The Kondo scale $T_{\mathrm{K}}$ for impurity systems is expected to guarantee universal scaling of physical quantities. However, in practice, not every definition of $T_{\mathrm{K}}$ necessarily supports this notion away from the strict scaling limit. Specifically, this paper addresses the role of finite bandwidth $D$ in the strongly correlated Kondo regime. For this, various theoretical definitions of $T_{\mathrm{K}}$ are analyzed based on the inverse magnetic impurity susceptibility at zero temperature. While conventional definitions in that respect quickly fail to ensure universal Kondo scaling for a large range of $D$, this paper proposes an altered definition of $T_{\mathrm{K}}^{\mathrm{sc}}$ that allows universal scaling of dynamical or thermal quantities for a given fixed Hamiltonian. If the scaling is performed with respect to an external parameter that directly enters the Hamiltonian, such as magnetic field, the corresponding $T_{\mathrm{K}}^{\mathrm{sc}},\mathrm{B}$ for universal scaling differs, yet becomes equivalent to $T_{\mathrm{K}}^{\mathrm{sc}}$ in the scaling limit. The only requirement for universal scaling in the full Kondo parameter regime with a residual error of less than 1% is a well-defined isolated Kondo feature with $T_{\mathrm{K}}\lesssim 0.01D$ irrespective of specific other impurity parameter settings. By varying $D$ over a wide range relative to the bare energies of the impurity, for example, this allows a smooth transition from the Anderson to the Kondo model.

We study the optically induced spin polarization, spin dephasing, and diffusion in several high-mobility two-dimensional electron systems, which are embedded in GaAs quantum wells grown on (110)-oriented substrates. The experimental techniques comprise a two-beam magneto-optical spectroscopy system and polarization-resolved photoluminescence. Under weak excitation conditions at liquid-helium temperatures, we observe spin lifetimes above 100 ns in one of our samples, which are reduced with increasing excitation density due to additional, hole-mediated, spin dephasing. The spin dynamic is strongly influenced by the carrier density and the ionization of remote donors, which can be controlled by temperature and above-barrier illumination. The absolute value of the average electron spin polarization in the samples is directly observable in the circular polarization of photoluminescence collected under circularly polarized excitation and reaches values of about 5%. Spin diffusion is studied by varying the distance between pump and probe beams in microspectroscopy experiments. We observe diffusion lengths above 100 $\mu$m and, at high excitation intensity, a nonmonotonic dependence of the spin polarization on the pump-probe distance.

Photoemission and phonon spectroscopies have yielded widely varying estimates of the electron-phonon coupling parameter $\lambda$ on the surfaces of topological insulators, even for a particular material and technique. We connect the results of these experiments by determining the Dirac fermion quasiparticle spectral function using information from measured spectra of a strongly interacting, low-lying optical surface phonon band. The manifest spectral features resulting from the coupling are found to vary on energy scales $<$1 meV and are distinct from those traditionally observed in the case of acoustic phonons in metals. We explore different means of determining $\lambda$ from the electron perspective and identify definitions that yield values consistent with phonon spectroscopy.

We show that the features of Klein tunneling make graphene a unique interface for implementing low control quantum gates between static and mobile qubits. A ballistic electron spin is considered as the mobile qubit, while the static qubit is the electronic spin of a quantum dot fixed in a graphene nanoribbon. Scattering is the low control mechanism of the gate, which in other systems is very difficult to exploit because of both backscattering and the momentum dependence of transmission. We find that the unique features of Klein tunneling enable quasideterministic quantum gates between the spin of a ballistic electron and a static spin held in a dot, regardless of the momenta or the shape of the incident electron wave function. The Dirac equation is used to describe the system in the one particle approximation, with the interaction between the static and the mobile spins modeled by a Heisenberg Hamiltonian. Furthermore, we discuss an application of this model to generate entanglement between two well-separated static qubits.

We investigate the correlation between spin signals measured in three-terminal (3T) geometry by the Hanle effect and the spin accumulation generated in a semiconductor channel in a lateral (Ga,Mn)As/GaAs Esaki diode device. We systematically compare measurements using a 3T configuration, probing spin accumulation directly beneath the injecting contact, with results from nonlocal measurements, where solely spin accumulation in the GaAs channel is probed. We find that the spin signal detected in the 3T configuration is dominated by a bias-dependent spin detection sensitivity, which in turn is strongly correlated with charge-transport properties of the junction. This results in a particularly strong enhancement of the detected spin signal in a region of increased differential resistance. We find additionally that two-step tunneling via localized states in the gap of (Ga,Mn)As does not compromise spin injection into the semiconductor conduction band.

We have succeeded in fully describing dynamic properties of spin current including the different spin absorption mechanisms for longitudinal and transverse spins in lateral spin valves, which enable one to elucidate intrinsic spin transport and relaxation mechanisms in the nonmagnet. The deduced spin lifetimes are found independent of the contact type. From the transit-time distribution of spin current extracted from the Fourier transform in Hanle measurement data, the velocity of the spin current in Ag with Py/Ag Ohmic contact turns out much faster than that expected from the widely used model.

We extend the simple and efficient lowest order expansion (LOE) for inelastic electron tunneling spectroscopy (IETS) to include variations in the electronic structure on the scale of the vibration energies. This enables first-principles calculations of IETS line shapes for molecular junctions close to resonances and band edges. We demonstrate how this is relevant for the interpretation of experimental IETS using both a simple model and first-principles simulations.

Strongly correlated materials such as transition metal oxides (TMOs) often exhibit large satellites in their x-ray photoemission (XPS) and x-ray absorption spectra (XAS). These satellites arise largely from localized charge transfer excitations that accompany the sudden creation of a core hole. Here we use a two-step approach to treat such excitations in a localized system embedded in a condensed-matter environment and coupled to a photoelectron. The total XAS is then given by a convolution of an energy-dependent spectral function representing the localized excitations coupled to the photoelectron and the XAS of the extended system. The local system is modeled roughly in terms of a simplified three-level model, leading to a double-pole approximation for the spectral function that represents dynamically weighted contributions from the dominant neutral and charge transfer excitations. This method is implemented using a resolvent approach, with potentials, radial wave functions, and matrix elements from the real-space Green's function code feff9, and parameters fitted to XPS experiments. Representative calculations for several TMOs are found to be in reasonable agreement with experiment and with other calculations.

Noncollinear and noncoplanar spin textures in solids manifest themselves not only in their peculiar magnetism but also in unusual electronic and transport properties. We here report our theoretical studies of a noncoplanar order on a simple cubic lattice and its influence on the electronic structure. We show that a four-sublattice triple-$Q$ order induces three-dimensional massless Dirac electrons at commensurate electron fillings. The Dirac state is doubly degenerate, while it splits into a pair of Weyl nodes by lifting the degeneracy by an external magnetic field; the system is turned into a Weyl semimetal in an applied field. In addition, we point out the triple-$Q$ Hamiltonian in the strong coupling limit is equivalent to the 3D $\pi$-flux model relevant to an AIII topological insulator. We examine the stability of such a triple-$Q$ order in two fundamental models for correlated electron systems: a Kondo lattice model with classical localized spins and a periodic Anderson model. For the Kondo lattice model, performing a variational calculation and Monte Carlo simulation, we show that the triple-$Q$ order is widely stabilized around 1/4 filling. For the periodic Anderson model, we also show the stability of the same triple-$Q$ state by using the mean-field approximation. For both models, the triple-$Q$ order is widely stabilized via the couplings between conduction electrons and localized electrons even without any explicit competing magnetic interactions and geometrical frustration. We also show that the Dirac electrons induce peculiar surface states: Fermi “arcs” connecting the projected Dirac points, similar to Weyl semimetals.

We present a microscopic theory of electronic and optical properties of colloidal graphene quantum dots (CGQDs). The single-particle properties are described in the tight-binding model based on the $p_z$ carbon orbitals. Electron-electron screened Coulomb direct, exchange, and scattering matrix elements are calculated using Slater $p_z$ orbitals. The many-body ground state and excited states are constructed as a linear combination of a finite number of excitations from the Hartree-Fock (HF) ground state (GS) by exact diagonalization techniques. HF ground states corresponding to semiconductor, Mott-insulator, and spin-polarized phases are obtained as a function of the strength of the screened interaction versus the tunneling matrix element. In the semiconducting phase of a triangular CGQD, the top of the valence band and the bottom of the conduction band are found to be degenerate due to rotational symmetry. The singlet and triplet exciton spectra from the HF GS are obtained by solving the Bethe-Salpeter equation. The low-energy exciton spectrum is predicted to consist of two bright-singlet exciton states corresponding to two circular polarizations of light and a lower-energy band of two dark singlets and 12 dark triplets. The robustness of the bright degenerate singlet pair against correlations in the many-body state is demonstrated as well as the breaking of the degeneracy by the lowering of symmetry of the CGQD. The band-gap renormalization, electron-hole attraction, fine structure, oscillator strength, and polarization of the exciton are analyzed as a function of the size, shape, screening, and symmetry of the CGQD. The theoretical results are compared with experimental absorption spectra.

Three-dimensional, ion-induced nanoscale pattern formation in the growth mode is studied for a bicomponent thin film. C:Ni films were grown by dual ion beam cosputtering applying an assisting oblique-incidence low-energy ${\text{Ar}}^{+}$ ion beam. Their microstructure was determined by scanning electron, atomic force, and transmission electron microscopy, as well as by grazing-incidence small-angle x-ray scattering. The role of ion-induced collisional effects was investigated by binary collision computer simulations. The formation of compositionally modulated ripples on the C:Ni film surface is demonstrated. They consist of metal-enriched topographic crests and carbon-enriched valleys. Since the surface is constantly covered by incoming species, this pattern is transferred into the bulk as a periodic array of ${\text{Ni}}_3\text{C}$ nanoparticles or of Ni-enriched regions in a carbon matrix. Lateral ripple propagation is shown to be one of the crucial phenomena for the film morphology. The essential experimental features are reproduced by the computer simulations. The results reveal the importance of ion-induced preferential displacements as the driving factor for a surface instability, which gives rise to the observed pattern formation.

A theoretical approach for characterizing the influence of asymmetry of noise distribution on the escape rate of a multistable system is presented. This was carried out via the estimation of an action, which is defined as an exponential factor in the escape rate, and discussed in the context of full counting statistics paradigm. The approach takes into account all cumulants of the noise distribution and demonstrates an excellent agreement with the results of numerical simulations. An approximation of the third-order cumulant was shown to have limitations on the range of dynamic stochastic system parameters. The applicability of the theoretical approaches developed so far is discussed for an adequate characterization of the escape rate measured in experiments.

A number of experiments have demonstrated that destructive quantum interference (QI) effects in molecular junctions lead to very low conductances even at room temperature. On the other hand, another recent experiment showed increasing conductance with temperature which was attributed to decoherence effects destroying QI at finite temperatures. Here we study the influence of finite temperatures and electron-phonon interactions on QI in molecular junctions. Two different models leading to two inherently different types of QI effects are considered. Each model is exemplified by specific molecules and studied using first-principles calculations. We find that the molecules exhibiting QI show a much stronger temperature dependence of the conductance compared to molecules without QI. However, the large QI-induced suppression of the conductance remains, showing that QI effects are indeed robust against finite temperatures and inelastic scattering.

The familiar Rabi model, comprising a two-level system coupled to a quantum harmonic oscillator, continues to produce rich and surprising physics when the coupling strength becomes comparable to the individual subsystem frequencies. We construct approximate solutions for the eigenstates and energies in the regime in which the oscillator frequency is small compared to that of the two-level system and the coupling strength matches or exceeds the oscillator frequency. The resulting oscillator dynamics closely resembles that of a particle tunneling in a classical double-well potential. Relating our calculation to an earlier semiclassical approximation in which coupling to the two-level system creates an effective potential for the oscillator, we examine the extent to which this picture is valid. We find that, for certain parameter regimes, the interpretation of the oscillator dynamics in terms of tunneling holds to a good approximation despite the fundamentally entangled nature of the joint system. We assess the prospects for observation of oscillator tunneling in the context of nano- or micromechanical experiments and find that it should be possible if suitably high coupling strengths can be engineered.

We present a theoretical analysis of the rate equations for irreversible growth with a monomer influx, desorption, and a power-law dependence of the capture coefficients on the number of monomers $s$. Special emphasis is given to the size distribution shapes and their time invariance in terms of a new variable which is distinctly different from the conventional $s/s_{*}$ ratio, with $s_{*}$ being a representative size in the distribution. Our results can be briefly formulated as follows. First, we generalize the earlier results to systems with desorption. Second, the analytical size distributions are obtained by applying the transformation to a certain invariant size variable ($\rho$) for which the regular growth rate is independent of the cluster size, and the Green function in the form of Gaussian with a spreading dispersion. Third, the size distribution shapes reflect the time dependence of the monomer concentration inverted in terms of the $z-\rho$ variable, with $z$ as a representative invariant size. Fourth, the fluctuation-induced broadening of these spectra depends critically on the growth law. Fifth, the obtained distributions show a refined time-invariant scaling in the appropriate variables for a broad range of conditions and for all but very small $z$, while the scaling in terms of $\rho /z$ works only in the formal limit $z\to \infty$.

We theoretically and numerically study magnetic domain wall (DW) pinning at a notch in a magnetic nanowire. Based on the static DW equation, a general relationship between an external field and a DW structure for a given notch geometry is found. By estimating the field below which this relationship holds, we obtain the depinning field theoretically. Our theoretical estimate of the depinning field compares well with simulation results. Furthermore, our theory explains well why the depinning field of a transverse wall of one chirality is larger than that of the opposite chirality.

A remarkable discovery in recent years is that there exist various kinds of topological insulators and superconductors characterized by a periodic table according to the system symmetry and dimensionality. To physically realize these peculiar phases and study their properties, a critical step is to construct experimentally relevant Hamiltonians that support these topological phases. We propose a general and systematic method based on the quaternion algebra to construct the tight-binding Hamiltonians for all the three-dimensional topological phases in the periodic table characterized by arbitrary integer topological invariants, which include the spin-singlet and the spin-triplet topological superconductors, the Hopf, and the chiral topological insulators as particular examples. For each class, we calculate the corresponding topological invariants through both geometric analysis and numerical simulation.

Spin polarization induced by an external electric field in graphene is considered theoretically in the linear-response regime. The graphene is assumed to be deposited on a substrate which leads to the spin-orbit interaction of Rashba type. The induced spin polarization is shown to be in the graphene plane and perpendicular to the electric field. However, orientation of the spin polarization becomes reversed when the Fermi level, the position of which can be controlled by an external gate voltage, crosses the Dirac points.

The influence of out-of-plane and in-plane contact vibrations and temperature on the friction force acting on a sharp tip elastically pulled on a crystal surface is studied using a generalized Prandtl-Tomlinson model. The average friction force is significantly lowered in a frequency range determined by the “washboard” frequency of the stick-slip motion and the viscous damping accompanying the tip motion. An approximately linear relationship between the actuation amplitude and the effective corrugation of the surface potential is derived in the case of in-plane actuation, extending a similar conclusion for out-of-plane actuation. Temperature causes an additional friction reduction with a scaling relation in formal agreement with the predictions of reaction rate theory in the absence of contact vibrations. In this case the actuation effects can be described by the effective energy or, more accurately, by introducing an effective temperature.