The Hall effect in InMnAs layers with MnAs inclusions of 20–50 nm in size is studied both theoretically and experimentally. We find that the anomalous Hall effect can be explained by the Lorentz force caused by the magnetic field of ferromagnetic inclusions and by an inhomogeneous distribution of the current density in the layer. The hysteretic dependence of the average magnetization of ferromagnetic inclusions on an external magnetic field results in a hysteretic dependence of $R_{\mathrm{H}}\left(H_{\mathrm{ext}}\right)$. Thus, we show the possibility of a hysteretic $R_{\mathrm{H}}\left(H_{\mathrm{ext}}\right)$ dependence (i.e., observation of the anomalous Hall effect) in thin conductive layers with ferromagnetic inclusions in the absence of carriers' spin polarization.

A spin-singlet ground state with a spin gap has been discovered in antiferromagnetic spin chain substances when the spin value is 1/2, 1, or 2. To find spin-gap (singlet-triplet) excitations in spin-$\frac{3}{2}$ chain substances, we performed inelastic neutron scattering and magnetization measurements on $R\mathrm{CrGeO}{}_5$ ($R=\text{Y}$ or Sm) powders. As expected, we observed spin-gap excitations and the dispersion relation of the lowest magnetic excitations. We proved that the spin system of $\mathrm{Cr}{}^{3+}$ was an antiferromagnetic alternating spin-$\frac{3}{2}$ chain. We describe the influence of frustration between nearest-neighbor and next-nearest-neighbor exchange interactions in the chain.

In many cases, the relativistic spin-orbit (SO) interaction can be regarded as a small perturbation to the electronic structure of solids and treated using regular perturbation theory. The major obstacle on this route comes from the fact that the SO interaction can also polarize the electron system and produce some additional contributions to the perturbation theory expansion, which arise from the electron-electron interactions in the same order of the SO coupling. In electronic structure calculations, it may even lead to the necessity of abandoning the perturbation theory and returning to the original self-consistent solution of Kohn-Sham-like equations with the effective potential $\widehat{v}$, incorporating simultaneously the effects of the electron-electron interactions and the SO coupling, even though the latter is small. In this work, we present the theory of self-consistent linear response (SCLR), which allows us to get rid of numerical self-consistency and formulate the last step fully analytically in the first order of the SO coupling. This strategy is applied to the unrestricted Hartree-Fock solution of an effective Hubbard-type model, derived from the first-principles electronic structure calculations in the basis of Wannier functions for the magnetically active states. We show that by using $\widehat{v}$, obtained in SCLR, one can successfully reproduce results of ordinary self-consistent calculations for the orbital magnetization and other properties, which emerge in the first order of the SO coupling. Particularly, SCLR appears to be an extremely useful approach for calculations of antisymmetric Dzyaloshinskii-Moriya (DM) interactions based on the magnetic force theorem, where only by using the total perturbation one can make a reliable estimate for the DM parameters. Furthermore, due to the powerful $2n+1$ theorem, the SCLR theory allows us to obtain the total energy change up to the third order of the SO coupling, which can be used in calculations of magnetic anisotropy of compounds with low crystal symmetry. The fruitfulness of this approach for the analysis of complex magnetic structures is illustrated in a number of examples, including the quantitative description of the spin canting in ${\mathrm{YTiO}}_3$ and ${\mathrm{LaMnO}}_3$, formation of the spin-spiral order in ${\mathrm{BiFeO}}_3$, and the magnetic inversion symmetry breaking in ${\mathrm{BiMnO}}_3$, which gives rise to both ferroelectric activity and DM interactions, responsible for the ferromagnetism. In all these cases, the use of SCLR tremendously reduces the computational efforts related to the search for noncollinear magnetic structures in the ground state.

Using quasiparticle self-consistent $GW$ calculations, we examined the electronic structure of $\mathrm{LaNiO}{}_3$ and the $\mathrm{LaNiO}{}_3/\mathrm{LaAlO}{}_3$ superlattice. The effects of electron correlation in Ni-$d$ bands were reasonably well described without any ad hoc parameter and without the ambiguity related to the double-counting and downfolding issues. The effective mass is about 30% enhanced compared to the GGA result. One band feature, which is believed to be essential for the cupratelike superconductivity, is not realized and the central Fermi surface pocket does not disappear. Our result is consistent with a recent dynamical mean-field calculation based on the $d\text{−}p$ model and in contrast to the result from a $d$-band-only model.

We investigate the transfer between carrier and Mn spins due to the $s$-$d$-exchange interaction in a Mn-doped bulk semiconductor within a microscopic quantum kinetic theory. We demonstrate that the spin transfer dynamics is qualitatively different for components of the carrier spin parallel and perpendicular to the Mn magnetization. From our quantum kinetic equations we have worked out the corresponding Markov limit, which is equivalent to rate equations based on Fermi's golden rule. The resulting equations resemble the widely used Landau-Lifshitz-Gilbert equations, but also describe genuine spin transfer due to quantum corrections. Although it is known that the Markovian rate description works well for bulk systems when the initial Mn magnetization is zero, we find large qualitative deviations from the full quantum kinetic theory for finite initial Mn magnetizations. These deviations mainly reflect corrections of higher than leading order in the interaction, which are not accounted for in golden-rule-type rates.

A majority of the point defects in GaN that are responsible for broad photoluminescence (PL) bands remain unidentified. One of them is the green luminescence band (GL2) having a maximum at 2.35 eV which was observed previously in undoped GaN grown by molecular-beam epitaxy in Ga-rich conditions. The same PL band was observed in Mg-doped GaN, also grown in very Ga-rich conditions. The unique properties of the GL2 band allowed us to reliably identify it in different samples. The best candidate for the defect which causes the GL2 band is a nitrogen vacancy $\left(V_{\mathrm{N}}\right)$. We propose that transitions of electrons from the conduction band to the +/2+ transition level of the $V_{\mathrm{N}}$ defect are responsible for the GL2 band in high-resistivity undoped and Mg-doped GaN.

We consider charge transport across a finite graphene flake with a circular antidot defined in its center. The flake is connected to thin metallic armchair nanoribbons and the study covers the energy range within the neighborhood of the neutrality point. We solve the scattering problem using the tight-binding Hamiltonian and find that conductance of the system is nonzero only near narrow resonances that are quasibound in either the entire cavity or the antidot itself. We demonstrate that the scanning probe technique can be used for the purpose of determination whether the state is localized within the antidot or in the entire cavity. We indicate that the potential of the perturbation shifts the position of the resonances and that the shifts are related to the localization of the scattering probability density. The resonance lifetime can be both decreased or increased as the perturbation introduced by the probe interferes with the current vortices inside the antidot.

The growth of heteroepitaxial planar fully strained SiGe layers with high Ge concentration and large thickness enables tailoring electronic properties for enhanced transport properties and photoemission. We give here the first experimental and theoretical proof that high temperature flashed porous silicon layers (HT-PSi) perfectly accommodate the stress of SiGe layers and provide compliant substrates with unprecedented capabilities for the fabrication of planar SiGe nanomembranes. We show that the stress driven morphological evolution leading to self-organized quantum dots commonly observed on nominal Si (001) is fully inhibited when growing SiGe on such a HT-PSi substrate. The elastic behavior of HT-PSi results from two specific features: It is ten times softer than Si and tensily strained. Theoretical analysis proves that the compliant behavior of HT-PSi is due to the strain effect, while on the contrary its elastic softness favors the development of 3D growth. The inhibition due to the tensile strain produces atomically flat layers free of misfit dislocation.

We consider theoretically effects of random charged impurity disorder on the quality of high-mobility two-dimensional (2D) semiconductor structures, explicitly demonstrating that the sample mobility is not necessarily a reliable or universal indicator of the sample quality in high-mobility modulation-doped 2D GaAs structures because, depending on the specific system property of interest, mobility and quality may be controlled by different aspects of the underlying disorder distribution, particularly since these systems are dominated by long-range Coulomb disorder from both near and far random quenched charged impurities. We show that in the presence of both channel and remote charged impurity scattering, which is a generic situation in modulation-doped high-mobility 2D carrier systems, it is quite possible for higher (lower) mobility structures to have lower (higher) quality as measured by the disorder-induced single-particle level broadening. In particular, we establish that there is no reason to expect a unique relationship between mobility and quality in 2D semiconductor structures as both are independent functionals of the disorder distribution, and are therefore, in principle, independent of each other. Using a simple, but reasonably realistic, “2-impurity” minimal model of the disorder distribution, we provide concrete examples of situations where higher (lower) mobilities correspond to lower (higher) sample qualities. We discuss experimental implications of our theoretical results and comment on possible strategies for future improvement of 2D sample quality.

We study the Kondo screening of a magnetic impurity adsorbed in graphene in the presence of Rashba spin-orbit interaction. The system is described by an effective single-channel Anderson impurity model, which we analyze using the numerical renormalization group. The nontrivial energy dependence of the host density of states gives rise to interesting behaviors under variation of the chemical potential or the spin-orbit coupling. Varying the Rashba coupling produces strong changes in the Kondo temperature characterizing the many-body screening of the impurity spin, and at half filling allows an approach to a quantum phase transition separating the strong-coupling Kondo phase from a free-moment phase. Tuning the chemical potential close to sharp features of the hybridization function results in striking features in the temperature dependencies of thermodynamic quantities and in the frequency dependence of the impurity spectral function.

We study Andreev reflection and Josephson currents in topological bilayer exciton condensates (TECs). These systems can create 100% spin-entangled nonlocal currents with high amplitudes due to perfect nonlocal Andreev reflection. This Andreev reflection process can be gate tuned from a regime of purely retro reflection to purely specular reflection. We have studied the bound states in TEC–topological-insulator–TEC Josephson junctions and find a gapless dispersion for perpendicular incidence. The presence of a sharp transition in the supercurrent-phase relationship when the system is in equilibrium is a signature of fractional charge, which can be further revealed in ac measurements faster than relaxation processes via Landau-Zener processes.

Quantum thermal transport in armchair and zigzag graphene nanoribbons is investigated in the presence of single atomic vacancies and subject to different boundary conditions. We start with a full comparison of the phonon polarizations and energy dispersions as given by a fifth-nearest-neighbor force-constant model (5NNFCM) and by elasticity theory of continuum membranes (ETCM). For free-edge ribbons, we discuss the behavior of an additional acoustic edge-localized flexural mode, known as fourth acoustic branch (4ZA), which has a small gap when it is obtained by the 5NNFCM. Then, we show that ribbons with supported edges have a sample-size dependent energy gap in the phonon spectrum which is particularly large for in-plane modes. Irrespective to the calculation method and the boundary condition, the dependence of the energy gap for the low-energy optical phonon modes against the ribbon width $W$ is found to be proportional to $1/W$ for in-plane, and $1/W^2$ for out-of-plane phonon modes. Using the 5NNFCM, the ballistic thermal conductance and its contributions from every single phonon mode are then obtained by the nonequilibrium Green's function technique. We found that, while edge and central localized single atomic vacancies do not affect the low-energy transmission function of in-plane phonon modes, they reduce considerably the contributions of the flexural modes. On the other hand, in-plane modes contributions are strongly dependent on the boundary conditions and at low temperatures can be highly reduced in supported-edge samples. These findings could open a route to engineer graphene based devices where it is possible to discriminate the relative contribution of polarized phonons and to tune the thermal transport on the nanoscale.

We report on two-photon interference of highly indistinguishable single photons emitted by a quantum dot. Strictly resonant excitation with picosecond laser pulses has been used to prepare coherent states with a significantly increased coherence time $(T_2\sim 1\text{ns})$ and reduced lifetime $(T_1\sim 650\text{ps})$, as compared to a nonresonant excitation scheme. Indistinguishable photons, with visibilities greater than 70%, have been observed by measuring the Hong-Ou-Mandel dip without postselection of the interfering photons. Near-unity indistinguishable photons should be achievable by preventing fluctuations in the electrostatic environment in the vicinity of the dots, considered as an important source of decoherence.

The kinetic friction of the (0001) graphite surface has been mapped at different speeds and scales by means of an atomic force microscope. The maps show nanoscale domains of various sizes and friction strengths. Each domain presents a transition between two friction regimes and a specific logarithmic scaling of friction with speed. The gradient of this variation is determined by the angle between the macroscopic sliding direction and a stiff crystal axis of the surface lattice. The experimental results are analyzed by considering thermally activated sliding regimes within the puckering friction mechanism.

We study electronic states and topological invariants of (001) films of the topological crystalline insulator (TCI) ${\mathrm{Pb}}_x{\mathrm{Sn}}_{1-x}\mathrm{Te}$. Gapless surface Dirac cones on bulk TCIs become gapped in thin films due to the finite-size effect, which is the hybridization between the states on the top and bottom surfaces. We clarify that the TCI film has a strong finite-size effect as compared to three-dimensional topological insulators such as ${\mathrm{Bi}}_2{\mathrm{Se}}_3$. Moreover, the energy gap oscillates with the thickness of film. The oscillation stems from topological phase transitions in two dimensions. The obtained data of the topological invariants and energy gap serve as guide to TCI-device applications.

We investigate Josephson junctions on the surface of a three-dimensional topological insulator in planar, step, and edge geometries. The elliptical nature of the Dirac cone representing the side surface states of the topological insulator results in a scaling factor in the Josephson current in a step junction as compared to the planar junction. In edge junctions, the contribution of the Andreev bound states to the Josephson current vanishes due to spin-momentum locking of the surface states. Furthermore, we consider a junction with a ferromagnetic insulator between the superconducting regions. In these ferromagnetic junctions, we find an anomalous finite Josephson current at zero phase difference if the magnetization is pointing along the junction (and perpendicular to the Josephson current). An out-of-plane magnetization with respect to the central region of the junction opens up an exchange gap and leads to a nonmonotonic behavior of the critical Josephson current for sufficiently large magnetization as the chemical potential increases.

The temperature dynamics of the radiative heat propagation in a multilayer structure is theoretically treated with a formalism combining the scattering matrix and Green's-functions methods. The time evolution of the temperature of parallel plates of silicon carbide in vacuum is simulated for different interplate distances and thicknesses of plates. The characteristic radiative heat exchange time and temperature of the plates at stationary state are determined from the time evolutions. The threshold interplate distance which separates heating and cooling regimes for the sink plate is found. We show that the variation of the interplate distance allows us to control the relaxation processes in the system of absorber and emitter.

We predict the coexistence of both transverse-electric- and transverse-magnetic-polarized localized electromagnetic waves that can propagate in the same frequency range along a graphene layer inserted in a photonic crystal. In addition, we studied the excitation of these modes by an external wave and have shown that the resonance peaks of the sample transmissivity should be observed due to the excitation of the localized waves, independently of the polarization of the exciting wave. The simplicity of the derived dispersion relations for the localized modes and the possibility to excite waves of both polarizations provide a method for measuring graphene conductivity.

We investigate the scattering of long-wavelength flexural phonons against grain boundaries in graphene using molecular dynamics simulations. Three symmetric tilt grain boundaries are considered: one with a misorientation angle of $17.9^{\circ }$ displaying an out-of-plane buckling 1.5 nm high and 5 nm wide, one with a misorientation angle of $9.4^{\circ }$ and an out-of-plane buckling 0.6 nm high and 1.7 nm wide, and one with a misorientation angle of $32.2^{\circ }$ and no out-of-plane buckling. At the flat grain boundary, the phonon transmission exceeds 95% for wavelengths above 1 nm. The buckled boundaries have a substantially lower transmission in this wavelength range, with a minimum transmission of 20% for the $17.9^{\circ }$ boundary and 40% for the $9.4^{\circ }$ boundary. At the buckled boundaries, coupling between flexural and longitudinal phonon modes is also observed. The results indicate that scattering of long-wavelength flexural phonons at grain boundaries in graphene is mainly due to out-of-plane buckling. A continuum mechanical model of the scattering process has been developed, providing a deeper understanding of the scattering process as well as a way to calculate the effect of a grain boundary on long-wavelength flexural phonons based on the buckling size.