We study the Kondo effect in three-dimensional (3D) Dirac materials and Weyl semimetals. We find the scaling of the Kondo temperature with respect to the doping $n$ and the coupling $J$ between the moment of the magnetic impurity and the carriers of the semimetal. We consider the interplay of long-range scalar disorder and Kondo screening and find that it causes the Kondo effect to be characterized not by a Kondo temperature, but by a distribution of Kondo temperatures with features that cause the appearance of strong non-Fermi-liquid behavior. We then consider the effect of Kondo screening, and of the interplay of Kondo screening and long-range scalar disorder, on the transport properties of Weyl semimetals. Finally, we compare the properties of the Kondo effect in 3D and 2D Dirac materials such as graphene and topological insulators.

Graphene, a two-dimensional (2D) carbon sheet, acquires many of its amazing properties from the Dirac point nature of its electronic structures with negligible spin-orbit coupling. Extending to 3D space, graphene networks with negative curvature, called Mackay-Terrones crystals (MTCs), have been proposed and experimentally explored, yet their topological properties have yet to be discovered. Based on the first-principle calculations, we report an all-carbon MTC with topologically nontrivial electronic states by exhibiting node lines in bulk. When the node lines are projected onto surfaces to form circles, “drumhead”-like flat surface bands nestled inside of the circles are formed. The bulk node line can evolve into a 3D Dirac point in the absence of inversion symmetry, the existence of which has been shown to be plausible in recent experiments.

Despite a plethora of materials suggested for spintronic applications, a new class of materials has emerged, namely spin gapless semiconductors (SGS), which offers potentially more advantageous properties than existing ones. These magnetic semiconductors exhibit a finite band gap for one spin channel and a closed gap for the other. Here, supported by electronic-structure calculations, we report evidence of SGS behavior in equiatomic quaternary CoFeCrGa, having a cubic Heusler (prototype LiMgPdSn) structure but exhibiting chemical disorder (${\mathrm{DO}}_3$ structure). CoFeCrGa is found to transform from SGS to half-metallic phase under pressure, which is attributed to unique electronic-structure features. The saturation magnetization $\left(M_S\right)$ obtained at $8\mathrm{K}$ agrees with the Slater-Pauling rule and the Curie temperature $\left(T_C\right)$ is found to exceed $400\mathrm{K}$. Carrier concentration (up to $250\mathrm{K}$) and electrical conductivity are observed to be nearly temperature independent, prerequisites for SGS. The anomalous Hall coefficient is estimated to be $185\mathrm{S}/\mathrm{cm}$ at $5\mathrm{K}$. Considering the SGS properties and high $T_C$, this material appears to be promising for spintronic applications.

We propose a local real-space formulation for orbital-free density functional theory (DFT) with density dependent kinetic energy functionals and a unified variational framework for computing the configurational forces associated with geometry optimization of both internal atomic positions as well as the cell geometry. The proposed real-space formulation, which involves a reformulation of the extended interactions in electrostatic and kinetic energy functionals as local variational problems in auxiliary potential fields, also readily extends to all-electron orbital-free DFT calculations that are employed in warm dense matter calculations. We use the local real-space formulation in conjunction with higher-order finite-element discretization to demonstrate the accuracy of orbital-free DFT and the proposed formalism for the Al-Mg materials system, where we obtain good agreement with Kohn-Sham DFT calculations on a wide range of properties and benchmark calculations. Finally, we investigate the cell-size effects in the electronic structure of point defects, in particular, a monovacancy in Al. We unambiguously demonstrate that the cell-size effects observed from vacancy formation energies computed using periodic boundary conditions underestimate the extent of the electronic structure perturbations created by the defect. On the contrary, the bulk Dirichlet boundary conditions, accessible only through the proposed real-space formulation, which correspond to an isolated defect embedded in the bulk, show cell-size effects in the defect formation energy that are commensurate with the perturbations in the electronic structure. Our studies suggest that even for a simple defect like a vacancy in Al, we require cell sizes of $\sim {10}^3$ atoms for convergence in the electronic structure.

$\mathrm{NaCaN}{\mathrm{i}}_2{\mathrm{F}}_7$ is an insulating, frustrated $A_2{B}_2{\mathrm{F}}_7$ pyrochlore with magnetic $S=1\mathrm{N}{\mathrm{i}}^{2+}$ on the pyrochlore B site. Nonmagnetic Na and Ca are disordered on the A site. Magnetic susceptibility measurements made on an oriented single crystal, grown in a floating zone furnace, show isotropic behavior at temperatures between 5 and $300\mathrm{K}$, with an effective moment of $3.7{\mu }_{\mathrm{B}}/\mathrm{Ni}$. Despite displaying a large Curie-Weiss theta $(-129\mathrm{K})$, spin-ordering-related features are not seen in the susceptibility or specific heat until a spin glass transition at $3.6\mathrm{K}$. This yields an empirical frustration index of $f=-{\theta }_{\mathrm{CW}}/{\mathrm{T}}_{\mathrm{f}}\approx 36$. The spin glass behavior is substantiated by a shift of the freezing temperature with frequency in the ac susceptibility, bifurcation in the dc susceptibility, and by a broad maximum in the magnetic specific heat. The observations as made on large single crystals suggest that $\mathrm{NaCaN}{\mathrm{i}}_2{\mathrm{F}}_7$ is likely a realization of a frustrated spin 1 pyrochlore antiferromagnet with weak bond disorder.

We study a voltage-biased Josephson junction coupled to two resonators of incommensurate frequencies. Using a density matrix approach to analyze the cavity fields and an input-output description to analyze the emitted photonic fluxes and their correlation functions, we have shown, both for infinite- and finite-bandwidth detectors, that the emitted radiation is nonclassical in the sense that the correlators violate Cauchy-Schwarz inequalities. We have also studied the time dependence of the photonic correlations and showed that their linewidth becomes narrower with the increase of the emission rate approaching from below the threshold limit.

The morphology transition from the thermodynamically favorable to the unfavorable phase during growth of freestanding copper nanoclusters is studied by molecular dynamics simulations. We give a detailed description of the kinetics and thermodynamics of the process. A universal mechanism of a solid-solid transition, from icosahedral to decahedral morphology in the nanoclusters, is proposed. We show that a formation of distorted NC during the growth process with islands of incoming atoms localized in certain parts of the grown particle may shift the energy balance between Ih and Dh phases in favor of the latter leading to the morphology transition deep within the thermodynamic stability field of the former. The role of diffusion in the morphology transition is revealed. In particular, it is shown that fast diffusion should suppress the morphology transition and favor homogeneous growth of the nanoclusters.

We study the dynamics of an antiferromagnetic soliton under a temperature gradient. To this end, we start by phenomenologically constructing the stochastic Landau-Lifshitz-Gilbert equation for an antiferromagnet with the aid of the fluctuation-dissipation theorem. We then derive the Langevin equation for the soliton's center of mass by the collective coordinate approach. An antiferromagentic soliton behaves as a classical massive particle immersed in a viscous medium. By considering a thermodynamic ensemble of solitons, we obtain the Fokker-Planck equation, from which we extract the average drift velocity of a soliton. The diffusion coefficient is inversely proportional to a small damping constant $\alpha$, which can yield a drift velocity of tens of m/s under a temperature gradient of 1 K/mm for a domain wall in an easy-axis antiferromagnetic wire with $\alpha \sim {10}^{-4}$.

The thermal evolution of electronic order in the complex Verwey ground state of magnetite $\left(\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4\right)$ has been determined through 22 high-accuracy synchrotron x-ray structure refinements using three $10–40\mu \mathrm{m}$ grains of stoichiometric magnetite. A robust fitting function is introduced to extract values of order parameterlike quantities at zero temperature and at the upper limit of the Verwey phase $T_{\mathrm{u}}=123.4\mathrm{K}$. The low-temperature structural distortion is found to be almost frozen below the Verwey transition but small changes in lattice and local mode amplitudes and Fe-Fe distances reveal an increase in electron localization on cooling. These distortions confirm that electron localization within trimerons is the driving force behind the Verwey transition. Electron localization is also revealed by anomalous decreases in the largest principal thermal displacement factors of Fe cations as electron-phonon decoupling occurs on cooling.

Magnetocaloric properties of ${\text{KEr}\left({\mathrm{MoO}}_4\right)}_2$ single crystals were investigated using magnetization and specific heat measurements in the magnetic field applied along the easy and hard axis. Large conventional magnetocaloric effect was found around 10 K ($-\mathrm{\Delta }{S}_{\max }=14$ J/kg K for 5 T) in the field applied along the easy axis. What is more, a huge magnetic anisotropy in the $ab$ plane leads to a large anisotropy of magnetocaloric effect, $-\mathrm{\Delta }{S}_{\mathrm{R},\max }=10$ and 13 J/kg K obtained by a simple rotating of the single crystal within the $ab$ plane in the constant magnetic field 2 and 5 T, respectively. Large $\mathrm{\Delta }{S}_{\mathrm{R}}$ values with no hysteresis losses and rather wide working temperature spans imply that ${\text{KEr}\left({\mathrm{MoO}}_4\right)}_2$ may serve as a promising candidate for the implementation of a compact rotary magnetic cryorefrigerator.

Recent findings of anomalous superlinear scaling of low-temperature $\left(T\right)$ penetration depth (PD) in several nodal superconductors near putative quantum critical points suggest that the low-temperature PD can be a useful probe of quantum critical fluctuations in a superconductor. On the other hand, cuprates, which are poster child nodal superconductors, have not shown any such anomalous scaling of PD, despite growing evidence of quantum critical points (QCP). Then it is natural to ask when and how can quantum critical fluctuations cause anomalous scaling of PD? Carrying out the renormalization group calculation for the problem of two-dimensional superconductors with point nodes, we show that quantum critical fluctuations associated with a point group symmetry reduction result in nonuniversal logarithmic corrections to the $T$ dependence of the PD. The resulting apparent power law depends on the bare velocity anisotropy ratio. We then compare our results to data sets from two distinct nodal superconductors: ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.95}$ and ${\mathrm{CeCoIn}}_5$. Considering all symmetry-lowering possibilities of the point group of interest, $C_{4v}$, we find our results to be remarkably consistent with ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.95}$ being near a vertical nematic QCP and ${\mathrm{CeCoIn}}_5$ being near a diagonal nematic QCP. Our results motivate a search for diagonal nematic fluctuations in ${\mathrm{CeCoIn}}_5$.

Charge order appears to be an ubiquitous phenomenon in doped Mott insulators, which is currently under intense experimental and theoretical investigations particularly in the high $T_c$ cuprates. This phenomenon is conventionally understood in terms of Hartree-Fock-type mean-field theory. Here we demonstrate a mechanism for charge modulation which is rooted in the many-particle quantum physics arising in the strong coupling limit. Specifically, we consider the problem of a single hole in a bipartite $t\text{−}J$ ladder. As a remnant of the fermion signs, the hopping hole picks up subtle phases pending the fluctuating spins, the so-called phase-string effect. We demonstrate the presence of charge modulations in the density matrix renormalization group solutions which disappear when the phase strings are switched off. This form of charge modulation can be understood analytically in a path-integral language with a mean-field-like approximation adopted, showing that the phase strings give rise to constructive interferences leading to self-localization. When the latter occurs, left- and right-moving propagating modes emerge inside the localization volume and their interference is responsible for the real space charge modulation.

All-dielectric metamaterials consisting of high-dielectric inclusions in a low-dielectric matrix are considered as a low-loss alternative to resonant metal-based metamaterials. In this paper we investigate the applicability of the point electric and magnetic dipoles approximation to dielectric meta-atoms on the example of a dielectric ring metamaterial. Despite the large electrical size of high-dielectric meta-atoms, the dipole approximation allows for accurate prediction of the metamaterials properties for the rings with diameters up to $\approx 0.8$ of the lattice constant. The results provide important guidelines for design and optimization of all-dielectric metamaterials.

We present a screened exact-exchange (SXX) method for the efficient and accurate calculation of the optical properties of solids, where the screening is achieved through the zero-wave-vector limit of the inverse dielectric function. The SXX approach can be viewed as a simplification of the Bethe-Salpeter equation (BSE) or, in the context of time-dependent density-functional theory, as a first step towards a new class of hybrid functionals for the optical properties of solids. SXX performs well for bound excitons and continuum spectra in both small-gap semiconductors and large-gap insulators, with a computational cost much lower than that of the BSE.

Using the Feynman diagram techniques, we derive the finite-temperature conductivity and magnetoconductivity formulas from the quantum interference and electron-electron interaction, for a three-dimensional disordered Weyl semimetal. For a single valley of Weyl fermions, we find that the magnetoconductivity is negative and proportional to the square root of magnetic field at low temperatures, as a result of the weak antilocalization. By including the contributions from the weak antilocalization, Berry curvature correction, and Lorentz force, we compare the calculated magnetoconductivity with a recent experiment. The weak antilocalization always dominates the magnetoconductivity near zero field, thus gives one of the transport signatures for Weyl semimetals. In the presence of strong intervalley scattering and correlations, we expect a crossover from the weak antilocalization to weak localization. In addition, we find that the interplay of electron-electron interaction and disorder scattering always dominates the conductivity at low temperatures and leads to a tendency to localization. Finally, we present a systematic comparison of the transport properties of single-valley Weyl fermions, 2D massless Dirac fermions, and 3D conventional electrons.

A variational theory is presented of $A^{1-}$ and $A^{2-}$ centers, i.e., of a negative acceptor ion localizing one and two conduction electrons, respectively, in a GaAs/GaAlAs quantum well in the presence of a magnetic field parallel to the growth direction. A combined effect of the well and magnetic field confines conduction electrons to the proximity of the ion, resulting in discrete repulsive energies above the corresponding Landau levels. The theory is motivated by our experimental magnetotransport results which indicate that, in a heterostructure doped in the GaAs well with Be acceptors, one observes a boil-off effect in which the conduction electrons in the crossed-field configuration are pushed by the Hall electric field from the delocalized Landau states to the localized acceptor states and cease to conduct. A detailed analysis of the transport data shows that, at high magnetic fields, there are almost no conducting electrons left in the sample. It is concluded that one negative acceptor ion localizes up to four conduction electrons.

We study the $S=1/2$ Heisenberg model on the triangular lattice with nearest- and next-nearest-neighbor interactions $J_1$ and $J_2$ with the density matrix renormalization group, on long open cylinders with widths up to nine lattice spacings. In an intermediate $J_2$ region $0.06\lesssim J_2/J_1\lesssim 0.17$, we find evidence for a spin liquid (SL) state with short range spin-spin, bond-bond, and chiral correlation lengths, bordered by a classical ${120}^{\circ }$ Néel ordered state at small $J_2$ and by a two sublattice collinear magnetically ordered state at larger $J_2$. Focusing on $J_2/J_1=0.1$, we find a number of signatures of a gapped SL phase.

We present a tunnel spectroscopy study of single PbS quantum dots (QDs) as a function of temperature and gate voltage. Three distinct signatures of strong electron-phonon coupling are observed in the electron tunneling spectrum (ETS) of these QDs. In the shell-filling regime, the $8\times$ degeneracy of the electronic levels is lifted by the Coulomb interactions and allows the observation of phonon subbands that result from the emission of optical phonons. At low bias, a gap is observed in the ETS that cannot be closed with the gate voltage, which is a distinguishing feature of the Franck-Condon blockade. From the data, a Huang-Rhys factor in the range $S\sim 1.7\text{–}2.5$ is obtained. Finally, in the shell-tunneling regime, the optical phonons appear in the inelastic ETS $d^{2}I/d{V}^2$.