The synthesis and crystallographic and physical properties of polycrystalline EuNiGe${}_3$ are reported. EuNiGe${}_3$ crystallizes in the noncentrosymmetric body-centered tetragonal BaNiSn${}_3$-type structure (space group $I4mm$), in agreement with previous reports, with the Eu atoms at the corners and body center of the unit cell. The physical property data consistently demonstrate that this is a metallic system in which Eu spins $S=7/2$ order antiferromagnetically at a temperature $T_{\mathrm{N}}=13.6$ K. Magnetic susceptibility $\chi$ data for $T>T_{\mathrm{N}}$ indicate that the Eu atoms have spin 7/2 with $g=2$, that the Ni atoms are nonmagnetic, and that the dominant interactions between the Eu spins are ferromagnetic. Thus we propose that EuNiGe${}_3$ has a collinear A-type antiferromagnetic structure, with the Eu ordered moments in the $ab$ plane aligned ferromagnetically and with the moments in adjacent planes along the $c$ axis aligned antiferromagnetically. A fit of $\chi (T\le T_{\mathrm{N}})$ by our molecular field theory is consistent with a collinear magnetic structure. Electrical resistivity $\rho$ data from $T_{\mathrm{N}}$ to 350 K are fitted by the Bloch-Grüneisen model for electron-phonon scattering, yielding a Debye temperature of 265(2) K. A strong decrease in $\rho$ occurs below $T_{\mathrm{N}}$ due to loss of spin-disorder scattering. Heat capacity data at $25\mathrm{K}\le T\le 300$ K are fitted by the Debye model, yielding the same Debye temperature 268(2) K as found from $\rho \left(T\right)$. The extracted magnetic heat capacity is consistent with $S=7/2$ and shows that significant short-range dynamical spin correlations occur above $T_{\mathrm{N}}$. The magnetic entropy at $T_{\mathrm{N}}=13.6$ K is $83\%$ of the expected asymptotic high-$T$ value, with the remainder recovered by 30 K.

We study the zero temperature phase diagram of the three-dimensional Kugel-Khomskii model on a cubic lattice using the cluster mean field theory and different perturbative expansions in the orbital sector. The phase diagram is rich, and goes beyond the single-site mean field theory due to spin-orbital entanglement. In addition to the antiferromagnetic (AF) and ferromagnetic (FM) phases, one finds also a plaquette valence-bond phase with singlets ordered either on horizontal or vertical bonds. More importantly, for increasing Hund's exchange we identify three phases with exotic magnetic order stabilized by orbital fluctuations in between the AF and FM order: (i) an AF phase with two mutually orthogonal antiferromagnets on two sublattices in each $ab$ plane and AF order along the $c$ axis (ortho-$G$-type phase), (ii) a canted-$A$-type AF phase with a nontrivial canting angle between nearest neighbor FM layers along the $c$ axis, and (iii) a striped-AF phase with anisotropic AF order in the $ab$ planes. We elucidate the mechanism responsible for each of the above phases by deriving effective spin models which involve second and third neighbor Heisenberg interactions as well as four-site spin interactions going beyond Heisenberg physics, and explain how the entangled nearest neighbor spin-orbital superexchange generates spin interactions between more distant spins.

We present a detailed investigation performed at low temperature ($T<50$ K) concerning the exciton dynamics in GaN epilayers grown on $c$-plane sapphire substrates, focusing on the exciton formation and the transition from the nonthermal to the thermal regime. The time-resolved kinetics of longitudinal-optical-phonon replicas is used to address the energy relaxation in the excitonic band. From picosecond time-resolved spectra, we bring evidence for a long lasting nonthermal excitonic distribution, which accounts for the first 50 ps. Such a behavior is confirmed in different experimental conditions when both nonresonant and resonant excitations are used. At low excitation power density, the exciton formation and their subsequent thermalization are dominated by impurity scattering rather than by acoustic phonon scattering. The estimate of the average energy of the excitons as a function of delay after the excitation pulse provides information on the relaxation time, which describes the evolution of the exciton population to the thermal regime.

Motivated by interesting recent experimental results, we consider theoretically charged-impurity scattering-limited two-dimensional (2D) electronic transport in (100), (110), and (111)-Si inversion layers at low temperatures and carrier densities, where screening effects are important. We show conclusively that, given the same bare Coulomb disorder, the 2D mobility for a given system increases monotonically with increasing valley degeneracy. We also show that the temperature and the parallel magnetic field dependence of the 2D conductivity is strongly enhanced by increasing valley degeneracy. We analytically consider the low-temperature limit of 2D transport, particularly its theoretical dependence on valley degeneracy, comparing with our full numerical results and with the available experimental results. We make qualitative and quantitative predictions for the parallel magnetic field induced 2D magnetoresistance in recently fabricated high-mobility 6-valley Si(111)-on-vacuum inversion layers. We also provide a theory for 2D transport in ultrahigh mobility Si(111) structures recently fabricated in the laboratory, discussing the possibility of observing the fractional quantum Hall effect in such Si(111) structures.

The selective optical excitation of coherent zone-folded acoustic phonon modes in a semiconductor superlattice is demonstrated. By using a time-delayed control pulse, we show the modification of phonon amplitudes within a phonon triplet and demonstrate that the phase relation of phonon modes can be mapped over time delays of several tens of picoseconds. This method with high spectral resolution has the potential to tailor specific amplitudes of phonon modes that are otherwise only collectively excited.

We report on giant circular dichroism (CD) of a molecule inserted into a plasmonic hot spot. Naturally occurring molecules and biomolecules typically have CD signals in the UV range, whereas plasmonic nanocrystals exhibit strong plasmon resonances in the visible spectral interval. Therefore, excitations of chiral molecules and plasmon resonances are typically off-resonant. Nevertheless, we demonstrate theoretically that it is possible to create strongly enhanced molecular CD utilizing the plasmons. This task is doubly challenging since it requires both creation and enhancement of the molecular CD in the visible region. We demonstrate this effect within the model which incorporates a chiral molecule and a plasmonic dimer. The associated mechanism of plasmonic CD comes from the Coulomb interaction, which is greatly amplified in a plasmonic hot spot. An important feature of the system is anisotropy that results in giant enhancement for the molecular dipoles parallel to the dimer axis. The proposed effect offers very interesting possibilities for enhanced sensing of chiral molecules using visible light.

We demonstrate the formation of a ferromagnetic two-dimensional $d_{xy}$ electron sheet strictly confined to the TiO${}_2$ interface layer in LaAlO${}_3$/SrTiO${}_3$ heterostructures. Based on first-principles density functional calculations we show that the complex subband structure of the two-dimensional electron gas (2DEG) generated at the LaO/TiO${}_2$ (001) interface is universal, and almost independent of the SrTiO${}_3$ thickness. It is composed of a ladder of $d_{xy}$ states of light electrons and only one degenerate $d_{xz,yz}$ heavier subband. All the states are spin polarized although the exchange splitting is only significant for the lowest energy $d_{xy}$ subband, which leads to magnetic moments ferromagnetically coupled and localized at the interface. The SrTiO${}_3$ ferroelectric-like lattice distortions determine the subband occupation and therefore their orbital character, exchange splitting, and charge density profile. The complex structure of the 2DEG can explain the coexistence in the same sample of superconductivity and magnetism.

The vibrational properties of ultrathin Bi(111) films have been calculated by applying density functional perturbation theory with and without the inclusion of spin-orbit interaction. Phonon dispersion curves of dynamically stable bilayers are presented and analyzed. Surprisingly, the Rayleigh mode is found to have the largest amplitude on the second atomic layer. Moreover an optical surface phonon branch is found to be localized above the optical band and confined within the first surface bilayer. The analysis of this mode as a function of the number of bilayers allows one to estimate the contribution of the spin-orbit coupling to the electron-phonon interactions.

We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main ingredient, we introduce the superposed multioptimization method, which allows an efficient optimization of exponentially many MPS of different lengths at different sites all in one step. Here, the algorithm becomes protected against position-dependent effects as caused by spontaneously broken translational invariance. So far, these have been a major obstacle to convergence for the iMPS algorithm if no prior knowledge of the system's translational symmetry was accessible. Further, we investigate some more general methods to speed up calculations and improve convergence, which might be partially interesting in a much broader context, too. As a more special problem, we also look into translational invariant states close to an invariance-breaking phase transition and show how to avoid convergence into wrong local minima for such systems. Finally, we apply these methods to polar bosons with long-range interactions. We calculate several detailed Devil's staircases with the corresponding phase diagrams and investigate some supersolid properties.

We study how the Fermi energy of a graphene monolayer separated from a conducting substrate by a dielectric spacer depends on the properties of the substrate and on an applied voltage. An analytical model is developed that describes the Fermi level shift as a function of the gate voltage, of the substrate work function, and of the type and thickness of the dielectric spacer. The parameters of this model, that should describe the effect of gate electrodes in field effect devices, can be obtained from density functional theory (DFT) calculations on single layers or interfaces. The doping of graphene in metal$|$dielectric$|$graphene structures is found to be determined not only by the difference in work function between the metal and graphene and the dielectric properties of the spacer but potential steps that result from details of the microscopic bonding at the interfaces also play an important role. The doping levels predicted by the model agree very well with the results obtained from first-principles DFT calculations on metal$|$dielectric$|$graphene structures with the metals Al, Co, Ni, Cu, Pd, Ag, Pt, or Au, and a $h$-BN or vacuum dielectric spacer.

We use polarized inelastic neutron scattering (INS) to study spin excitations of optimally hole-doped superconductor Ba${}_{0.67}$K${}_{0.33}$Fe${}_2$As${}_2$ ($T_c=38$ K). In the normal state, the imaginary part of the dynamic susceptibility, ${\chi }^{\prime \prime }(Q,\omega )$, shows magnetic anisotropy for energies below $\sim$7 meV with $c$-axis polarized spin excitations larger than that of the in-plane component. Upon entering into the superconducting state, previous unpolarized INS experiments have shown that spin gaps at $\sim$5 and 0.75 meV open at wave vectors $Q=(0.5,0.5,0)$ and $(0.5,0.5,1)$, respectively, with a broad neutron spin resonance at $E_r=15$ meV. Our neutron polarization analysis reveals that the large difference in spin gaps is purely due to different spin gaps in the $c$ axis and in-plane polarized spin excitations, resulting in a resonance with different energy widths for the $c$-axis and in-plane spin excitations. The observation of spin anisotropy in both optimally electron- and hole-doped BaFe${}_2$As${}_2$ is due to their proximity to the AF ordered BaFe${}_2$As${}_2$ where spin anisotropy exists below $T_N$.

We report a chemically specific x-ray photoelectron diffraction (XPD) investigation using synchrotron radiation of the thermally induced growth of epitaxial graphene on the 6$H$-SiC(0001). The XPD results show that the buffer layer on the SiC(0001) surface is formed by two domain regions rotated by ${60}^{\circ }$ with respect to each other. The experimental data supported by a comprehensive multiple scattering calculation approach indicates the existence of a long-range ripple due the $(6\sqrt{3}\times 6\sqrt{3})R{30}^{\circ }$ reconstruction, in addition to a local range buckling in the (0001) direction of the two sublattices that form the honeycomb structure of the buffer layer. This displacement supports the existence of an $s{p}^2$-to-$s{p}^3$ rehybridization in this layer. For the subsequent graphene layer this displacement is absent, which can explain several differences between the electronic structures of graphene and the buffer layer.

We directly observed the gradual thinning and eventual failure of single-crystalline gold (Au) contacts under increasing electric bias. The contacts fractured in a controlled manner at a current density of around (2–3) × 10${}^{10}$ A/cm${}^2$, so that nanogaps 1–2 nm wide were formed reproducibly. Also, the surface migration of Au atoms was observed to be enhanced by stretching the contact, suggesting that the surface migration of the Au atoms was sensitive to the stress distribution. The Au contact is probably fractured in a controlled manner, when it becomes stress free.

An efficient method for computing the Landauer-Büttiker conductance of an open quantum system within $\mathrm{DFT}+U$ is presented. The Hubbard potential is included in electronic-structure and transport calculations as a simple renormalization of the nonlocal pseudopotential coefficients by restricting the integration for the onsite occupations within the cutoff spheres of the pseudopotential. We apply the methodology to the case of an Au monatomic chain in the presence of a CO molecule adsorbed on it. We show that the Hubbard $U$ correction removes the spurious magnetization in the pristine Au chain at the equilibrium spacing, as well as the unphysical contribution of $d$ electrons to the conductance, resulting in a single (spin-degenerate) transmission channel and a more realistic conductance of $1G_0$. We find that the conductance reduction due to CO adsorption is much larger for the atop site than for the bridge site, so that the general picture of electron transport in stretched Au chains given by the local density approximation remains valid at the equilibrium Au-Au spacing within $\mathrm{DFT}+U$.

We introduce two-dimensional fermionic band models with two orbitals per lattice site, or one spinful orbital, and which have a nonzero topological Chern number that can be changed by varying the ratio of hopping parameters. A topologically nontrivial insulator is then realized if there is one fermion per site. When interactions in the framework of the Hubbard model are introduced, the effective hopping parameters are renormalized and the system's topological number can change at a certain interaction strength, $U=\overline{U}$, smaller than that for the Mott transition. Two different situations may then occur: Either the anomalous Hall conductivity ${\sigma }_{xy}$ changes abruptly at $\overline{U}$, as the system undergoes a transition from one topologically nontrivial insulator to another, or the transition is through an anomalous Hall metal, and ${\sigma }_{xy}$ changes smoothly between two different quantized values as $U$ grows. Restoring time-reversal symmetry by adding spin to spinless models, the half-filled system becomes a ${\mathbb{Z}}_2$ topological insulator. The topological number $\nu$ then changes at a critical coupling $\overline{U}$ and the quantized spin Hall response changes abruptly.

Methods of determining surface diffusion coefficients of molecules from signal fluctuations of a locally fixed probe are revisited and refined. Particular emphasis is put on the influence of the molecule's extent. In addition to the formerly introduced autocorrelation method and residence time method, we develop a further method based on the distribution of intervals between successive peaks in the signal. The theoretical findings are applied to scanning tunneling microscopy measurements of copper phthalocyanine (CuPc) molecules on the Ag(100) surface. We discuss advantages and disadvantages of each method and suggest a combination to obtain accurate results for diffusion coefficients.

Using ab initio density-functional perturbation theory we have examined the effects of atomic relaxation on the phonon dispersion relations and thermal properties of ultrathin (Si)${}_n$(Ge)${}_n$[001] ($1\le n\le 5$) superlattices. It is found that atomic relaxation effects governed by the minimum energy requirement lead to significant changes in the location of phonon frequencies above 200 cm${}^{-1}$ as well as in the location and width of phononic gaps. These changes result in a decrease of around $7\%$ in the zone-average phonon relaxation time and up to a $5\%$ decrease in the thermal conductivity tensor components ${\kappa }_{zz}$ and ${\kappa }_{xx}$ of the (Si)${}_1$(Ge)${}_1$[001] superlattice.

Quantum oscillations can be used to determine properties of the Fermi surface of metals by varying the magnitude and orientation of an external magnetic field. Topological insulator surface states are an unusual mix of normal and Dirac fermions. Unlike in graphene and simple metals, Berry's geometric phase in topological insulator surface states is not necessarily quantized. We show that reliably extracting this geometric phase from the phase offset associated with the quantum oscillations is subtle. This is especially so in the presence of a Dirac gap such as that associated with the Zeeman splitting or interlayer tunneling. We develop a semiclassical theory for general mixed normal-Dirac systems in the presence of a gap, and in doing so clarify the role of topology and broken particle-hole symmetry. We propose a systematic procedure of fitting Landau-level index plots at large filling factors to reliably extract the phase offset associated with Berry's phase.

We present an analytical effective theory for the magnetic phase diagram for zigzag-edge terminated honeycomb nanoribbons described by a Hubbard model with an interaction parameter $U$. We show that the edge magnetic moment varies as $\ln U$ and uncover its dependence on the width $W$ of the ribbon. The physics of this owes its origin to the sensory-organ-like response of the nanoribbons, demonstrating that considerations beyond the usual Stoner-Landau theory are necessary to understand the magnetism of these systems. A first-order magnetic transition from an antiparallel orientation of the moments on opposite edges to a parallel orientation occurs upon doping with holes or electrons. The critical doping for this transition is shown to depend inversely on the width of the ribbon. Using variational Monte Carlo calculations, we show that magnetism is robust to fluctuations. Additionally, we show that the magnetic phase diagram is generic to zigzag-edge terminated nanostructures such as nanodots. Furthermore, we perform first-principles modeling to show how such magnetic transitions can be realized in substituted graphene nanoribbons.

In a magnetic field graphene trilayers support a characteristic multiplet of 12 zero (energy) mode Landau levels with a threefold degeneracy in Landau orbitals. It was earlier noted for bilayer graphene that Coulombic vacuum fluctuations, specific to graphene, lift the orbital degeneracy of such zero-energy modes and that these “Lamb-shifted” orbital modes, with filling, get mixed via the Coulomb interaction. It is pointed out that an analogous orbital Lamb shift and mixing of zero-mode levels can also take place, with an enriched symmetry content, in $ABC$-stacked trilayer graphene, and its consequences are discussed in the light of experimental results.