Anisotropic Dirac cones in monoatomic hexagonal lattices: a DFT study

In the last few years, the fascinating properties of graphene have been thoroughly investigated. The existence of Dirac cones is the most important characteristic of the electronic band-structure of graphene. In this theoretical paper, hexagonal monolayers of silicon (h-Si) and germanium (h-Ge) are examined using density functional theory, within the generalized gradient approximation. Our numerical results indicate that both h-Si and h-Ge are chemically stable. The lattice parameters, electronic dispersion relations and densities of states for these systems are reported. The electronic dispersion relations display Dirac cones with the symmetry of an equilateral triangle (the group D₃) in the vicinity of the K-points. Hence, the Fermi velocity depends on the wave vector direction around K-points. Fermi velocities for holes and electrons are significantly different. The maximum and minimum Fermi velocities are also reported.     

Electronic structure and anomalous photoemission line-shape of quasi-2D oxide η-Mo4O11

The η-Mo₄O₁₁ compound is a layered two-dimensional (2D) metallic system whose reduced dimensionality originates non-linear properties as charge density wave (CDW) instabilities. We report on synchrotron radiation angle resolved photoemission spectroscopy (ARPES) measurements in order to obtain a detailed picture of the electronic structure of this material. The symmetry of the states near the Fermi level (E_F) has been discussed in relation to the photoemission symmetry selections rules. Our results are in excellent agreement with previous tight-binding calculations and support the hidden nesting concept proposed to explain the CDW instabilities exhibited by this family of compounds. In addition, a very peculiar photoemission line-shape has been found with the presence of localized non-dispersive states. Some possible explanations are discussed.     

Fundamental monopoles and multimonopole solutions for arbitrary simple gauge groups

Magnetic monopole solutions for an arbitrary compact simple gauge group are considered in the Prasad-Sommerfield limit. For each group and choice of symmetry breaking there is a set of fundamental monopoles with minimal topological charges and possessing no internal degrees of freedom; the number of these is less than or equal to the rank of the gauge group. It is shown that if the unbroken gauge group is abelian, all solutions with higher topological charges belong to p-parameter families, where p is the number of position and group orientation parameters needed to describe a set of non-interacting fundamental monopoles with the given topological charge. It is argued that these solutions, some examples of which are given, should therefore be interpreted as multimonopole configurations. An extension of these results to the case of a non-albelian unbroken gauge symmetry is conjecture and shown to be valid for a number of examples.     

Central charges and Lorentz and internal symmetries in massive supersymmetric quantum field theory

The properties of central charges in the framework of the massive supersymmetric quantum field theory related to internal symmetries, Lorentz covariance and locality of the fields are investigated. It is shown that in the presence of z central charges the largest semisimple part of the internal symmetry algebra is a direct sum of z compact symplectic group algebras and possibly an additional term representing the unimodular unitary group algebra. Next it is shown that 4j ? N + K, where j is the highest spin value of the underlying fields, N is the number of spinorial charges and K the number of these spinorial charges which are not linked to other spinorial charges by a central charge. It is further demonstrated that, in general, the central charge can not be redefined in such a way that it is at the same time real and preserves the locality principle. The discussion of the obtained results concludes the paper.     

Exact statements about many-particle systems with higher symmetries

A new method of calculating the energy spectrum of a system of A identical Fermi particles with translationally invariant interaction is developed under the assumption that there exists a high symmetry in the 3A-dimensional space of particle coordinates. For a special class of symmetries the many-body problem is split exactly into two sets of equations: one containing only totally symmetric combinations of the particle coordinates which are called “collective variables” and the other equation taking essentially into account the requirements of the Pauli principle and connected symmetry properties. In several cases it is possible to obtain the excitation spectra exactly showing qualitatively new features. They depend on “many-particle quantum numbers” varying independently of each other in an interval which sometimes depends on A. For special high symmetries the collective variables obey equations which are very similar to one-particle equations providing a new explanation of the “Independent-Particle Model” for arbitrary strength and form of the interaction potential. A manifold of unknown up to now excitation spectra of many-particle systems is obtained and discussed.     

Asymmetric Tunneling Conductance and the Non-Fermi Liquid Behavior of Strongly Correlated Fermi Systems

Tunneling differential conductivity (or resistivity) is a sensitive tool to experimentally test the non-Fermi liquid behavior of strongly correlated Fermi systems. In the case of common metals the Landau–Fermi liquid theory demonstrates that the differential conductivity is a symmetric function of bias voltage V. This is because the particle–hole symmetry is conserved in the Landau–Fermi liquid state. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition, its Landau–Fermi liquid properties disappear so that the particle–hole symmetry breaks making the differential tunneling conductivity to be asymmetric function of V. This asymmetry can be observed when a strongly correlated metal is in its normal, superconducting or pseudogap states. We show that the asymmetric part of the dynamic conductance does not depend on temperature provided that the metal is in its superconducting or pseudogap states. In normal state, the asymmetric part diminishes at rising temperatures. Under the application of magnetic field the metal transits to the Landau–Fermi liquid state and the differential tunneling conductivity becomes a symmetric function of V. These findings are in good agreement with recent experimental observations.     

The structure of the gauge theory vacuum

The finite action Euclidean solutions of gauge theories are shown to indicate the existence of tunneling between topologically distinct vacuum configurations. Diagonalization of the Hamiltonian then leads to a continuum of vacua. The construction and properties of these vacua are analyzed. In non-abelian theories of the strong interactions one finds spontaneous symmetry breaking of axial baryon number without the generation of a Goldstone boson, a mechanism for chiral SU(N) symmetry breaking and a possible source of T violation.     

Topological nodal line semimetals

We review the recent,mainly theoretical,progress in the study of topological nodal line semimetals in three dimensions.In these semimetals,the conduction and the valence bands cross each other along a one-dimensional curve in the three-dimensional Brillouin zone,and any perturbation that preserves a certain symmetry group(generated by either spatial symmetries or time-reversal symmetry) cannot remove this crossing line and open a full direct gap between the two bands.The nodal line(s) is hence topologically protected by the symmetry group,and can be associated with a topological invariant.In this review,(ⅰ) we enumerate the symmetry groups that may protect a topological nodal line;(ⅱ) we write down the explicit form of the topological invariant for each of these symmetry groups in terms of the wave functions on the Fermi surface,establishing a topological classification;(ⅲ) for certain classes,we review the proposals for the realization of these semimetals in real materials;(ⅳ) we discuss different scenarios that when the protecting symmetry is broken,how a topological nodal line semimetal becomes Weyl semimetals,Dirac semimetals,and other topological phases;and(ⅴ) we discuss the possible physical effects accessible to experimental probes in these materials.     

Properties of electrons near a Van Hove singularity

The Fermi surface of most hole-doped cuprates is close to a Van Hove singularity at the M point. A two-dimensional electronic system, whose Fermi surface is close to a Van Hove singularity, shows a variety of weak coupling instabilities. It is a convenient model to study the interplay between antiferromagnetism and anisotropic superconductivity. The renormalization group approach is reviewed with emphasis on the underlying physical processes. General properties of the phase diagram and possible deformations of the Fermi surface due to the Van Hove proximity are described.     

Interchain coupling in Hg3−δAsF6

An electronic bandstructure of the incommensurate linear chain compound Hg_3?δAsF₆ has been calculated by considering various commensurate compounds approximating the real compound. From these calculations a Fermi surface has been determined in qualitative and even close quantitative agreement with experiment. The interchain coupling is found to be strong (?60mRy) but some corners of the Fermi surface are infinitely sharp because of the screw axis symmetry element of the space group with a concommitant vanishing of the structure constant. This work solves a previously posed dilemma.     

Charge-density-wave partial gap opening in quasi-2D KMo6O17 purple bronze studied by angle resolved photoemission spectroscopy

Low dimensional (LD) metallic oxides have been a subject of continuous interest in the last two decades, mainly due to the electronic instabilities that they present at low temperatures. In particular, charge density waves (CDW) instabilities associated with a strong electron-phonon interaction have been found in Molybdenum metallic oxides such as KMo₆O₁₇ purple bronze. We report an angle resolved photoemission (ARPES) study from room temperature (RT) to T ∼40 K well below the Peierls transition temperature for this material, with CDW transition temperature T_CDW ∼120 K. We have focused on photoemission spectra along ΓM high symmetry direction as well as photoemission measurements were taken as a function of temperature at one representative k_F point in the Brillouin zone in order to look for the characteristic gap opening after the phase transition. We found out a pseudogap opening and a decrease in the density of states near the Fermi energy, E_F, consistent with the partial removal of the nested portions of the Fermi surface (FS) at temperature below the CDW transition. In order to elucidate possible Fermi liquid (FL) or non-Fermi liquid (NFL) behaviour we have compared the ARPES data with that one reported on quasi-1D K_0.3MoO₃ blue bronze.     

Spinorial charges and their role in the fusion of internal and space-time symmetries

The advent of supersymmetry immediately led to speculations that a non-trivial mixing of internal and space-time symmetries could be achieved within its framework. In fact, the well-known no-go theorems do not apply to the supersymmetry algebra due to the presence, in the latter, of (anticommuting) spinorial charges. However, not until the recent work of Haag, Lopuszanski and Sohnius did a clearcut picture emerge as to how the aforementioned nontrivial mixing can take place. Most notably, the presence of the conformal algebra within the supersymmetry algebra turns out to be vital. We solidify the findings of Haag et al. through an explicit construction which uses as underlying space the pseudo-Euclidean space E(4,2), i.e. the space for which the conformal group is the group of rotations, and which employs as main tools the spinors associated with the space E(4,2). We follow the algebro-geometric approach of Cartan in order to understand both the introduction and the properties of these spinors. In this manner, we gain many insights regarding the mathematical foundations of supersymmetry. Thus, we fully understand the emergence of the anticommutator, rather than the commutator, among spinor charges as a natural algebraic consequence and not as an a priori given fact. In addition, we clearly see how an (internal) unitary symmetry group can make its appearance within the supersymmetry scheme and verify, via our explicit construction, the results of Haag et al.     

Null-plane charges and fourier transforms for explicitly and spontaneously broken symmetries

It is shown that the existence of null-plane charges and null-plane Fourier transforms (which enter into the discussion of current algebra at infinite momentum) depends on the high energy asymptotic behaviour of off mass shell scattering amplitudes; s In s behaviour is the maximum growth allowed. Under the assumption that asymptotic states exist, these results also hold in the case of spontaneously broken chiral symmetry with massless pseudoscalar Goldstone bosons. In this case, the resulting charges are the non-conserved pole-free charges suggested by Carlitz et al.     

Electronic properties of iron arsenic high temperature superconductors revealed by angle resolved photoemission spectroscopy (ARPES)

We present an overview of the electronic properties of iron arsenic high temperature superconductors with emphasis on low energy band dispersion, Fermi surface and superconducting gap. ARPES data is compared with full-potential linearized plane wave (FLAPW) calculations. We focus on single layer NdFeAsO_0.9F_0.1 (R1111) and two layer Ba_1?xK_xFe₂As₂ (B122) compounds. We find general similarities between experimental data and calculations in terms of character of Fermi surface pockets, and overall band dispersion. We also find a number of differences in details of the shape and size of the Fermi surfaces as well as the exact energy location of the bands, which indicate that magnetic interaction and ordering significantly affects the electronic properties of these materials. The Fermi surface consists of several hole pockets centered at Γ and electron pockets located in zone corners. The size and shape of the Fermi surface changes significantly with doping. Emergence of a coherent peak below the critical temperature T_c and diminished spectral weight at the chemical potential above T_c closely resembles the spectral characteristics of the cuprates, however the nodeless superconducting gap clearly excludes the possibility of d-wave order parameter. Instead it points to s-wave or extended s-wave symmetry of the order parameter.     

Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity

It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three dimensional gravity with a negative cosmological constant. The asymptotic symmetry group in that case is eitherR×SO(2) or the pseudo-conformal group in two dimensions, depending on the boundary conditions adopted at spatial infinity. In the latter situation, a nontrivial central charge appears in the algebra of the canonical generators, which turns out to be just the Virasoro central charge.     

Discrete Charges on a Two Dimensional Conductor

We investigate the electrostatic equilibria of N discrete charges of size 1/N on a two dimensional conductor (domain). We study the distribution of the charges on symmetric domains including the ellipse, the hypotrochoid and various regular polygons, with an emphasis on understanding the distributions of the charges, as the shape of the underlying conductor becomes singular. We find that there are two regimes of behavior, a symmetric regime for smooth conductors, and a symmetry broken regime for “singular” domains. For smooth conductors, the locations of the charges can be determined, to within $O\left( {\sqrt {\log {N \mathord{\left/ {\vphantom {N {N^2 }}} \right. \kern-0em} {N^2 }}} } \right)$ by an integral equation due to Pommerenke [ Math. Ann., 179: 212–218, (1969)]. We present a derivation of a related (but different) integral equation, which has the same solutions. We also solve the equation to obtain (asymptotic) solutions which show universal behavior in the distribution of the charges in conductors with somewhat smooth cusps. Conductors with sharp cusps and singularities show qualitatively different behavior, where the symmetry of the problem is broken, and the distribution of the discrete charges does not respect the symmetry of the underlying domain. We investigate the symmetry breaking both theoretically, and numerically, and find good agreement between our theory and the numerics. We also find that the universality in the distribution of the charges near the cusps persists in the symmetry broken regime, although this distribution is very different from the one given by the integral equation.     

First-principles study on structural and electronic properties of AlNSix heterosheet

Under generalized gradient approximation (GGA), the structural and electronic properties of AlN and Si sheets, hydrogen terminated AlN and Si nanoribbons with hexagonal morphology and 2, 4, 6 zigzag chains across the ribbon width and the hexagonally bonded heterosheets AlNSi_x (x=2, 4, and 6) consisting of hexagonal networks of AlN (h-AlN) strips and silicene sheets with zigzag shaped borders have been investigated using the first-principles projector-augmented wave (PAW) formalism within the density function theory (DFT) framework. The AlN sheet is an indirect semiconductor with a band gap of 2.56 eV, while the Si sheet has a metallic character since the lowest unoccupied conduction band (LUCB) and the highest occupied valence band (HOVB) meet at one k point from Γ to Z. In the semiconductor 6-ZAlNNR, for example, the states of LUCB and HOVB at zone boundary Z are edge states whose charges are localized at edge Al and N atoms, respectively. In metallic 6-ZSiNR, a flat edge state is formed at the Fermi level E_F near the zone boundary Z because its charges are localized at edge Si atoms. The hybridizations between the edge states of h-AlN strips and silicene sheets result in the appearance of border states in the zigzag borders of heterosheets AlNSi_x whose charges are localized at two atoms of the borders with either bonding or antibonding π character.     

Magnetic monopoles with Zn charges

Under some circumstances magnetic monopoles can be formed with charges which are additive modulo n. We speak of these as monopoles with Z_n charges. The conditions under which such monopoles arise are examined, and illustrated with some specific examples. These monopoles can be produced at intermediate stages of symmetry breakdown and converted at subsequent stages to ones with ordinary additive charges, specified by the group Z ≡ Z_∞. Simultaneously, new light monopoles with n times the Dirac charge can be produced. It is argued that such monopoles may be exempt from the most stringent cosmological bounds, and hence may be easiest to observe.