We use a band unfolding technique to recover an effective primitive cell picture of the band structure of graphene under the influence of different types of perturbations. This involves intrinsic perturbations, such as structural defects, and external ones, comprising nitrogen substitutions and the inclusion of graphene in adsorbed systems. In such cases, the band unfolding provides a reliable and efficient tool for quantitatively analyzing the effect of doping and defects on the electronic structure of graphene. We envision that this approach will become a standard method in the computational analysis of graphene's electronic structure in related systems.

We investigate the finite-frequency thermal transport through a quantum dot subject to strong interactions by providing an exact, nonperturbative formalism that allows us to carry out a systematic analysis of the thermopower at any frequency. Special emphasis is put on the dc and high-frequency limits. We demonstrate that, in the Kondo regime, the ac thermopower is characterized by a universal function that we determine numerically.

Inhomogeneities and junctions in wires are natural sources of scattering, and hence resistance. A conducting fixed point usually requires an adiabatically smooth system. One notable exception is “healing,” which has been predicted in systems with special symmetries, where the system is driven to the homogeneous fixed point. Here we present theoretical results for a different type of conducting fixed point which occurs in inhomogeneous wires with an abrupt jump in hopping and interaction strength. We show that it is always possible to tune the system to an unstable conducting fixed point which does not correspond to translational invariance. We analyze the temperature scaling of correlation functions at and near this fixed point and show that two distinct boundary exponents appear, which correspond to different effective Luttinger liquid parameters. Even though the system consists of two separate interacting parts, the fixed point is described by a single conformally invariant boundary theory. We present details of the general effective bosonic field theory including the mode expansion and the finite size spectrum. The results are confirmed by numerical quantum Monte Carlo simulations on spinless fermions. We predict characteristic experimental signatures of the local density of states near junctions.

We have developed an iterative one-dimensional model to study the narrow band gap and the associated nonparabolic dispersion relations for bismuth antimony nanowires. An analytical approximation has also been developed. Based on the general model we have developed, we have calculated and analyzed the electronic phase diagrams and the band-gap/band-overlap map for bismuth antimony nanowires, as a function of stoichiometry, growth orientation, and wire width.

The possibility of electron beam guiding is theoretically explored on the surface of a topological insulator through the proximity interaction with a magnetic material. The electronic band modification induced by the exchange coupling at the interface defines the path of electron propagation in analogy to the optical fiber for photons. Numerical simulations indicate the guiding efficiency is much higher than that in the “waveguide” formed by an electrostatic potential barrier such as $p$-$n$ junctions. Furthermore, the results illustrate effective flux control and beam steering that can be realized by altering the magnetization/spin texture of the adjacent magnetic materials. Specifically, the feasibility to switch on and off and make a large-angle turn is demonstrated under realistic conditions. Potential implementation to logic and interconnect applications is also examined in connection with electrically controlled magnetization switching.

Spin waves in the rare-earth orthorferrite YFeO${}_3$ have been studied by inelastic neutron scattering and analyzed with a full four-sublattice model including contributions from both the weak ferromagnetic and antiferromagnetic orders. Antiferromagnetic exchange interactions of $J_1=-4.23\pm 0.08$ (nearest neighbors only) or $J_1=-4.77\pm 0.08$ meV and $J_2=-0.21\pm 0.04$ meV lead to excellent fits for most branches at both low and high energies. An additional branch associated with the weak antiferromagnetic order was observed. This work paves the way for studies of other materials in this class containing spin reorientation transitions and magnetic rare-earth ions.

An approach for the investigation of vortex core switching is presented. Thermal effects up to the Curie point are included in a micromagnetic framework based on the recently developed Landau-Lifshitz-Bloch equation. In this approach it is easier to avoid numerical discretization artifacts, commonly present when a Bloch point is mediating the switching process. Switching in thin circular permalloy disks caused by the application of a slowly increasing magnetic field oriented orthogonally to the disk is considered. An energy barrier which can be overcome by thermal fluctuations is taken into account, leading to a strong influence of the temperature on the switching field. In particular, the switching field goes to zero at a significantly smaller temperature than the Curie temperature. The deduced nucleation volume is smaller than the typical grain size in permalloy.

The magnetic structure of the Eu${}^{2+}$ moments in the superconducting EuFe${}_2$(As${}_{1-x}$P${}_x$)${}_2$ sample with $x=0.15$ has been determined using element-specific x-ray resonant magnetic scattering. Combining magnetic, thermodynamic, and scattering measurements, we conclude that the long-range ferromagnetic order of the Eu${}^{2+}$ moments aligned primarily along the c axis coexists with the bulk superconductivity at zero field. At an applied magnetic field $\ge$0.6 T, superconductivity still coexists with the ferromagnetic Eu${}^{2+}$ moments, which are polarized along the field direction. We propose a spontaneous vortex state for the coexistence of superconductivity and ferromagnetism in EuFe${}_2$(As${}_{0.85}$P${}_{0.15}$)${}_2$.

A spin texture called skyrmion has been recently observed in certain chiral magnets without inversion symmetry. The observed skyrmions are extended objects with typical linear sizes of 10 to 100 nm that contain ${10}^3$ to ${10}^5$ spins and can be deformed in response to external perturbations. Weak deformations are characterized by internal modes, which are localized around the skyrmion center. Knowledge of internal modes is crucial to assess the stability and rigidity of these topological textures. Here, we compute the internal modes of a skyrmion in a ferromagnetic background state by numerical diagonalization of the dynamical matrix. We find several internal modes below the magnon continuum, such as the mode corresponding to the translational motion and different kinds of breathing modes. The number of internal modes is larger for lower magnetic fields. Indeed, several modes become gapless in the low-field region indicating that the single skyrmion solution becomes unstable, although a skyrmion lattice remains thermodynamically stable. On the other hand, only three internal modes exist at high fields and the skyrmion texture remains locally stable even when the ferromagnetic state becomes thermodynamically stable. We also show that the presence of out-of-plane easy-axis anisotropy stabilizes the single skyrmion solution. Finally, we discuss the effects of damping and possible experimental observations of these internal modes.

Multiferroics with coplanar magnetic order are discussed in terms of a superfluid condensate, with special emphasis on spin supercurrents created by phase gradients of the condensate and the effect of external electric fields. By drawing the analogy to a superconducting condensate, phenomena such as persistent currents in rings, the Little-Parks effect, fluxoid quantization, the Josephson-like effect through spin domain walls, and interference behavior in a superconducting quantum interference device (SQUID)-like geometry are analyzed for coplanar multiferroics.

Longitudinal magnetoresistivity ${\rho }_{xx}\left(B\right)$ and Hall resistivity ${\rho }_{xy}\left(B\right)$ of KMo${}_6$O${}_{17}$ single crystals have been measured up to 60 T in a pulse magnet. Remarkable and unusual features at characteristic magnetic fields were found in both ${\rho }_{xx}\left(B\right)$ and ${\rho }_{xy}\left(B\right)$, which were attributed to Fermi surface reconstructions caused by field-induced density-wave transitions. To understand these transitions in detail, we analyzed ${\rho }_{xx}\left(B\right)$ and ${\rho }_{xy}\left(B\right)$ based on a multiband model. This model successfully described the experimental results, revealing that charge carriers are increased significantly at these transitions with increasing magnetic field as a result of the Fermi surface reconstruction. In particular, the charge carriers are increased by two orders of magnitude at $B_{\mathrm{osc}}=\sim 40$ T, above which a quantum oscillation emerges in both ${\rho }_{xx}\left(B\right)$ and ${\rho }_{xy}\left(B\right)$. This strongly suggests that the field-induced quantum oscillation is closely related with the induced charge carriers.

We studied the electronic structure of Fe- or Co-doped Sr${}_2$IrO${}_4$, using density functional calculations including spin-orbit coupling and electron correlation. Our results show that upon the doping ($x\le$ 0.5), a Fe${}^{3+}$-Ir${}^{5+}$ or Co${}^{3+}$-Ir${}^{5+}$ charge state appears on the Ir${}^{4+}$ matrix. Contrary to the effective $j=1/2$ state of the Ir${}^{4+}$ ion due to a strong spin-orbit coupling, the Ir${}^{5+}$ ($5d^4$, $t_{2g}^4$) ion could form a closed $j_{\mathrm{eff}}=3/2$ subshell and hence behave like a singlet. The Fe${}^{3+}$ and Co${}^{3+}$ ions are both in a high-spin state, with their respective $S=5/2$ and 2, and the Co${}^{3+}$ ion also carries a big orbital moment. This coupled charge-spin-orbital state, assisted by spin-orbit coupling and electron correlation, gives rise to an insulating behavior of Fe- or Co-doped Sr${}_2$IrO${}_4$ and accounts for their varying magnetic moments.

We investigate the nature of the insulating phases in a bilayer Hubbard model with intralayer coupling $t$ and interlayer coupling $t_{\perp }$ at large interaction strength $U/t$ and half-filling. We consider a dynamical cluster approximation with a cluster size of $N_c=2\times 4$, where short-range spatial fluctuations as well as on-site dynamical fluctuations are emphasized. By varying the band splitting ($t_{\perp }/t$), we find that at $t_{\perp }/t\simeq 1.5$ the Mott behavior is rapidly suppressed in the momentum sectors ($\pi ,0$) and ($0,\pi$). At $t_{\perp }/t\simeq 2.5$, Mott features dominate in the momentum sectors ($\pi ,\pi$) of the bonding band and ($0,0$) of the antibonding band, and at $t_{\perp }/t\simeq 3.0$, a tiny scattering rate is observed in all momentum sectors at the Fermi level, indicating a transition from a Mott to a band insulator. We attribute such a momentum-dependent evolution of the insulating behavior to the competition and cooperation between short-range spatial fluctuations and interlayer coupling $t_{\perp }$ with the help of the Coulomb interaction $U$. Finally, we also discuss the possible appearance of non-Fermi liquid behavior away from half-filling.

A theory of action spectroscopy, i.e., a reaction rate or yield as a function of bias voltage, is presented for single-molecule reactions induced by the inelastic tunneling current with a scanning tunneling microscope. A formula for the reaction yield is derived using the adsorbate resonance model, which provides a versatile tool to analyze vibrationally mediated reactions of single adsorbates on conductive surfaces. This allows us to determine the energy quantum of the excited vibrational mode, the effective broadening of the vibrational density of states (as described by Gaussian or Lorentzian functions), and a prefactor characterizing the elementary process behind the reaction. The underlying approximations are critically discussed. We point out that observation of reaction yields at both bias voltage polarities can provide additional insight into the adsorbate density of states near the Fermi level. As an example, we apply the theory to the case of flip motion of a hydroxyl dimer (OD)${}_2$ on Cu(110) which was experimentally observed by Kumagai et al. [Phys. Rev. B 79, 035423 (2009)]. In combination with density functional theory calculations for the vibrational modes, the vibrational damping due to electron-hole pair generation, and the potential energy landscape for the flip motion, a detailed microscopic picture for the switching process is established. This picture reveals that the predominant mechanism is excitation of the OD stretch modes which couple anharmonically to the low-energy frustrated rotation mode.

Application of a perpendicular electric field induces a band gap in bilayer graphene, and it also creates a “Mexican hat” structure in the dispersion relation. This structure has unusual implications for the hydrogen-like bound state of an electron to a Coulomb impurity. We calculate the ground state energy of this hydrogen-like state as a function of the applied interlayer voltage and the effective fine structure constant. Unlike in the conventional hydrogen atom, the resulting wave function has many nodes even in the ground state. Further, the electron state undergoes “atomic collapse” into the Dirac continuum both at small and large voltage.

Low-temperature electrical measurements were performed on arrays of metallic nanoparticles coated by alkylamines. The length of the alkyl molecules was varied (18, 12, and four carbons), while the size of the metallic nanoparticles was fixed at 10.3 nm. This allowed us to investigate the effect of interdot coupling on the electronic transport. We show that in the Coulomb-blockade regime, the temperature and bias dependence of the resistivity are governed by the length of the organic barriers and are well described by theories that consider inelastic cotunneling to be the main mechanism of interparticle transfer. Indeed, quantitative agreement between theory and experiments is obtained when considering the interparticle distance deduced from transmission electron microscopy with respect to the relevant characteristic energies (activation temperature and charging energy).

The in-plane thermal conductivity $\kappa$ and electrical resistivity $\rho$ of the heavy-fermion metal ${\text{YbRh}}_2$${\text{Si}}_2$ were measured down to 50 mK for magnetic fields $H$ parallel and perpendicular to the tetragonal $c$ axis, through the field-tuned quantum critical point $H_c$, at which antiferromagnetic order ends. The thermal and electrical resistivities, $w\equiv L_{0}T/\kappa$ and $\rho$, show a linear temperature dependence below 1 K, typical of the non-Fermi-liquid behavior found near antiferromagnetic quantum critical points, but this dependence does not persist down to $T=0$. Below a characteristic temperature $T^{☆}\simeq 0.35$ K, which depends weakly on $H$, $w\left(T\right)$ and $\rho \left(T\right)$ both deviate downward and converge as $T\to 0$. We propose that $T^{☆}$ marks the onset of short-range magnetic correlations, persisting beyond $H_c$. By comparing samples of different purity, we conclude that the Wiedemann-Franz law holds in ${\text{YbRh}}_2$${\text{Si}}_2$, even at $H_c$, implying that no fundamental breakdown of quasiparticle behavior occurs in this material. The overall phenomenology of heat and charge transport in ${\text{YbRh}}_2$${\text{Si}}_2$ is similar to that observed in the heavy-fermion metal ${\text{CeCoIn}}_5$, near its own field-tuned quantum critical point.

We generalized the commonly used Gutzwiller approximation for calculating the electronic structure and total energy of strongly correlated electron systems. In our method, the evaluation of one-body and two-body density matrix elements of the Hamiltonian is simplified using a renormalization approximation to achieve better scaling of the computational effort as a function of system size. To achieve a clear presentation of the concept and methodology, we describe the detailed formalism for a finite hydrogen system with minimal basis set. We applied the correlation matrix renormalization approximation approach to a H${}_2$ dimer and H${}_8$ cubic fragment with minimal basis sets, as well as a H${}_2$ molecule with a large basis set. The results compare favorably with sophisticated quantum chemical calculations. We believe our approach can serve as an alternative way to build up the exchange-correlation energy functional for an improved density functional theory description of systems with strong electron correlations.

We present results of electronic structure calculations on the N-related localized vibrational modes in the dilute nitride alloy GaSb${}_{1-x}$N${}_x$. By calculating the formation energies of various possible N incorporation modes in the alloy, we determine the most favorable N configurations, and we calculate their vibrational mode frequencies using density functional theory under the generalized gradient approximation to electron exchange and correlation, including the effects of the relativistic spin-orbit interactions. For a single N impurity, we find substitution on an Sb site, N${}_{\mathrm{Sb}}$, to be most favorable, and for a two-N-atom complex, we find the N-N split interstitial on an Sb site to be most favorable. For these defects, as well as, for comparison, defects comprising two N atoms on neighboring Sb sites and a N-Sb split interstitial on an Sb site, we find well-localized vibration modes (LVMs), which should be experimentally observable. The frequency of the triply degenerate LVM associated with N${}_{\mathrm{Sb}}$ is determined to be 427.6 cm${}^{-1}$. Our results serve as a guide to future experimental studies to elucidate the incorporation of small concentrations of N in GaSb, which is known to lead to a reduction of the band gap and opens the possibility of using the material for long-wavelength applications.