We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local mean-field approximation of their pseudospin Hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their $N_{\text{OP}}$-component order parameters, with Landau free energies that have a single zero-strain “austenite” minimum at high temperatures, and spontaneous-strain “martensite” minima of $N_V$ structural variants at low temperatures. The total free energy also has gradient terms, and power-law anisotropic effective interactions, induced by “no-dislocation” St Venant compatibility constraints. In a reduced description, the strains at Landau minima induce temperature dependent, clocklike ${\mathbb{Z}}_{N_V+1}$ Hamiltonians, with $N_{\text{OP}}$-component strain-pseudospin vectors $\vec{S}$ pointing to $N_V+1$ discrete values (including zero). We study elastic texturing in five such first-order structural transitions through a local mean-field approximation of their pseudospin Hamiltonians, that include the power-law interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component pseudospin taking $N_V+1=3$ values of $S=0,\pm 1$, as in a generalized Blume-Capel model. We then consider transitions with two-component $\left(N_{\text{OP}}=2\right)$ pseudospins: the equilateral to centered rectangle $\left(N_V=3\right)$; the square to oblique polygon $\left(N_V=4\right)$; the triangle to oblique $\left(N_V=6\right)$ transitions; and finally the three-dimensional (3D) cubic to tetragonal transition $\left(N_V=3\right)$. The local mean-field solutions in two-dimensional and 3D yield oriented domain-wall patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related Hamiltonians illustrate that structural transitions in materials science can be the source of interesting spin models in statistical mechanics.

We present a detailed numerical study of the electronic properties of single-layer graphene with resonant (hydrogen) impurities and vacancies within a framework of noninteracting tight-binding model on a honeycomb lattice. The algorithms are based on the numerical solution of the time-dependent Schrödinger equation and applied to calculate the density of states, quasieigenstates, ac and dc conductivities of large samples containing millions of atoms. Our results give a consistent picture of evolution of electronic structure and transport properties of functionalized graphene in a broad range of concentration of impurities (from graphene to graphane), and show that the formation of impurity band is the main factor determining electrical and optical properties at intermediate impurity concentrations, together with a gap opening when approaching the graphane limit.

We present a study of the charge state conversion of single nitrogen-vacancy (NV) defects hosted in nanodiamonds (NDs). We first show that the proportion of negatively charged ${\text{NV}}^{-}$ defects, with respect to its neutral counterpart ${\text{NV}}^0$, decreases with the size of the ND. We then propose a simple model based on a layer of electron traps located at the ND surface which is in good agreement with the recorded statistics. By using thermal oxidation to remove the shell of amorphous carbon around the NDs, we demonstrate a significant increase in the proportion of ${\text{NV}}^{-}$ defects in 10 nm NDs. These results are invaluable for further understanding, control, and use of the unique properties of negatively charged NV defects in diamond.

We consider the effect of weak disorder on eigenstates in a special class of tight-binding models. Models in this class have short-range hopping on periodic lattices; their defining feature is that the clean systems have some energy bands that are dispersionless throughout the Brillouin zone. We show that states derived from these flat bands are generically critical in the presence of weak disorder, being neither Anderson localized nor spatially extended. Further, we establish a mapping between this localization problem and the one of resonances in random impedance networks, which previous work has suggested are also critical. Our conclusions are illustrated using numerical results for a two-dimensional lattice, known as the square lattice with crossings or the planar pyrochlore lattice.

Using the Ginzburg-Landau theory for two-band superconductors, we determine the surface energy ${\sigma }_s$ between coexisting normal and superconducting states at the thermodynamic critical magnetic field. Close to the transition temperature, where the Ginzburg-Landau theory is applicable, we demonstrate that the two-band problem maps onto an effective single band problem. While the order parameters of the two bands may have different amplitudes in the homogeneous bulk, near $T_c$ the Josephson-type coupling between the bands leads to the same spatial dependence of both order parameters near the interface. This finding puts into question the possibility of intermediate, so-called type-1.5 superconductivity, in the regime where the Ginzburg-Landau theory applies.

Scanning tunneling microscopy (STM) is today the most powerful and versatile tool available for imaging and manipulating single molecules on surfaces. Here, we explore its ultimate limit by demonstrating the possibility of controlling sequential di-dehydrogenation of single Co-Salen molecules sublimated on Cu. In particular, we are able to explore the final products of the ${\text{H}}_2$ dissociation as well as the intermediate state, in which only one H atom is separated from the molecule. This is achieved by low-temperature STM with the dissociation induced by either point spectroscopy or in the standard constant-current mode. Crucial for the interpretation of the data is our ability to perform state-of-the-art density-functional theory simulations of both topographic and spectroscopical STM images. This work demonstrates that STM combined with theory can give access to the atomic details of a chemical reaction even when the reaction products are completely unknown.

Epitaxial graphene on SiC possesses, quite remarkably, an electron spectrum similar to that of free-standing samples. Yet, the coupling to the substrate, albeit small, affects the quasiparticle properties. Combining ab initio calculations with symmetry analysis, we derive a modified Dirac-Weyl Hamiltonian for graphene epilayers. While for the epilayer on the C-face the Dirac cone remains almost intact, for epilayers on the Si-face the band splitting is about 30 meV. At certain energies, the Dirac bands are significantly distorted by the resonant interaction with interface states, which should lead to mobility suppression, especially on the Si-face.

The electronic structure of LaFeAsO, a parent compound of iron-arsenic superconductors, is studied by angle-resolved photoemission spectroscopy. By examining its dependence on photon energy, polarization, and sodium dosing, both the bulk and the surface contributions are identified. We find that a bulk band moves toward high binding energies below the structural transition temperature, and shifts smoothly across the spin-density-wave transition by about 25 meV. Our data suggest that the band reconstruction may play a crucial role in the spin-density-wave and the structural transitions. For the surface states, both the LaO-terminated and FeAs-terminated components are revealed. Certain small band shifts are observed for the FeAs-terminated surface states in the spin-density-wave state, which might be a reflection of the bulk electronic-structure reconstruction. Moreover, sharp quasiparticle peaks quickly rise at low temperatures, indicating drastic reduction in the scattering rate. A kink structure in one of the surface band is shown to be possibly related to the enhanced electron-phonon interactions on the polar surface.

In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors that pervade many fundamental aspects of density-functional predictions. Here, we first examine self-interaction in terms of the discrepancy between total and partial electron removal energies, and then highlight the importance of imposing the generalized Koopmans’ condition—that identifies orbital energies as opposite total electron removal energies—to resolve this discrepancy. In the process, we derive a correction to approximate functionals that, in the frozen-orbital approximation, eliminates the unphysical occupation dependence of orbital energies up to the third order in the single-particle densities. This non-Koopmans correction brings physical meaning to single-particle energies; when applied to common local or semilocal density functionals it provides results that are in excellent agreement with experimental data—with an accuracy comparable to that of GW many-body perturbation theory—while providing an explicit total energy functional that preserves or improves on the description of established structural properties.

For more than three decades, research on tunneling through planar barriers has focused principally on processes that conserve momentum parallel to the barrier. Here we investigate transport in which scattering destroys lateral momentum conservation and greatly enhances the tunneling probability. We have measured its energy dependence using capacitance spectroscopy, and we show that for electrons confined in a quantum well, the scattering enhancement can be quenched in an applied magnetic field, enabling this mechanism to function as an external probe of the origin of the quantum Hall effect.

We present a neutron-diffraction, small-angle scattering, and magnetometry study of the narrow bandwidth perovskite cobaltite ${\text{Pr}}_{1-x}{\text{Ca}}_x{\text{CoO}}_3$, demonstrating an unusual form of magnetoelectronic phase separation where long-range ordered ferromagnetism coexists spatially with short-range ferromagnetism. The two phases have very different coercivities and, remarkably, are strongly exchange coupled. The electronic phase separation thus leads to spontaneous formation of a hard-soft nanocomposite, exhibiting prototypical exchange-spring behavior in the absence of chemical interfaces.

We present a combined theoretical and experimental study of the electronic structure and equation of state (EOS) of crystalline ${\text{PdN}}_2$. The compound forms above 58 GPa in the pyrite structure and is metastable down to 11 GPa. We show that the EOS cannot be accurately described within either the local density or generalized gradient approximations. The Heyd-Scuseria-Ernzerhof exchange-correlation functional (HSE06), however, provides very good agreement with experimental data. We explain the strong pressure dependence of the Raman intensities in terms of a similar dependence of the calculated band gap, which closes just below 11 GPa. At this pressure, the HSE06 functional predicts a first-order isostructural transition accompanied by a pronounced elastic instability of the longitudinal-acoustic branches that provides the mechanism for the experimentally observed decomposition. Using an extensive Wannier function analysis, we show that the structural transformation is driven by a phase transition of the electronic structure, which is manifested by a discontinuous change in the hybridization between $\text{Pd}d$ and $\text{N}p$ electrons as well as a conversion from single to triple bonded nitrogen dimers. We argue for the possible existence of a critical point for the isostructural transition, at which massive fluctuations in both the electronic as well as the structural degrees of freedom are expected.

We present a detailed study of the influence of various interactions on the spin quantum tunneling in a ${\text{Mn}}_{12}$ wheel molecule. The effects of single-ion and exchange (spin-orbit) anisotropy are first considered, followed by an analysis of the roles played by secondary influences, e.g., disorder, dipolar and hyperfine fields, and magnetoelastic interactions. Special attention is paid to the role of the antisymmetric Dzyaloshinski-Moriya (DM) interaction. This is done within the framework of a 12-spin microscopic model, and also using simplified dimer and tetramer approximations in which the electronic spins are grouped in two or four blocks, respectively. If the molecule is inversion symmetric, the DM interaction between the dimer halves must be zero. In an inversion symmetric tetramer, two independent DM vectors are allowed but no new tunneling transitions are generated by the DM interaction. In an effort to explain the experiments, we consider a breaking of the molecular inversion symmetry, and we explore this in detail using both models, focusing on the asymmetric disposition and rounding of Berry phase minima associated with quantum interference between states of opposite parity. A remarkable behavior exists for the “Berry phase zeroes” as a function of the directions of the internal DM vectors and the external transverse field. However, in both dimer and tetramer models, a rather drastic breaking of the molecular inversion symmetry is required to explain the experiments using DM interactions. Such a symmetry breaking cannot be attributed to sample disorder, and there is no evidence for it in experiments. In the absence of DM interactions, we suggest a number of other ways to explain the experiments. These results are of general interest for the quantum dynamics of tunneling spins, and lead to some interesting experimental predictions.

We study the screening of the Coulomb interaction in a quasi-one-dimensional superconductor by the presence of either a one- or a two-dimensional electron gas nearby. To that end, we derive an effective low-energy phase-only action, which amounts to treating the Coulomb and superconducting correlations in the random-phase approximation. We concentrate on the study of dissipation effects in the superconductor, induced by the effect of Coulomb coupling to the diffusive modes in the electron gas, and study its consequences on the behavior of the one-dimensional plasma mode, and the static and dynamical conductivity. Our results point toward the importance of the dimensionality of the screening metal in the behavior of the superconducting plasma mode of the wire at low energies. In absence of topological defects, and when the screening is given by a one-dimensional electron gas, the superconducting plasma mode is completely damped in the limit $k\to 0$, and consequently superconductivity is lost in the wire. In contrast, we recover a Drude-type response in the conductivity when the screening is provided by a two-dimensional electron gas.

We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians $\mathcal{H}\left(\mathbf{k},\mathbf{r}\right)$ that vary slowly with adiabatic parameters $\mathbf{r}$ surrounding the defect and belong to any of the ten symmetry classes defined by time-reversal symmetry and particle-hole symmetry. The topological classes for such defects are identified and explicit formulas for the topological invariants are presented. We introduce a generalization of the bulk-boundary correspondence that relates the topological classes to defect Hamiltonians to the presence of protected gapless modes at the defect. Many examples of line and point defects in three-dimensional systems will be discussed. These can host one dimensional chiral Dirac fermions, helical Dirac fermions, chiral Majorana fermions, and helical Majorana fermions, as well as zero-dimensional chiral and Majorana zero modes. This approach can also be used to classify temporal pumping cycles, such as the Thouless charge pump, as well as a fermion parity pump, which is related to the Ising non-Abelian statistics of defects that support Majorana zero modes.

A method is described for levitating micron-sized few-layer graphene flakes in an electric quadrupole ion trap. Starting from a liquid suspension containing graphene, charged flakes are injected into the trap using the electrospray ionization technique and are probed optically. At micro-torr pressures, torques from circularly polarized light cause the levitated particles to rotate at frequencies $>1\text{MHz}$, which can be inferred from modulation of light scattering off the rotating flake when an electric field resonant with the rotation rate is applied. Possible applications of these techniques will be presented, both to fundamental measurements of the mechanical and electronic properties of graphene and to new approaches to graphene crystal growth, modification, and manipulation.

We report the first terahertz Kerr measurements on bulk crystals of the topological insulator ${\text{Bi}}_2{\text{Se}}_3$. At $T=10\text{K}$ and fields up to 8 T, the real and imaginary Kerr angle and reflectance measurements utilizing both linearly and circularly polarized incident radiation were measured at a frequency of 5.24 meV. A single fluid free carrier bulk response cannot describe the line shape. Data from one sample is quantitatively described by a surface state with a small mass and surprisingly large associated spectral weight. However, an alternative interpretation in terms of bulk carrier-density variations remains a possibility

In a recent paper [P. Wochner et al., Proc. Natl. Acad. Sci. U.S.A. 106, 11511 (2009)] x-ray scattering intensity correlations around a ring, in the speckle diffraction pattern of a colloidal glass, were shown to display a remarkable $\sim \text{cos}\left(n\phi \right)$ dependence on the angular coordinate $\phi$ around the ring, with integer index $n$ depending on the magnitude of the scattering wave vector. With an analytical derivation that preserves full generality in the Fraunhofer diffraction limit, we clarify the relationship between this result and previous x-ray studies of bond-orientation order, and provide a sound basis to the statement that the angular intensity correlations deliver information on local bond arrangements in a disordered (or partially ordered) system. We present a detailed analysis of the angular cross-correlation function and show its applicability for studies of a wide range of structural properties of disordered systems, from local structure to spatial correlations between distant structural elements.

The behavior of minor hysteresis loops in perpendicular anisotropy [Co/Pt] and [Co/Pd] multilayers has been investigated. Upon applying a succession of identical magnetic field cycles, we observe a very substantial cumulative growth of the minor loop area. For the [Co/Pt] multilayers this effect only saturates near complete magnetization reversal while the behavior is slightly more limited for [Co/Pd] multilayers. We also find this cumulative growth to occur even if the minor loop field cycles are made asymmetric by means of a positive bias field. The cumulative behavior persists up to a sample-dependent threshold value above which this effect disappears. In all samples, the cumulative minor loop growth is correlated with a small reduction in the maximum magnetization value in each cycle. Magneto-optical Kerr microscopy studies correlate the minor loop growth with the memory and cumulative expansion of lateral domain cycling. All experimental observations can be consistently explained as an accumulation of small nucleation domains that aid subsequent reversals and facilitate the cumulative minor loop growth.

We report experimental and numerical studies on photonic band-gap (PBG) formation and light propagation in a recently proposed unique photonic structure, “photonic amorphous diamond (PAD).” PADs have been fabricated in a microwave regime, and the formation of a full three-dimensional (3D) PBG has been substantiated experimentally. This proves unambiguously that periodicity is not essential to the realization of a 3D-PBG, contrary to the common belief. The 3D-PBG has been demonstrated to be completely isotropic, regardless of the light polarization direction, which, in principle, cannot be realized in conventional photonic crystals. In passbands, the PAD has exhibited diffusive light propagation, where the scattering strength increases significantly as the frequency approaches the band edge, indicating a precursor of light localization. Localized states have indeed been identified at the band edges by a numerical calculation. Numerical studies have also indicated that the picture of dielectric and air bands in conventional photonic crystals can be applied to the PBG formation in PAD as well. These findings provide different insights into the physical origin of PBGs and issues such as light diffusion and localization in photonic materials.