We study the electronic structures of $ABA$ (Bernal) -stacked multilayer graphenes in a uniform perpendicular electric field, and we show that the interplay of the trigonal warping and the potential asymmetry gives rise to a number of emergent Dirac cones nearly touching at zero energy. The band velocity and the energy region (typically a few tens of meV) of these gate-induced Dirac cones are tunable with the external electric field. In $ABA$-trilayer graphene, in particular, applying an electric field induces a nontrivial valley Hall state, where the energy gap at the Dirac point is filled by chiral edge modes which propagate in opposite directions between two valleys. In four-layer graphene, in contrast, the valley Hall conductivity is zero and there are no edge modes filling in the gap. A nontrivial valley Hall state generally occurs in asymmetric odd-layer graphenes, and this is closely related to a hidden chiral symmetry which exists only in odd-layer graphenes.

We study an electrically controlled quantum spin Hall antidot embedded in a two-dimensional topological insulating bar. Helical edge states around the antidot and along the edges of the bar are tunnel coupled. The close connection between spin and chirality, typical of helical systems, allows to generate a spin-polarized current flowing across the bar. This current is studied as a function of the external voltages, by varying the asymmetry between the barriers. For asymmetric setups, a switching behavior of the spin current is observed as the bias is increased, both in the absence and in the presence of electron interactions. This device allows to generate and control the spin-polarized current by simple electrical means.

A peculiar feature of the majority of three-dimensional topological insulator surface states studied experimentally thus far, namely their particle-hole asymmetry, makes quantum oscillations (Shubnikov–de Haas and de Haas–van Alphen oscillations) in these materials particularly rich. I show that this peculiarity can be exploited to measure the Chern number and detect topological phase transitions in topological insulator surface states from the quantum spin Hall phase to the quantum anomalous Hall phase. I consider the behavior of quantum oscillations in topological insulator thin-film surface states in the presence of a topological exciton condensate or hybridization between the two surfaces. As a function of Zeeman field, the Chern number and phase transition from a quantum spin Hall to a quantum anomalous Hall phase can be measured using standard techniques. This effect relies necessarily on the particle-hole asymmetry, which is ubiquitous in currently known materials that exhibit topological insulator surface states.

We report theoretical analysis of thermal-spin and thermoelectric properties of noncollinear spin valves driven by a high-frequency ac voltage bias. The spin valve consists of two ferromagnetic contacts sandwiching a single-level or multilevel quantum dot (QD). A general formulation for the time-averaged thermal-spin and thermoelectric properties of spin valves is derived within the nonequilibrium Green's function theory, which provides a starting point for further numerical calculations of these properties. Numerical results of a spin valve having a spin-degenerate single-level QD are given as an example. The ac bias induces various photon-assisted transmission peaks which can greatly enhance the Seebeck coefficients and the figures of merit, and offer a new possibility to tune both the spin-dependent and normal thermoelectric properties of the spin valve. Details of these properties and how they depend on the noncollinearity of the spin valve, magnetic polarization, ac frequency, ac bias, and other control parameters are reported. A particularly interesting result is the opposite dependency of the thermoelectric properties on the magnetic polarization and noncollinearity for contacts with or without spin accumulation.

Fully relativistic calculations are used to perform a systematic study on the energetic stability, and electronic properties of group III (Al, Ga, In, and Tl) impurities in the cation-site (Pb) of PbSe: bulk and nanowire (NW). Our results show that group III impurities have lower formation energies in the NW than in the bulk. The impurities are site-dependent in the nanowires: they are more stable on the surface of the NW as compared to the core. In the bulk, Al and In are donor levels, while Ga and Tl are acceptor impurities. For the NW, the same trend is obtained for Al and Tl, whereas Ga and In are deep donors. A two-level model based on the interaction between the impurity states and the host crystalline field explains the electronic properties of group III impurity doped PbSe bulk and NW. This model agrees with the projected density of states and helps us to understand the unexpected $n$-type character of some group III impurity doped PbSe.

The bonding geometry of tin-phthalocyanine (SnPc) on Ag(111) has been studied using x-ray and ultraviolet photoelectron diffraction (XPD and UPD, respectively). Experimental diffraction patterns were compared to single-scattering-cluster calculations. XPD data could be well reproduced by the simulations and allowed for the determination of several structural parameters. At a coverage of 0.9 ML, all molecules are in a “tin-down” configuration and the nonplanar shuttlecock-shaped SnPc molecule undergoes flattening upon absorption on Ag(111). UPD data from the second highest occupied molecular orbital and comparison to simulations show a high sensitivity to minor structural changes, including also the vertical distance between tin atoms of the SnPc and the surface layer of the substrate, which is found to be 2.3 Å. We thus demonstrate how UPD can complement the well-established XPD method and discuss remaining challenges in the theoretical description of photoelectron diffraction from molecular orbitals at low energies. The UPD method is particularly attractive in view of the increasing availability of ultrashort pulsed laser sources in the XUV regime, which could enable pump-probe experiments with high structural sensitivity.

Regular nanoscale perforations in graphene (graphene antidot lattices, GALs) are known to lead to a gap in the energy spectrum, thereby paving a possible way towards many applications. This theoretical prediction relies on a perfect placement of identical perforations, a situation not likely to occur in the laboratory. Here, we present a systematic study of the effects of disorder in GALs. We consider both geometric and chemical disorder, and evaluate the density of states as well as the optical conductivity of disordered GALs. The theoretical method is based on an efficient algorithm for solving the time-dependent Schrödinger equation in a tight-binding representation of the graphene sheet [Yuan et al., Phys. Rev. B 82, 115448 (2010)], which allows us to consider GALs consisting of 6400 $\times$ 6400 carbon atoms. The central conclusion for all kinds of disorder is that the gaps found for pristine GALs do survive at a considerable amount of disorder, but disappear for very strong disorder. Geometric disorder is more detrimental to gap formation than chemical disorder. The optical conductivity shows a low-energy tail below the pristine GAL band gap due to disorder-introduced transitions.

Topological insulators are new states of matter with a bulk gap and robust gapless surface states protected by time-reversal symmetry. When time-reversal symmetry is broken, the surface states are gapped, which induces a topological response of the system to electromagnetic field—the topological magnetoelectric effect. In this paper we study the behavior of topological surface states in heterostructures formed by a topological insulator and a magnetic insulator. Several magnetic insulators with compatible magnetic structure and relatively good lattice matching with topological insulators Bi${}_2$Se${}_3$, Bi${}_2$Te${}_3$, Sb${}_2$Te${}_3$ are identified, and the best candidate material is found to be MnSe, an antiferromagnetic insulator. We perform first-principles calculations in Bi${}_2$Se${}_3$/MnSe superlattices and obtain the surface state band structure. The magnetic exchange coupling with MnSe induces a gap of $\sim$54 meV at the surface states. In addition we tune the distance between Mn ions and the topological insulator surface to study the distance dependence of the exchange coupling.

If bilayer graphene is placed in a strong perpendicular magnetic field, several quantum Hall plateaux are observed at low enough temperatures. Of these, the ${\sigma }_{xy}=4n{e}^2/h$ sequence ($n\ne 0$) is explained by standard Landau quantization, while the other integer plateaux arise due to interactions. The low-energy excitations in both cases are magnetoexcitons, whose dispersion relation depends on single- and many-body effects in a complicated manner. Analyzing the magnetoexciton modes in bilayer graphene, we find that the mixing of different Landau level transitions not only renormalizes them, but essentially changes their spectra and orbital character at finite wavelength. These predictions can be probed in inelastic light scattering experiments.

Studies of network-forming oxide liquids are combined with studies of network-forming chalcogenide glasses to demonstrate a universal dependence of the glass forming fragility on the topological connectivity of the network. This connection between structure and dynamics is congruent with theoretical predictions for a rigidity transition near an average bond number of 2.4, and the common pattern of fragility may be traced via a simple two-state bond model to a common variation of configurational entropy with connectivity. However, in order for this universality to appear the connectivity of the oxide networks must be defined in a progressive manner that accommodates the presence of those rigid structural units that comprise both the short-range and intermediate-range order. Replacement of these robust structural units by equivalent network nodes is necessary but can be viewed as a coarse-graining of the network to a bond lattice of weakest links that are most relevant to zero-frequency properties like the fragility.

Recent neutron scattering measurements on the spinel CdCr${}_2$O${}_4$ revealed a rare example of helical magnetic order in geometrically frustrated pyrochlore antiferromagnet. The spin spiral characterized by an incommensurate wave vector $\mathbf{Q}=2\pi (0,\delta ,1)$ with $\delta \approx 0.09$ is accompanied by a tetragonal distortion. Here we conduct a systematic study on the magnetic ground state resulting from the interplay between the Dzyaloshinskii-Moriya interaction and further neighbor exchange couplings, two of the most important mechanisms for stabilizing incommensurate spin orders. We compute the low-energy spin-wave spectrum based on a microscopic spin Hamiltonian and find a dispersion relation characteristic of the helimagnons. By numerically integrating the Landau-Lifshitz-Gilbert equation with realistic model parameters, an overall agreement between experiment and the numerical spectrum, lending further support to the view that a softened optical phonon triggers the magnetic transition and endows the lattice a chirality.

The ground state and zero-temperature magnetization process of the spin-1/2 Ising-Heisenberg model on two-dimensional triangles-in-triangles lattices are exactly calculated using eigenstates of the smallest commuting spin clusters. Our ground-state analysis of the investigated classical-quantum spin model reveals three unconventional dimerized or trimerized quantum ground states besides two classical ground states. It is demonstrated that the spin frustration is responsible for a variety of magnetization scenarios with up to three or four intermediate magnetization plateaus of either quantum or classical nature. The exact analytical results for the Ising-Heisenberg model are confronted with the corresponding results for the purely quantum Heisenberg model, which were obtained by numerical exact diagonalizations based on the Lanczos algorithm for finite-size spin clusters of 24 and 21 sites, respectively. It is shown that the zero-temperature magnetization process of both models is quite reminiscent, and hence, one may obtain some insight into the ground states of the quantum Heisenberg model from the rigorous results for the Ising-Heisenberg model even though exact ground states for the Ising-Heisenberg model do not represent true ground states for the pure quantum Heisenberg model.

We have theoretically studied oblique surface waves (OSWs) which propagate along the interface between a dielectric and a layered superconductor. We assume that this interface is perpendicular to the superconducting layers, and OSWs at the interface can propagate at an arbitrary angle with respect to them. The electromagnetic field of the OSWs in a layered superconductor is a superposition of an ordinary wave (with its electric field parallel to the layers) and an extraordinary wave (with its magnetic field parallel to the layers). We have derived the dispersion equation for the OSWs and shown that the dispersion curves have end points where the extraordinary mode transforms from evanescent wave to bulk wave, propagating deep into the superconductor. In addition, we have analytically solved the problem of the resonance excitation of the OSWs by the attenuated-total-reflection method using an additional dielectric prism. Due to the strong current anisotropy in the boundary of the superconductor, the excitation of the OSWs is accompanied by an additional important phenomenon: The electromagnetic field component with the orthogonal polarization appears in the wave reflected from the bottom of the prism. We show that, for definite optimal combinations of the problem parameters (the wave frequency, the direction of the incident wave vector, the thickness of the gap between dielectric prism and superconductor, etc.), there is a complete suppression of the reflected wave with its polarization coinciding with the polarization of the incident wave. Contrary to the isotropic case, this phenomenon can be observed even in the dissipationless limit. In such a regime, the complete transformation of the incident wave into a reflected wave with orthogonal polarization can be observed.

I present the results of first-principles calculations of the phonon dispersions and electron-phonon coupling for BaTi${}_2$Sb${}_2$O. The phonon dispersions show a weak lattice instability near the zone corners that leads to a charge-density wave phase. The calculations of the electron-phonon coupling reveal strong coupling, especially to the in-plane Ti modes. The total coupling is large enough to readily explain the superconductivity in this compound. As the Fermi surfaces are disconnected with different orbital character weights, this compound is likely to host a multiband superconductivity.

Building upon recent theoretical proposals for creating an effective gauge field for photons, we experimentally demonstrate the photonic Aharonov-Bohm effect. The effect relies on the nonreciprocal phase acquired by photons during photonic transitions. Our photonic Aharonov-Bohm interferometer is broadly tunable with a contrast ratio above 30 dB, as the operating frequency varies between 8 and 12 MHz.

Using the full-potential linearized augmented plane-wave method within the density functional theory, we compute all contributions to the scattering-independent part of the thermoelectric conductivity tensor $\widehat{\alpha }$, namely, the intrinsic contribution ${\widehat{\alpha }}^{\mathrm{ic}}$ and the side-jump contribution ${\widehat{\alpha }}^{\mathrm{sj}}$. For the ferromagnetic materials bcc Fe, hcp Co, fcc Ni, and $L{1}_0$ ordered alloys FePd and FePt, our investigations of the energy and temperature dependence of the intrinsic and side-jump contributions show that they are both of equal importance. Overall, our calculations are able to correctly reproduce the order of magnitude and sign of the experimentally measured signal, suggesting that the scattering-independent part plays an important role in the anomalous Nernst effect of ferromagnets.

Spin-orbit coupled semiconductor nanowires with Zeeman splitting in proximity contact with bulk $s$-wave superconductivity have recently been proposed as a promising platform for realizing Majorana fermions. However, in this setup the chemical potential of the nanowire is generally pinned by the Fermi surface of the superconductor. This makes the tuning of the chemical potential by external electrical gates, a crucial requirement for unambiguous detection of Majorana fermions, very challenging in experiments. Here we show that a tunable topological superconducting regime supporting Majorana fermions can be realized in semiconductor nanowires using uniaxial stress. For $n$-type nanowires the uniaxial stress tunes the effective chemical potential, while for $p$-type systems the effective pairing may also be modified by stress, thus significantly enhancing the topological minigap. We show that the required stress, of the order of $0.1\%$, is within current experimental reach using conventional piezocrystals.

A generic nonaligned Josephson junction in the presence of an external magnetic field is theoretically considered and an unusual flux-dependent current-phase relation (CPR) is revealed. We explain the origin of the anomalous CPR via the current density flow induced by the external field within a two-dimensional quasiclassical Keldysh-Usadel framework. In particular, it is demonstrated that nonaligned Josephson junctions can be utilized to obtain a ground state other than 0 and $\pi$, corresponding to a so-called $\phi$ junction, which is tunable via the external magnetic flux. Furthermore, we show that the standard Fraunhofer central peak of the critical supercurrent may be inverted into a local minimum solely due to geometrical factors in planar junctions. This yields good consistency with a recent experimental measurement displaying such type of puzzling feature [Keizer et al., Nature (London) 439, 825 (2006)].

We study a Majorana-carrying quantum wire, driven into a trivial phase by breaking the spatial inversion symmetry with a tilted magnetic field. Interestingly, we predict that a supercurrent applied in the proximate superconductor is able to restore the topological phase and therefore the Majorana end states. Using Abelian bosonization, we further confirm this result in the presence of electron-electron interactions and show a profound connection of this phenomenon to the commensurate-incommensurate transition in one-dimensional doped Mott insulators. These results have important applications in, e.g., realizing a supercurrent-assisted braiding of Majorana fermions, which proves highly useful in topological quantum computation with realistic Majorana networks.

We report the observation of zero resistivity (ρ) in a hydrocarbon superconductor, and describe the temperature dependence of ρ in metal-doped hydrocarbons. The resistivity of K-doped picene (K${}_x$picene) has been recorded from pellet samples in a four-terminal measurement mode. A drop in $\rho$ is observed below 7 K for K${}_{3.1}$picene and below 11 K for K${}_{3.5}$picene, which clearly displays zero resistivity. The resistivity drop at 7 K is consistent with the superconducting critical temperature ($T_{\mathrm{c}}$) obtained from the magnetic susceptibility of the 7 K phase of K${}_3$picene, while the drop at 11 K is inconsistent with the $T_{\mathrm{c}}$'s of both the 7 and 18 K phases of K${}_3$picene reported previously. The temperature dependence of ρ for both samples exhibits granular-metal-like behavior in the normal state.