We study the problem of two Dirac particles interacting through nonrelativistic potentials and confined to a two-dimensional sheet, which is the relevant case for graphene layers. The two-body problem cannot be mapped into that of a single particle, due to the nontrivial coupling between the center-of-mass and the relative coordinates, even in the presence of central potentials. We focus on the case of zero total momentum, which is equivalent to that of a single particle in a Sutherland lattice. We show that zero-energy states induce features such as discontinuities in the relative wave function, for particles interacting through a step potential, and a concentration of relative density near the classical turning point, if particles interact via a Coulomb potential. In the latter case we also find that the two-body system becomes unstable above a critical coupling. These phenomena may have bearing on the nature of strong-coupling phases in graphene.

We have investigated magnetic field dependences of a ferroelectric incommensurate-helimagnetic order in a trigonal magnetoelectric multiferroic ${\text{CuFe}}_{1-x}{\text{Al}}_x{\text{O}}_2$ with $x=0.015$, which exhibits the ferroelectric phase as a ground state, by means of neutron diffraction, magnetization, and dielectric polarization measurements under magnetic fields applied along various directions. From the present results, we have established the $H\text{−}T$ magnetic phase diagrams for the three principal directions of magnetic fields; (i) parallel to the $c$ axis, (ii) parallel to the helical axis, and (iii) perpendicular to the $c$ and the helical axes. While the previous dielectric polarization $\left(P\right)$ measurements on ${\text{CuFe}}_{1-x}{\text{Ga}}_x{\text{O}}_2$ with $x=0.035$ have demonstrated that the magnetic field dependence of the “magnetic domain structure” results in distinct magnetic field responses of $P$ [S. Seki et al., Phys. Rev. Lett. 103, 237601 (2009)], the present study have revealed that the anisotropic magnetic field dependence of the ferroelectric helimagnetic order “in each magnetic domain” can be also a source of a variety of magnetic field responses of $P$ in ${\text{CuFe}}_{1-x}{A}_x{\text{O}}_2$ systems $\left(A=\text{Al},\text{Ga}\right)$.

Spin-polarized band structure of the three-dimensional quantum spin Hall insulator ${\text{Bi}}_{1-x}{\text{Sb}}_x$ $\left(x=0.12–0.13\right)$ was fully elucidated by spin-polarized angle-resolved photoemission spectroscopy using a high-yield spin polarimeter equipped with a high-resolution electron spectrometer. Between the two time-reversal-invariant points, $\overline{\Gamma }$ and $\overline{\text{M}}$, of the (111) surface Brillouin zone, a spin-up band (${\Sigma }_1^{\prime }$ band) was found to cross the Fermi energy only once, providing unambiguous evidence for the strong topological insulator phase. The observed spin-polarized band dispersions determine the “mirror chirality” to be $-1$, which agrees with the theoretical prediction based on first-principles calculations.

We propose a nonlocal kinetic energy density functional (KEDF) for semiconductors based on the expected asymptotic behavior of its susceptibility function. The KEDF’s kernel depends on both the electron density and the reduced density gradient, with an internal parameter formally related to the material’s static dielectric constant. We determine the accuracy of the KEDF within orbital-free density functional theory (DFT) by applying it to a variety of common semiconductors. With only two adjustable parameters, the KEDF reproduces quite well the exact noninteracting KEDF (i.e., Kohn-Sham DFT) predictions of bulk moduli, equilibrium volumes, and equilibrium energies. The two parameters in our KEDF are sensitive primarily to changes in the local crystal structure (such as atomic coordination number) and exhibit good transferability between different tetrahedrally-bonded phases. This local crystal structure dependence is rationalized by considering Thomas-Fermi dielectric screening theory.

Recently, it was reported that $\beta$-rhombohedral boron has a negative defect formation energy, which explains the presence of a macroscopic amount $\left(4\text{at}\text{.}\mathrm{\%}\right)$ of intrinsic defects. In this work, it is shown that the defects in boron have geometrical frustration described by an antiferromagnetic Ising model on an expanded kagome lattice, which is responsible for the reported macroscopic residual entropy. We suggest that the reported anomalies in the transport properties of $\beta$-boron are due to the hopping of boron atoms between nearly degenerate configurations.

A two-wave shock structure—elastic precursor followed by an inelastic compression wave—is observed in single crystal and polycrystalline diamond laser shock compressed to peak stresses as high as 800 GPa. The Hugoniot elastic limits are measured to be 80 $\left(\pm 12\right)$, 81 $\left(\pm 6\right)$, and 60 $\left(\pm 3\right)\text{GPa}$ for the $⟨100⟩$, $⟨110⟩$, and $⟨111⟩$ orientations of single crystals with the directional dependence attributable to the relative increase in strength under confining stress. These values imply a single crystal yield strength approximately 1/3 of theoretical predictions. The measurements reveal clear deviations from an elastic-plastic response upon dynamic yielding with significant relaxation toward an isotropic stress state for shock stresses of at least 160 GPa. Previously reported signatures of melting at 700–800 GPa along the diamond Hugoniot may be related to the transition from a two-wave to a single-wave structure, supporting the interpretation that melting begins at lower stresses $\left(\sim 600\text{GPa}\right)$ with the appearance of an optically reflecting phase of carbon.

The low-energy single-particle excitations of highly ordered ${\text{C}}_{60}$ chains adsorbed on a vicinal copper substrate are investigated by angle-resolved photoemission spectroscopy. The interface state previously identified on ${\text{C}}_{60}/\text{Cu}\left(111\right)$ shows a one-dimensional dispersion on Cu(553). In contrast, no significant momentum dependence is detected for emission from the lowest unoccupied molecular orbital (LUMO). The LUMO displays similar phonon features as in ${\text{C}}_{60}/\text{Cu}\left(111\right)$ but it does not peak toward the Fermi level for all considered potassium dopings and its photoemission lineshape is broader than in any other monolayer system investigated so far. This behavior is not easily reconciled with existing theory and indicates that the one-dimensional character of the chains affects the electronic structure of the monolayer in an intricate way.

We followed the Shastry-Shraiman formulation of Raman scattering in Hubbard systems and considered the Raman intensity profile in the spin-$\frac{1}{2}$ “perfect” kagome lattice herbertsmithite ${\text{ZnCu}}_3{\left(\text{OH}\right)}_6{\text{Cl}}_2$, assuming the ground state is well-described by the U(1) Dirac spin-liquid state. In the derivation of the Raman $T$ matrix, we found that the spin-chirality term appears in the $A_{2g}$ channel in the kagome lattice at the $t^4/{\left({\omega }_i-U\right)}^3$ order, but (contrary to the claims by Shastry and Shraiman) vanishes in the square lattice to that order. In the ensuing calculations on the spin-$\frac{1}{2}$ kagome lattice, we found that the Raman intensity profile in the $E_g$ channel is invariant under an arbitrary rotation in the kagome plane, and that in all ($A_{1g}$, $E_g$, and $A_{2g}$) symmetry channels the Raman intensity profile contains broad continua that display power-law behaviors at low energy, with exponent approximately equal to 1 in the $A_{2g}$ channel and exponent approximately equal to 3 in the $E_g$ and the $A_{1g}$ channels. For the $A_{2g}$ channel, the Raman profile also contains a characteristic $1/\omega$ singularity, which arose in our model from an excitation of the emergent U(1) gauge field.

We report the modification of the density of states of the $\text{Ag}/\text{Si}\left(111\right)\text{−}\surd 3\times \surd 3R30°$ surface by a self-assembled molecular network at energies much higher than the height of the potential barriers induced by the molecules. Map of the differential conductance obtained by scanning tunneling spectroscopy reveals an increase in the electron density in the pores of the network. This enhanced electronic resonance is explained by theoretical calculations where the periodic potential introduced by the molecular network causes band replica with an alteration of the surface band structure.

We report a comprehensive small angle neutron scattering study of the magnetic phase diagram of the doped semiconductor ${\text{Fe}}_{1-x}{\text{Co}}_x\text{Si}$ for $x=0.2$. For magnetic field parallel to the neutron beam we observe a sixfold intensity pattern under field cooling. The regime of the skyrmion lattice is highly hysteretic and extents over a wide temperature range as may be expected due to the site disorder of the Fe and Co atoms. Our study identifies ${\text{Fe}}_{1-x}{\text{Co}}_x\text{Si}$ as the second material in which a skyrmion lattice forms and establishes that skyrmion lattices exist also in doped semiconductors.

We discuss the proximate phases of a three-dimensional system with Dirac-like dispersion. Using the cubic lattice with plaquette $\pi$-flux as a model, we find, among other phases, a chiral topological insulator and singlet topological superconductor. While the former requires a special “chiral” symmetry, the latter is stable as long as time reversal and SU(2) spin rotation symmetry are present. These phases are characterized by stable surface Dirac fermion modes, and by an integer topological invariant in the bulk. The key features of these phases are readily understood in a two dimensional limit with an appropriate pairing of Dirac nodes between layers. This Dirac node-pairing picture is also shown to apply to ${\mathbb{Z}}_2$ topological insulators protected by time-reversal symmetry. The nature of pointlike topological defects in these phases is also investigated, revealing an interesting duality relation between these topological phases and the Neel phase.

Precise readout of spin states is crucial for any approach toward physical realization of a spin-based quantum computer and for magnetometry with single spins. Here, we report a method to strongly improve the optical readout fidelity of electron spin states associated with single nitrogen-vacancy (NV) centers in diamond. The signal-to-noise ratio is enhanced significantly by performing conditional flip-flop processes between the electron spin and the nuclear spin of the NV center’s nitrogen atom. The enhanced readout procedure is triggered by a short preparatory pulse sequence. As the nitrogen nuclear spin is intrinsically present in the system, this method is universally applicable to any nitrogen-vacancy center. Besides the readout method, our studies included coherent control over a single nitrogen nuclear spin for the first time.

We present neutron-scattering results on the magnetic excitations in the spinel compounds ${\text{Li}}_x\left[{\text{Mn}}_{1.96}{\text{Li}}_{0.04}\right]{\text{O}}_4$ $\left(x=0.2,0.6,0.8,1.0\right)$. We show that the dominant excitations below $T\sim 70\text{K}$ are determined by Mn ions located in clusters, and that these excitations mimic the dynamic scaling found in quantum critical systems that also harbor magnetic clusters, such as ${\text{CeRu}}_{0.5}{\text{Fe}}_{1.5}{\text{Ge}}_2$. We argue that our results for this classical spinel compound suggest that the unusual response at low temperatures as observed in quantum critical systems that have been driven to criticality through substantial chemical doping is (at least) partially the result of the fragmentation of the magnetic lattice into smaller units.

We discuss a feedback mechanism between electronic states in a two-electron double quantum dot and the underlying nuclear spin bath. We analyze two pumping cycles for which this feedback provides a force for the Overhauser fields of the two dots to either equilibrate or diverge. Which of these effects is favored depends on the $g$ factor and Overhauser coupling constant of the material. The strength of the effect increases with the ratio of Overhauser coupling to electron exchange energy and also increases as the external magnetic field decreases.

The giant magnetostriction observed in rare-earth transition-metal compounds such as Terfenol-D $\left({\text{Tb}}_{0.3}{\text{Dy}}_{0.7}{\text{Fe}}_2\right)$ is commonly associated with the huge anisotropy of the $4f$ electron cloud. We report here the experimental observation of this phenomenon at the atomic scale, in amorphous matter. By using extended x-ray absorption fine structure spectroscopy in a differential mode, the bond strains resulting from the coupling between the anisotropic shape of the $\text{Tb}4f$ charge density and the environment crystalline electric field are measured. In ${\text{a-TbFe}}_2$ we measure Fe-Fe and Fe-Tb bond contractions equal to $6\left(1\right)\times {10}^{-4}\text{Å}$ and of $9\left(2\right)\times {10}^{-4}\text{Å}$, respectively. These are the smallest atomic displacements ever detected in amorphous matter.

We present a microscopic model of the quantum paraelectric-ferroelectric phase transition with a focus on the influence of coupled fluctuating phonon modes. These may drive the continuous phase-transition first order through a metaelectric transition and furthermore stimulate the emergence of a textured phase that preempts the transition. We discuss two further consequences of fluctuations, first for the heat capacity, and second we show that the inverse paraelectric susceptibility displays ${\chi }^{-1}\sim T^2$ quantum critical behavior, and can also adopt a characteristic minimum with temperature. Finally, we discuss the observable consequences of our results.

Motivated by recent scanning tunneling microscopy experiments on surfaces of ${\text{Bi}}_{1-x}{\text{Sb}}_{x^{\prime }}$ and ${\text{Bi}}_2{\text{Te}}_3$, we theoretically study the electronic structure of a three-dimensional (3D) topological insulator in the presence of a local impurity or a domain wall on its surface using a 3D lattice model. While the local density of states (LDOS) oscillates significantly in space at energies above the bulk gap, the oscillation due to the in-gap surface Dirac fermions is very weak. The extracted modulation wave number as a function of energy satisfies the Dirac dispersion for in-gap energies and follows the border of the bulk continuum above the bulk gap. We have also examined analytically the effects of the defects by using a pure Dirac fermion model for the surface states and found that the LDOS decays asymptotically faster at least by a factor of $1/r$ than that in normal metals, consistent with the results obtained from our lattice model.

We analyze the behavior of an itinerant two-dimensional Fermi system near a charge nematic $\left(n=2\right)$ Pomeranchuk instability in terms of the Landau Fermi-liquid (FL) theory. A key object of our study is the fully renormalized vertex function ${\Gamma }^{\Omega }$, related to the Landau interaction function. We derive ${\Gamma }^{\Omega }$ for a model case of the long-range interaction in the nematic channel. Already within the random-phase approximation (RPA), the vertex is singular near the instability. The full vertex, obtained by resumming the ladder series composed of the RPA vertices, differs from the RPA result by a multiplicative renormalization factor $Z_{\Gamma }$, related to the single-particle residue $Z$ and effective-mass renormalization $m^{\ast }/m$. We employ the Pitaevski-Landau identities, which express the derivatives of the self-energy in terms of ${\Gamma }^{\Omega }$, to obtain and solve a set of coupled nonlinear equations for $Z_{\Gamma }$, $Z$, and $m^{\ast }/m$. We show that near the transition the system enters a critical FL regime, where $Z_{\Gamma }\sim Z\propto {\left(1+g_{c,2}\right)}^{1/2}$ and $m^{\ast }/m\approx 1/Z$, where $g_{c,2}$ is the $n=2$ charge Landau component which approaches $-1$ at the instability. We construct the Landau function of the critical FL and show that all but $g_{c,2}$ Landau components diverge at the critical point. We also show that in the critical regime the one-loop result for the self-energy $\Sigma \left(K\right)\propto \int dPG\left(P\right)D\left(K-P\right)$ is asymptotically exact if one identifies the effective interaction $D$ with the RPA form of ${\Gamma }^{\Omega }$.

We report the discovery of a binary icosahedral phase in a Sc-Zn alloy obtained through solution-growth, producing millimeter-sized, facetted, single grain quasicrystals that exhibit different growth morphologies, pentagonal dodecahedra, and rhombic triacontahedra, under only marginally different growth conditions. These two morphologies manifest different degrees of quasicrystalline order. The discovery of $i{\text{-Sc}}_{12}{\text{Zn}}_{88}$ suggests that a re-examination of binary phase diagrams at compositions close to crystalline approximant structures may reveal other binary quasicrystalline phases.

We show that a large class of two-dimensional spinless fermion models exhibit topological superconducting phases characterized by a nonzero Chern number. More specifically, we consider a generic one-band Hamiltonian of spinless fermions that is invariant under both time reversal, $\mathbb{T}$, and a group of rotations and reflections, $\mathbb{G}$, which is either the dihedral point-symmetry group of an underlying lattice, $\mathbb{G}=D_n$, or the orthogonal group of rotations in continuum, $\mathbb{G}=\text{O}\left(2\right)$. Pairing symmetries are classified according to the irreducible representations of $\mathbb{T}\otimes \mathbb{G}$. We prove a theorem that for any two-dimensional representation of this group, a time-reversal symmetry-breaking paired state is energetically favorable. This implies that the ground state of any spinless fermion Hamiltonian in continuum or on a square lattice with a singly connected Fermi surface is always a topological superconductor in the presence of attraction in at least one channel. Motivated by this discovery, we examine phase diagrams of two specific lattice models with nearest-neighbor hopping and attraction on a square lattice and a triangular lattice. In accordance with the general theorem, the former model exhibits only a topological $\left(p+ip\right)$-wave state while the latter shows a doping-tuned quantum phase transition from such state to a nontopological but still exotic $f$-wave superconductor.