.

The effects of size quantization on the nonlinear optical response of Ag nanoparticles are experimentally studied by spectroscopic ellipsometry and femtosecond spectroscopic pump-and-probe techniques. In the vicinity of a localized surface-plasmon resonance (2.0–3.5 eV), we have investigated the optical nonlinearity of Ag particles embedded in silica glass for particle diameters ranging from 3.0 to 16 nm. The intrinsic third-order optical susceptibility ${\chi }_m^{\left(3\right)}$ of Ag particles exhibited significant spectral and size dependences. These results are explained as quantum and dielectric confinements and are compared to the results of theoretical quantum finite-size effects calculation for metallic particles. In light of these results, we discuss the contribution of interband transitions to the size dependence of ${\chi }_m^{\left(3\right)}$. Quantum size effects lead to an increase in nonlinearity in small Ag particles.

This paper reports a theoretical study of the effect of boron and nitrogen codoping on the transport properties of carbon nanotubes (CNTs) at the mesoscopic scale. A new tight-binding parametrization has been set up, based on density functional theory calculations, that enables a reliable description of the electronic structure of realistic BN-doped CNTs. With this model, we have carried out a deep analysis of the electronic mean free path (MFP) exhibited by these nanostructures. The MFP is highly sensitive to the geometry of the scattering centers. We report that the relative distance between B and N atoms in the network influences drastically the electronic conduction. Moreover, we point out that the scattering induced by small hexagonal BN domains in the carbon network is less important than the BN-pair case.

Superconducting ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ has attracted significant attention as a candidate topological superconductor. Besides inducing superconductivity, the introduction of Cu atoms to this material has also been observed to produce a number of unusual features in DC transport and magnetic susceptibility measurements. To clarify the effect of Cu doping, we have performed a systematic optical spectroscopic study of the electronic structure of ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$ as a function of Cu doping. Our measurements reveal an increase in the conduction band effective mass, while both the free carrier density and lifetime remain relatively constant for Cu content greater than $x=0.15$. The increased mass naturally explains trends in the superfluid density and residual resistivity as well as hints at the complex nature of Cu doping in ${\mathrm{Bi}}_2{\mathrm{Se}}_3$.

We revisit the problem of the dynamic response of a superconducting bridge after abruptly switching on the supercritical current. In contrast to previous theoretical works we take into account spatial gradients and use both the local temperature approach and the kinetic equation for the distribution function of quasiparticles. We find that the temperature dependence of the finite delay time $t_d$ in the voltage response is model dependent and relatively large $t_d$ is connected with temporary cooling of quasiparticles during decay of superconducting order parameter $\left|\Delta \right|$ in time. It turns out that the presence of even small inhomogeneities in the bridge or finite length of the homogenous bridge favors a local suppression of $\left|\Delta \right|$ during the dynamic response. It results in a decrease of the delay time, in comparison with the spatially uniform model, due to the diffusion of nonequilibrium quasiparticles from the region with locally suppressed $\left|\Delta \right|$. In the case when the current density is maximal near the edge of a not very wide bridge the delay time is mainly connected with the time needed for the nucleation (entrance) of the first vortex and $t_d$ could be tuned by a weak external magnetic field. We also find that a short alternating current pulse (sinusoidlike) with zero time average may result in a nonzero time-averaged voltage response where its sign depends on the phase of the ac current.

We show that superconducting interlayer coupling, which coexists with and is depressed by stripe order in ${\mathrm{La}}_{1.885}{\mathrm{Ba}}_{0.115}{\mathrm{CuO}}_4$, can be enhanced by excitation with near-infrared laser pulses. For temperatures lower than $T_c=13$ K, we observe a blue shift of the equilibrium Josephson plasma resonance, detected by terahertz-frequency reflectivity measurements. Key to this measurement is the ability to probe the optical properties at frequencies as low as 150 GHz, detecting the weak interlayer coupling strengths. For $T>T_c$ a similar plasma resonance, absent at equilibrium, is induced up to the spin-ordering temperature $T_{\mathrm{SO}}\simeq 40$ K. These effects are reminiscent but qualitatively different from the light-induced superconductivity observed by resonant phonon excitation in ${\mathrm{La}}_{1.675}{\mathrm{Eu}}_{0.2}{\mathrm{Sr}}_{0.125}{\mathrm{CuO}}_{6.5}$. Importantly, enhancement of the below-$T_c$ interlayer coupling and its appearance above $T_c$ are preferentially achieved when the near-infrared pump light is polarized perpendicular to the superconducting planes, likely due to more effective melting of stripe order and the less effective excitation of quasiparticles from the Cooper pair condensate when compared to in-plane excitation.

${\mathrm{Ca}}_{10}$(${\mathrm{Pt}}_3{\mathrm{As}}_8$)(${\mathrm{Fe}}_2{\mathrm{As}}_2$)${}_5$ is the parent compound for a class of Fe-based high-temperature superconductors where superconductivity with transition temperatures up to 30 K can be introduced by partial element substitution. We present a combined high-resolution high-energy x-ray diffraction and elastic neutron scattering study on a ${\mathrm{Ca}}_{10}$(${\mathrm{Pt}}_3{\mathrm{As}}_8$)(${\mathrm{Fe}}_2{\mathrm{As}}_2$)${}_5$ single crystal. This study reveals the microscopic nature of two distinct and continuous phase transitions to be very similar to other Fe-based high-temperature superconductors: an orthorhombic distortion of the high-temperature tetragonal Fe-As lattice below $T_{\mathrm{S}}=110\left(2\right)$ K followed by stripelike antiferromagnetic ordering of the Fe moments below $T_{\mathrm{N}}=96\left(2\right)$ K. These findings demonstrate that major features of the Fe-based high-temperature superconductors are very robust against variations in chemical constitution as well as structural imperfection of the layers separating the Fe-As layers from each other and confirms that the Fe-As layers primarily determine the physics in this class of material.

We present a renormalization group (RG) analysis of a fermionic “hot-spot” model of interacting electrons on the square lattice. We truncate the Fermi-surface excitations to linearly dispersing quasiparticles in the vicinity of eight hot spots on the Fermi surface, with each hot spot separated from another by the wave vector $(\pi ,\pi )$. This is motivated by the importance of these Fermi-surface locations to the onset of antiferromagnetic order; however, we allow for all possible quartic interactions between the fermions, and also for all possible ordering instabilities. We compute the RG equations for our model, which depend on whether or not the hot spots are perfectly nested, and relate our results to earlier models. We also compute the RG flow of the relevant order parameters for both Hubbard and $J,V$ interactions, and present our results for the dominant instabilities in the nested and non-nested cases. In particular, we find that non-nested hot spots with $J,V$ interactions have competing singlet $d_{x^2-y^2}$ superconducting and $d$-form factor incommensurate density wave instabilities. We also investigate the enhancement of incommensurate density waves near experimentally observed wave vectors, and find dominant $d$-form factor enhancement for a range of couplings.

Here we study geometry, electronic structure, and effects of biaxial strain on ${\mathrm{RbHgF}}_3$ fluoro-perovskite from first-principles based density-functional theory computations. It has been shown that while an epitaxial strain of $\sim \pm 2\%$ is sufficient to produce a significant ferroelectric polarization in the prototypical cubic $Pm\overline{3}m$ structure, the ground state orthorhombic $Pnma$ structure remains effectively immune to the strain induced ferroelectricity even at biaxial strains as high as $\pm 5\%$. We further show that ${\mathrm{RbHgF}}_3$ in the $Pnma$ structure can accommodate compressive and tensile strains, respectively, by $a^{-}{a}^{-}{b}^0$ tilting (out-of-phase tilts along $a$ and $b$ axes) and $a^0{a}^0{b}^{+}$ rotations (in-phase rotations along $c$ axis) of ${\mathrm{HgF}}_2$ octahedra. Similar to many perovskite oxides, ${\mathrm{HgF}}_2$ octahedral rotations in ${\mathrm{RbHgF}}_3$ are found to be accompanied by large Rb-site antipolar displacements along the [001] direction. We demonstrate that this coupling between the octahedral rotations and Rb-site antipolar modes can be harnessed in ${\mathrm{RbHgF}}_3/{\mathrm{NaHgF}}_3$ and ${\mathrm{RbHgF}}_3/{\mathrm{KHgF}}_3$ superlattices to produce significant net polarizations of 4.93 $\mu \text{C}/{\mathrm{cm}}^2$ and 1.70 $\mu \text{C}/{\mathrm{cm}}^2$, respectively.

The effect of hyperfine interaction on the room-temperature defect-enabled spin filtering effect in GaAsN alloys is experimentally investigated and theoretically interpreted through a master equation approach based on the hyperfine and Zeeman interaction between electron and nuclear spin of the $\text{Ga}{}_i^{2+}$ interstitial spin filtering defect. We show that the nuclear spin polarization of the gallium defect can be tuned through the optically induced spin polarization of conduction band electrons.

Two-dimensional dielectric photonic crystals (PCs) having periodic air hole cylinders, when designed properly, exhibit near-zero effective refractive index and the wave impedance is dependent on local observation points. The incident wave is mostly reflected at the PC-air interface due to large impedance mismatch. We show, analytically and numerically, that even in the near-zero effective refractive index case the reflection can be suppressed by utilizing an antireflection structure consisting of a PC with the same lattice constant but a different radius for the periodic air hole cylinders. The antireflection PC must be truncated at properly selected cross sections in order to possess the same impedance at cross sections with the host PC and with the air structure. An analytical model combined with the plane-wave expansion method captures the antireflection behavior obtained by the full wave simulations.

The edge effect on a single vacancy state of semi-infinite graphene (SIG) has been studied using Green's function method within the tight-binding model. In the case of infinite graphene, it is known that a vacancy induces a zero-energy resonance state, whose wave function decays inversely with distance $\left(R\right)$ from the vacancy and is not normalizable. However, for SIG with an armchair edge, we find that the corresponding wave function decays as $R^{-2}$ and hence becomes normalizable owing to the intervalley interference caused by the armchair edge. For SIG with a zigzag edge, the vacancy state depends on the sublattice of the vacancy. When the vacancy and the edge belong to different sublattices, the vacancy has no effect on the zero-energy vacancy state. In contrast, when the vacancy is located on the same sublattice as the edge, the resonance state disappears but the wave function at zero energy is strongly distorted near the vacancy. Our results reveal that the presence of edges crucially changes the vacancy state in graphene, and thus such a state can be used to probe the edge structure.