We perform a detailed study of the electronic structure of ${\mathrm{Fe}}_{1-x}\mathrm{O}$ at moderate values of $x$. Our results evidence that the Fe vacancies introduce significant local modifications of the structural, electronic, and magnetic features, which serve to explain the origin of the measured dependencies of the physical properties on $x$. The final properties are determined by a complex interplay of the charge demand from O, the magnetic interactions, and the charge order at the Fe sublattice. Furthermore, polaronic distributions of charge resembling those at magnetite, ${\mathrm{Fe}}_3{\mathrm{O}}_4$, emerge for the most stable defect structures. This defines a unique scenario to understand the nature of the short-range correlations in ${\mathrm{Fe}}_3{\mathrm{O}}_4$, and unveils their intimate connection to the long-range charge order developed below the Verwey transition temperature.

We study the Mott phase of three-component bosons, with one particle per site, in an optical lattice by mapping it onto an SU(3) spin model. In the simplest case of full SU(3) symmetry, one obtains a ferromagnetic Heisenberg model. Introducing an SU(3) analog of spin-orbit coupling, additional spin-spin interactions are generated. We first consider the scenario of spin-dependent hopping phases, leading to Dzyaloshinskii-Moriya-type interactions. They result in the formation of spiral spin textures, which in one dimension can be understood by a local unitary transformation. Applying classical Monte Carlo simulations, we extend our study to two-dimensional systems, and systems with “true” spin-orbit coupling, involving spin-changing hoppings.

We have investigated the properties of cleaved ${\mathrm{SmB}}_6$ single crystals by x-ray photoelectron spectroscopy. At low temperatures and freshly cleaved samples a surface core level shift is observed which vanishes when the temperature is increased. A Sm valence between 2.5 and 2.6 is derived from the relative intensities of the ${\mathrm{Sm}}^{2+}$ and ${\mathrm{Sm}}^{3+}$ multiplets. The B/Sm intensity ratio obtained from the core levels is always larger than the stoichiometric value. Possible reasons for this deviation are discussed. The B 1s signal shows an unexpected complexity: An anomalous low energy component appears with increasing temperature and is assigned to the formation of a suboxide at the surface. While several interesting intrinsic and extrinsic properties of the ${\mathrm{SmB}}_6$ surface are elucidated in this manuscript, no clear indication of a trivial mechanism for the prominent surface conductivity is found.

The overscreened Kondo effect is shown to be feasible in a carbon nanotube quantum dot junction hosting a spin-$\frac{1}{2}$ atom with a single $s$-wave valence electron (e.g., Au). The idea is to use the two valleys $\xi =\mathbf{K},{\mathbf{K}}^{\prime }$ (located on two inequivalent corners of the first Brillouin zone) as two symmetry protected flavor quantum numbers. Exchange interaction between the itinerant electrons and the host atom is computed and shown to be antiferromagnetic, and it does not couple different flavors. Perturbative renormalization group analysis exposes a finite weak-coupling two-channel fixed point, where the Kondo temperature is estimated to be around $0.5–5$ K. Remarkably, occurrence of two different scaling regimes implies a nonmonotonic dependence of the conductance as a function of temperature. Consequently, in this system (unlike the “standard” two-channel Kondo effect), the physics of the overscreened Kondo effect is exposed already in the weak coupling regime.

We reformulate the topological symmetry-breaking scheme for phase transitions in systems with anyons in a graphical manner. A set of quantities called vertex lifiting coefficients (VLCs) is introduced and used to specify the full operator content of the broken phase. First, it is shown how the assumption that a set of charges behaves like the vacuum of a new theory naturally leads to diagrammatic consistency conditions for a condensate. This recovers the notion of a condensate used in earlier approaches and uncovers the connection to pure mathematics. The VLCs are needed to solve the consistency conditions and establish the mapping of the fusion and splitting spaces of the broken theory into the parent phase. This enables one to calculate the full set of topological data $(S,T,R$, and $F$ matrices) for the condensed phase and closed-form expressions in terms of the VLCs are provided. We furthermore furnish a concrete recipe to lift arbitrary diagrams directly from the condensed phase to the original phase using only a limited number of VLCs and we describe a method for the explicit calculation of VLCs for a large class of bosonic condensates. This allows for the explicit calculation of condensed-phase diagrams in many physically relevant cases and representative examples are worked out in detail.

We explore the static longitudinal and dynamic transverse spin susceptibilities in quantum dots and nanoparticles within the framework of the Hamiltonian that extends the universal Hamiltonian to the case of uniaxial anisotropic exchange. For the limiting cases of Ising and Heisenberg exchange interactions, we ascertain how fluctuations of single-particle levels affect the Stoner instability in quantum dots. We reduce the problem to the statistics of extrema of a certain Gaussian process. We prove that, despite possible strong randomness of the single-particle levels, the spin susceptibility and all its moments diverge simultaneously at the point which is determined by the standard criterion of the Stoner instability involving the mean level spacing only.

Nanocrystals can behave as quantum boxes with confined electronic states governing their optoelectronic properties. The formation of nanometer-size crystals of copper nitride $\left({\mathrm{Cu}}_3\mathrm{N}\right)$ grown by nitrogen sputtering of a Cu(110) surface is reported. Scanning tunneling spectroscopy shows that the nanocrystals exhibit a series of well-defined sharp electronic resonances, which correspond to confined free-electron-like states. We observe that electrons from a scanning tunneling microscope tip induce the emission of light with a larger efficiency than on the bare metal surface. The spectral analysis of the emitted photons reveals various radiative inelastic pathways enabled by the confined states, which explain the enhanced light emission. Thus, the ${\mathrm{Cu}}_3\mathrm{N}$ nanocrystals can be employed as nanometer-size light sources.

We consider Ge/Si core/shell nanowires with hole states coupled to an $s$-wave superconductor in the presence of electric and magnetic fields. We employ a microscopic model that takes into account material-specific details of the band structure such as strong and electrically tunable Rashba-type spin-orbit interaction and $g$ factor anisotropy for the holes. In addition, the proximity-induced superconductivity Hamiltonian is derived starting from a microscopic model. In the topological phase, the nanowires host Majorana fermions with localization lengths that depend strongly on both the magnetic and electric fields. We identify the optimal regime in terms of the directions and magnitudes of the fields in which the Majorana fermions are the most localized at the nanowire ends. In short nanowires, the Majorana fermions hybridize and form a subgap fermion whose energy is split away from zero and oscillates as a function of the applied fields. The period of these oscillations could be used to measure the dependence of the spin-orbit interaction on the applied electric field and the $g$ factor anisotropy.

We report the investigation of full-counting statistics (FCS) of transferred charge and spin in the transient regime where the connection between central scattering region (quantum dot) and leads are turned on at $t=0$. A general theoretical formulation for the generating function (GF) is presented using a nonequilibrium Green's function approach for the quantum dot system. In particular, we give a detailed derivation on how to use the method of path integral together with nonequilibrium Green's function technique to obtain the GF of FCS in electron transport systems based on the two-time quantum measurement scheme. The correct long-time limit of the formalism, the Levitov-Lesovik formula, is obtained. This formalism can be generalized to account for spin transport for the system with noncollinear spin as well as spin-orbit interaction. As an example, we have calculated the GF of spin-polarized transferred charge, transferred spin, as well as the spin transferred torque for a magnetic tunneling junction in the transient regime. The GF is compactly expressed by a functional determinant represented by Green's function and self-energy in the time domain. With this formalism, FCS in spintronics in the transient regime can be studied. We also extend this formalism to the quantum point contact system. For numerical results, we calculate the GF and various cumulants of a double quantum dot system connected by two leads in the transient regime. The signature of universal oscillation of FCS is identified. On top of the global oscillation, local oscillations are found in various cumulants as a result of the Rabi oscillation. Finally, the influence of the temperature is also examined.

We present the numerical results of a model calculation for the ${}^3\text{He}$ bilayer system, which captures the interplay between fast and slow dynamics of the different layers and incorporates an independent scale for the three-body ring exchange. By means of cluster dynamical mean-field theory in conjunction with continuous-time quantum Monte Carlo, we find remarkable similarities with the experiments: a suppression of the coherence temperature upon approaching the solidification point of the first layer accompanied by the onset of strong ferromagnetic correlations within the first layer. Based on the consistent results for different cluster sizes, we conjecture a first-order transition cutting short the Kondo breakdown, which allows us to interpret the experimental observation of an intervening phase preempting the quantum critical point in terms of a phase separation.

We study the phase diagram of the one-dimensional bosonic Hubbard model with contact $\left(U\right)$ and near neighbor $\left(V\right)$ interactions focusing on the gapped Haldane insulating (HI) phase which is characterized by an exotic nonlocal order parameter. The parameter regime $(U,V$, and $\mu )$ where this phase exists and how it competes with other phases, such as the supersolid (SS) phase, is incompletely understood. We use the stochastic Green function quantum Monte Carlo algorithm as well as the density matrix renormalization group to map out the phase diagram. Our main conclusions are that the HI exists only at $\rho =1$, the SS phase exists for a very wide range of parameters (including commensurate fillings), and displays power law decay in the one-body Green function. In addition, we show that at fixed integer density, the system exhibits phase separation in the $(U,V)$ plane.

An atomiclike basis representation is used to analyze the dielectric function $\epsilon (\vec{q}+\vec{G},\vec{q}+{\vec{G}}^{\prime };\omega )$ of Si. First, we show that a $s{p}^3{d}^5$ local basis set yields good results for the electronic band structure of this crystal and, then, we analyze the Si optical properties including local field and excitonic effects. In our formulation, we follow Hanke and Sham [W. Hanke and L. J. Sham, Phys. Rev. B 12, 4501 (1975); Phys. Rev. B 21, 4656 (1980)], and introduce excitonic effects using a many-body formulation that incorporates a static screened electron-hole interaction. Dynamical effects in this interaction are also analyzed and shown to introduce non-negligible corrections in the optical spectrum. Our results are found in reasonable agreement with the experimental evidence and with other theoretical results calculated with the computationally more demanding plane-wave representation. Finally, calculations for the stopping power of Si are also presented.

Cadmium telluride (CdTe), a compound widely used in devices, is a key base material for the experimental realization of the quantum spin Hall phase. We report herein a study of the electronic structure of CdTe by angle-resolved photoemission spectroscopy from well-ordered (110) surfaces. The results are compared with first-principles calculations to illustrate the topological distinction between CdTe and a closely related compound HgTe. Through a theoretical simulation a topological phase transition as well as the Dirac-Kane semimetal phase at the critical point was demonstrated in the mixed compound $\mathrm{H}{\mathrm{g}}_x\mathrm{C}{\mathrm{d}}_{1-x}\mathrm{Te}$.

Spin injection in high-quality epitaxial $\mathrm{M}{\mathrm{n}}_5\mathrm{G}{\mathrm{e}}_3$ Schottky contacts on $n$-type Ge has been investigated using a three-terminal Hanle effect measurement. Clear Hanle and inverted Hanle signals with features characteristic of spin accumulation and spin precession are observed up to 200 K. Strikingly, the observed spin voltage is several orders of magnitude larger than predicted by the theory of spin injection and diffusive spin transport. Since the devices have no oxide tunnel barrier, the discrepancy between theory and experiments cannot be explained by the often-invoked spin accumulation in localized states associated with the oxide or oxide/semiconductor interface. The observed spin voltages therefore must originate from the Ge itself, either from spins in the Ge bulk bands or its depletion region.

Based on the Gross-Pitaevskii equations, it is predicted that a repulsive interaction provides a way for a two-dimensional polariton condensate to accumulate energy in spite of dissipation under above-resonance optical pumping. The energy can be accumulated over a time much longer than the polariton lifetime, resulting in the state in which the blueshift of the polariton level compensates the mismatch of the pump frequency. The process starts when the field density reaches the parametric scattering threshold that is inversely proportional to the polariton lifetime. Although the increase in energy may be arbitrarily slow in the beginning, it is followed by a blowup. This scenario applies to the case of transitions between steady states in multistable cavity-polariton systems. There is a tradeoff between the latency of the transitions and the pump power.

We investigate the stability and coherence properties of one-dimensional exciton-polariton condensates under nonresonant pumping. We model the condensate dynamics using the open-dissipative Gross-Pitaevskii equation. In the case of spatially homogeneous pumping, we find that the instability of the steady state leads to significant reduction of the coherence length. We consider two effects that can lead to the stabilization of the steady state, i.e., the polariton energy relaxation and the influence of an inhomogeneous pumping profile. We find that, while the former has little effect on the stability, the latter is very effective in stabilizing the condensate, which results in a large coherence length.

We present temperature dependent time-resolved photoluminescence (PL) investigations on well-defined morphologies of the prototypical organic semiconductor rubrene. By their respective degree of spatial constraint these morphologies directly influence the temperature dependent excitonic processes and their dynamics. While in bulk single crystals singlet exciton decay is governed by thermally activated fission at a time constant of 20 ps, this mechanism appears to be absent in rubrene microcrystals. Here the dynamics are characterized by a pronounced increase of the average exciton lifetime as confirmed by the dominating PL decay channel with an effective time constant of 100 ps. The enhanced surface-to-volume ratio indicates that the participating states might originate from microcrystal boundaries which could be reached by the substantial amount of migrating excitons prior to the onset of other decay processes. The suppression of singlet fission in these crystalline microstructures is promoted by the significantly lower activation energy of 25 meV for the 100 ps channel compared to the singlet fission barrier of 44 meV and imposes severe consequences for its utilization in, e.g., thin film photovoltaics. For the crystalline samples, an additional relaxation channel with a time constant of around 500 ps becomes relevant at very low temperatures. As this process is the only one observed for amorphous rubrene thin films it points at the local nature of the underlying decay mechanism.

We investigate electron transport through multiterminal networks hosting Majorana bound states (MBS) in the framework of full counting statistics. In particular, we apply our general results to T-shaped junctions of two Majorana nanowires. When the wires are in the topologically nontrivial regime, three MBS are localized near the outer ends of the wires, while one MBS is localized near the crossing point, and when the lengths of the wires are finite adjacent MBS can overlap. We propose a combination of current and cross-correlation measurements to reveal the predicted coupling of four Majoranas in a topological T junction. Interestingly, we show that the elementary transport processes at the central lead are different compared to the outer leads, giving rise to characteristic nonlocal signatures in electronic transport. We find quantitative agreement between our analytical model and numerical simulations of a tight-binding model. Using the numerical simulations, we discuss the effect of weak disorder on the current and the cross-correlation functions.

A new family of the low-buckled Dirac materials which includes silicene, germanene, etc. is expected to possess a more complicated sequence of Landau levels than in pristine graphene. Their energies depend, among other factors, on the strength of the intrinsic spin-orbit (SO) and Rashba SO couplings and can be tuned by an applied electric field $E_z$. We studied the influence of the intrinsic Rashba SO term on the energies of Landau levels using both analytical and numerical methods. The quantum magnetic oscillations of the density of states are also investigated. A specific feature of the oscillations is the presence of the beats with the frequency proportional to the field $E_z$. The frequency of the beats becomes also dependent on the carrier concentration when Rashba interaction is present allowing experimental determination of its strength.