Graphene islands grown epitaxially on 6H-SiC(0001) were studied using scanning tunneling microscopy and spectroscopy. Under specific growth conditions, $\approx 10\text{nm}$ single-layer graphene islands are observed on top of the SiC buffer layer and align with the SiC(0001)-$1\times 1$ lattice directions. Atomic-resolution images show that the edges of the island closely follow an armchair-edge configuration.

A rigorous mathematical foundation for the cluster-expansion method is presented. It is shown that the cluster basis developed by Sanchez et al. [Physica A 128, 334 (1984)] is a multidimensional discrete Fourier transform while the general formalism of Sanchez [Phys. Rev. B 48, 14013 (1993)] corresponds to a multidimensional discrete wavelet transform. For functions that depend nonlinearly on the concentration, it is shown that the cluster basis corresponding to a multidimensional discrete Fourier transform does not converge, as it is usually assumed, to a finite cluster expansion or to an Ising-type model representation of the energy of formation of alloys. The multidimensional wavelet transform, based on a variable basis cluster expansion, is shown to provide a satisfactory solution to the deficiencies of the discrete Fourier-transform approach. Several examples aimed at illustrating the main findings and conclusions of this work are given.

We study the phase diagram of the Hubbard model in the limit where $U$, the onsite repulsive interaction, is much smaller than the bandwidth. We present an asymptotically exact expression for $T_c$, the superconducting transition temperature, in terms of the correlation functions of the noninteracting system which is valid for arbitrary densities so long as the interactions are sufficiently small. Our strategy for computing $T_c$ involves first integrating out all degrees of freedom having energy higher than an unphysical initial cutoff ${\Omega }_0$. Then, the renormalization group (RG) flows of the resulting effective action are computed and $T_c$ is obtained by determining the scale below which the RG flows in the Cooper channel diverge. We prove that $T_c$ is independent of ${\Omega }_0$. Using this method, we find a variety of unconventional superconducting ground states in two- and three-dimensional lattice systems, and present explicit results for $T_c$ and pairing symmetries as a function of the electron concentration.

The application of graphene in electronic devices requires large-scale epitaxial growth. The presence of the substrate, however, usually reduces the charge-carrier mobility considerably. We show that it is possible to decouple the partially $s{p}^3$-hybridized first graphitic layer formed on the Si-terminated face of silicon carbide from the substrate by gold intercalation, leading to a completely $s{p}^2$-hybridized graphene layer with improved electronic properties.

We employ a general Lagrange model to describe the chiral optical properties of stereometamaterials. We derive the elliptical eigenstates of a twisted stacked split-ring resonator taking phase retardation into account. Through this approach, we obtain a powerful Jones matrix formalism which can be used to calculate the polarization rotation, ellipticity, and circular dichroism of transmitted waves through stereometamaterials at any incident polarization. Our experimental measurements agree well with our model.

We investigate the mutual proximity effect in a normal metal contacted to a superconductor through a magnetic interface. Analytical and self-consistent numerical results are presented, and we consider both the diffusive and ballistic regimes. We focus on the density of states in both the normal and superconducting region, and find that the presence of spin-dependent phase shifts occurring at the interface qualitatively modifies the density of states. In particular, we find that the proximity-induced pairing amplitudes in the normal metal region undergo a conversion at the Fermi level from pure even frequency to odd frequency. Above a critical value of the interface spin polarization (or, equivalently, for fixed interface spin polarization, above a critical interface resistance), only odd frequency correlations remain. This is accompanied by the replacement of the familiar proximity minigap or pseudogap in the normal layer by an enhancement of the density of states above its normal state value for energies near the chemical potential. The robustness of this effect toward inelastic scattering, impurity scattering, and the depletion of the superconducting order parameter close to the interface is investigated. We also study the inverse proximity effect in the diffusive limit. We find that the above-mentioned conversion persists also for thin superconducting layers comparable in size to the superconducting coherence length ${\xi }_S$, as long as the inverse proximity effect is relatively weak. Concomitantly, we find a shift in the critical interface resistance where the pairing conversion occurs. Our findings suggest a robust and simple method for producing purely odd-frequency superconducting correlations, which can be tested experimentally.

It is found that the magnetoresistance of a nanometer-scale Al particle, attached between a ferromagnetic and an Al lead, has strong asymmetry with respect to the bias voltage. The asymmetric magnetoresistance is explained in terms of the injection of a spin-polarized current from the ferromagnetic lead and the spin accumulation in the particle. The magnetic moment in the particle is parallel to the magnetic field, which is not collinear with the magnetization of the ferromagnetic lead. The field direction changes either discontinuously as the magnetization switches, or continuously as an external magnetic field is being varied, explaining the magnetoresistance.

The magnetic properties, the magnetostriction, and the magnetoelectric effect in the $d$-electron free rare-earth aluminum borate ${\text{TmAl}}_3{\left({\text{BO}}_3\right)}_4$ are investigated between room temperature and 2 K. The magnetic susceptibility reveals a strong anisotropy with the hexagonal $c$ axis as the hard magnetic axis. Magnetostriction measurements show a large effect of an in-plane field reducing both the $a$-axis and $c$-axis lattice parameters. The magnetoelectric polarization change in $a$ and $c$ directions reaches up to $300\mu \text{C}/{\text{m}}^2$ at 70 kOe with the field applied along the $a$ axis. The magnetoelectric polarization is proportional to the lattice contraction in magnetic field. The results of this investigation prove the existence of a significant coupling between the rare-earth magnetic moment and the lattice in $R{\text{Al}}_3{\left({\text{BO}}_3\right)}_4$ compounds ($R=\text{rare}$ earth). They further show that the rare-earth moment itself will generate a large magnetoelectric effect which makes it easier to study and to understand the origin of the magnetoelectric interaction in this class of materials.

Thin solid films of metastable rocksalt structure (c-) ${\text{Sc}}_{1-x}{\text{Al}}_x\text{N}$ and ${\text{Ti}}_{1-x}{\text{Al}}_x\text{N}$ were employed as model systems to investigate the relative influence of volume mismatch and electronic structure driving forces for phase separation. Reactive dual magnetron sputtering was used to deposit stoichiometric ${\text{Sc}}_{0.57}{\text{Al}}_{0.43}\text{N}\left(111\right)$ and ${\text{Ti}}_{0.51}{\text{Al}}_{0.49}\text{N}\left(111\right)$ thin films, at $675°\text{C}$ and $600°\text{C}$, respectively, followed by stepwise annealing to a maximum temperature of $1100°\text{C}$. Phase transformations during growth and annealing were followed in situ using x-ray scattering. The results show that the as-deposited ${\text{Sc}}_{0.57}{\text{Al}}_{0.43}\text{N}$ films phase separate at $1000–1100°\text{C}$ into nonisostructural c-ScN and wurtzite structure (w-) AlN, via nucleation and growth at domain boundaries. ${\text{Ti}}_{0.51}{\text{Al}}_{0.49}\text{N}$, however, exhibits spinodal decomposition into isostructural coherent c-TiN and c-AlN, in the temperature interval of $800–1000°\text{C}$. X-ray pole figures show the coherency between c-ScN and w-AlN, with $\text{AlN}\left(0001\right)\parallel \text{ScN}\left(001\right)$ and $\text{AlN}⟨0\overline{1}10⟩\parallel \text{ScN}⟨\overline{1}10⟩$. First-principles calculations of mixing energy-lattice spacing curves explain the results on a fundamental physics level and open a route for design of novel metastable pseudobinary phases for hard coatings and electronic materials.

We express the high-frequency (antiadiabatic) limit of the exchange-correlation (xc) kernels of an inhomogeneous electron gas in terms of the following equilibrium properties: the ground-state density, the xc kinetic stress tensor, the pair-correlation function and the ground-state xc potential. Of these quantities, the first three are amenable to exact evaluation by quantum Monte Carlo methods while the last can be obtained from the inversion of the Kohn-Sham equation for the ground-state orbitals. The exact scalar kernel, in this limit, is found to be of very long range in space, at variance with the kernel that is used in the standard local density approximation. The antiadiabatic xc kernels will be useful in calculations of excitation energies by time-dependent density-functional theory in atoms, molecules, and solids, and provide a solid basis for interpolation between the low- and high-frequency limits of the xc kernels.

We present scanning superconducting quantum interference device microscopy data on the superconductors ${\text{Sr}}_2{\text{RuO}}_4\left(T_c=1.5\text{K}\right)$ and ${\text{PrOs}}_4{\text{Sb}}_{12}\left(T_c=1.8\text{K}\right)$. In both of these materials, superconductivity-related time-reversal symmetry-breaking fields have been observed by muon spin rotation; our aim was to visualize the structure of these fields. However, in neither ${\text{Sr}}_2{\text{RuO}}_4$ nor ${\text{PrOs}}_4{\text{Sb}}_{12}$ do we observe spontaneous superconductivity-related magnetization. In ${\text{Sr}}_2{\text{RuO}}_4$, many experimental results have been interpreted on the basis of a $p_x\pm i{p}_y$ superconducting order parameter. This order parameter is expected to give spontaneous magnetic induction at sample edges and order parameter domain walls. Supposing large domains, our data restrict domain wall and edge fields to no more than $\sim 0.1\mathrm{\%}$ and $\sim 0.2\mathrm{\%}$ of the expected magnitude, respectively. Alternatively, if the magnetization is of the expected order, the typical domain size is limited to $\sim 30\text{nm}$ for random domains or $\sim 500\text{nm}$ for periodic domains.

We report magnetic penetration depth and thermal-conductivity data for high-quality single crystals of ${\text{BaFe}}_2{\left({\text{As}}_{1-x}{\text{P}}_x\right)}_2\left(T_c=30\text{K}\right)$ which provide strong evidence that this material has line nodes in its energy gap. This is distinctly different from the nodeless gap found for $\left(\text{Ba},\text{K}\right){\text{Fe}}_2{\text{As}}_2$ which has similar $T_c$ and phase diagram. Our results indicate that repulsive electronic interactions play an essential role for Fe-based high-$T_c$ superconductivity but that uniquely there are distinctly different pairing states, with and without nodes, which have comparable $T_c$.

Epitaxial graphene on SiC(0001) suffers from strong intrinsic $n$-type doping. We demonstrate that the excess negative charge can be fully compensated by noncovalently functionalizing graphene with the strong electron-acceptor tetrafluorotetracyanoquinodimethane (F4-TCNQ). Charge neutrality can be reached in monolayer graphene as shown in electron-dispersion spectra from angular-resolved photoemission spectroscopy. In bilayer graphene the band-gap that originates from the SiC/graphene interface dipole increases with increasing F4-TCNQ deposition and, as a consequence of the molecular doping, the Fermi level is shifted into the band-gap. The reduction in the charge-carrier density upon molecular deposition is quantified using electronic Fermi surfaces and Raman spectroscopy. The structural and electronic characteristics of the graphene/F4-TCNQ charge-transfer complex are investigated by x-ray photoelectron spectroscopy and ultraviolet photoelectron spectroscopy. The doping effect on graphene is preserved in air and is temperature resistant up to $200°\text{C}$. Furthermore, graphene noncovalent functionalization with F4-TCNQ can be implemented not only via evaporation in ultrahigh vacuum but also by wet chemistry.

While evidence of a topologically nontrivial surface state has been identified in surface-sensitive measurements of ${\text{Bi}}_2{\text{Se}}_3$, a significant experimental concern is that no signatures have been observed in bulk transport. In a search for such states, nominally undoped single crystals of ${\text{Bi}}_2{\text{Se}}_3$ with carrier densities approaching ${10}^{16}{\text{cm}}^{-3}$ and very high mobilities exceeding $2{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}$ have been studied. A comprehensive analysis of Shubnikov-de Haas oscillations, Hall effect, and optical reflectivity indicates that the measured electrical transport can be attributed solely to bulk states, even at 50 mK at low Landau-level filling factor, and in the quantum limit. The absence of a significant surface contribution to bulk conduction demonstrates that even in very clean samples, the surface mobility is lower than that of the bulk, despite its topological protection.

We present a combined multimethod experimental and theoretical study of the geometric and electronic properties of Co-tetraphenyl-porphyrin (Co-TPP) molecules adsorbed on a Ag(111) surface. Scanning tunneling microscopy (STM) topographs reveal that Co-TPP forms highly regular arrays with a square unit cell. Hereby, the Co-TPP molecules do not occupy a unique adsorption site on the Ag(111) atomic lattice. The central Co atom of the Co-TPP is found to reside predominantly above fcc and hcp hollow sites of the substrate, as determined from the photoelectron diffraction patterns. A strong adsorption-induced deformation of Co-TPP involving a saddle-shaped macrocycle is evidenced by high-resolution STM images and quantified by near-edge x-ray absorption fine-structure measurements. By scanning tunneling spectroscopy we resolved discrete molecular electronic states and mapped the pertaining spatial charge-density distribution. Specifically, we discuss the interaction of orbitals originating from the Co-metal center with the porphyrin macrocycle and show that the varying adsorption sites induce a modulation in the Co-TPP lowest unoccupied molecular orbital. These findings are corroborated by density-functional-theory calculations.

The ground state of the spin-Peierls system TiOCl was probed using synchrotron x-ray diffraction on a single-crystal sample at $T=6\text{K}$. We tracked the evolution of the structural superlattice peaks associated with the dimerized ground state as a function of pressure. The dimerization along the $b$ axis is rapidly suppressed in the vicinity of a first-order structural phase transition at $P_C=13.1\left(1\right)\text{GPa}$. The high-pressure phase is characterized by an incommensurate charge-density wave perpendicular to the original spin-chain direction. These results show that the electronic ground state undergoes a fundamental change in symmetry, indicating a significant change in the principal interactions.

We analyze fermionic spectral function in the spin-density-wave (SDW) phase of quasi-two-dimensional (quasi-2D) cuprates at small but finite $T$. We use a nonperturbative approach and sum up infinite series of thermal self-energy terms, keeping at each order nearly divergent $\left(T/J\right)\left|\text{log}ϵ\right|$ terms, where $ϵ$ is a deviation from a pure 2D, and neglecting regular $T/J$ corrections. We show that, as SDW order decreases, the spectral function in the antinodal region acquires peak/hump structure: the coherent peak position scales with SDW order parameter while the incoherent hump remains roughly at the same scale as at $T=0$ when SDW order is the strongest. We identify the hump with the pseudogap observed in angle-resolved photoemission spectroscopy and argue that the presence of coherent excitations at low energies gives rise to magneto-oscillations in an applied field. We show that the same peak/hump structure appears in the density of states and in optical conductivity.

Recent studies show that quantum oscillations thought to be associated with a density wave reconstructed Fermi surface disappear at a critical value of the doping for ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{6+y}$ and the cyclotron mass diverges as the critical value is approached from the high doping side. We argue that the phenomenon is due to a Lifshitz transition where the pockets giving rise to the quantum oscillations connect to form an open (quasi-one-dimensional) Fermi surface. The estimated critical doping is close to that found by experiment and the theory predicts a logarithmic divergence of the cyclotron mass with a coefficient comparable to that observed in experiment.

We present a combined experimental and theoretical study on the $\text{Mn}3d$ orbital occupation in orthorhombic ${\text{DyMnO}}_3$ single crystals. We have observed a very strong polarization dependence in the $\text{Mn}{L}_{2,3}$ x-ray absorption spectra, indicative for a distinct anisotropic orbital occupation. Ab initio electronic-structure calculations clearly infer the existence of a strong orbital polarization in the $e_g$ band with a staggered $d_{3x^2-r^2}/d_{3y^2-r^2}$-type ordering pattern in the $ab$ plane. This finding is in excellent agreement with a quantitative analyis of the spectra using the atomic multiplet cluster approach.

We suggest a possible realization of a solid-state memory capacitive (memcapacitive) system. Our approach relies on the slow polarization rate of a medium between plates of a regular capacitor. To achieve this goal, we consider a multilayer structure embedded in a capacitor. The multilayer structure is formed by metallic layers separated by an insulator so that nonlinear electronic transport (tunneling) between the layers can occur. The suggested memcapacitor shows hysteretic charge-voltage and capacitance-voltage curves, and both negative and diverging capacitance within certain ranges of the field. This proposal can be easily realized experimentally and indicates the possibility of information storage in memcapacitive systems.