Entire Brillouin Zone Research Articles

Effective theory of Fermi pockets in fluctuating antiferromagnets

We describe fluctuating two-dimensional metallic antiferromagnets by transforming to a rotating reference frame in which the electron spin polarization is measured by its projections along the local antiferromagnetic order. This leads to a gauge-theoretic description of an ``algebraic charge liquid'' involving spinless fermions and a spin $S=1/2$ complex scalar. We propose a phenomenological effective lattice Hamiltonian which describes the binding of these particles into gauge-neutral, electronlike excitations, and describe its implications for the electron spectral function across the entire Brillouin zone. We discuss connections of our results to photoemission experiments in the pseudogap regime of the cuprate superconductors.

Bloch-state-based interpolation: An efficient generalization of the Shirley approach to interpolating electronic structure

We present an efficient generalization of the $k$-space interpolation scheme for electronic structure presented by Shirley [Phys. Rev. B 54, 16464 (1996)]. The method permits the construction of a compact $k$-dependent Hamiltonian using a numerically optimal basis derived from a coarse-grained set of effective single-particle electronic-structure calculations (based on density-functional theory in this work). We provide some generalizations of the initial approach which reduce the number of required initial electronic-structure calculations, enabling accurate interpolation over the entire Brillouin zone based on calculations at the zone center only for large systems. We also generalize the representation of nonlocal Hamiltonians, leading to a more efficient implementation which permits the use of both norm-conserving and ultrasoft pseudopotentials in the input calculations. Numerically interpolated electronic eigenvalues with accuracy that is within 0.01 eV can be produced at very little computational cost. Furthermore, accurate eigenfunctions---expressed in the optimal basis---provide easy access to useful matrix elements for simulating spectroscopy and we provide details for computing optical transition amplitudes. The approach is also applicable to other theoretical frameworks such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter equation for optical responses.

Modes of Shallow Photonic Crystal Waveguides: Semi-Analytic Treatment

We investigate the formation of photonic crystal waveguide (PCW) modes within the framework of perturbation theory. We derive a differential equation governing the envelope of PCW modes constructed from weak perturbations using an effective mass formulation based on the Luttinger-Kohn method from solid-state physics. The solution of this equation gives the frequency of the mode and its field. The differential equation lends itself to simple analytic approximations which reduce the problem to that of solving slab waveguide modes. By using this model, we demonstrate that the nature of the projected band structure and corresponding Bloch functions are central to the behaviour of PCW modes. With this understanding, we explain why the odd mode in a hexagonal PCW spans the entire Brillouin zone while the even mode is cut off.

Multi-band spectroscopy of inhomogeneous Mott-insulator states of ultracold bosons

In this work, we use inelastic scattering of light to study the response of inhomogeneous Mott-insulator gases to external excitations. The experimental setup and procedure to probe the atomic Mott states are presented in detail. We discuss the link between the energy absorbed by the gases and accessible experimental parameters as well as the linearity of the response to the scattering of light. We investigate the excitations of the system in multiple energy bands and a band-mapping technique allows us to identify band and momentum of the excited atoms. In addition, the momentum distribution in the Mott states that is spread over the entire first Brillouin zone enables us to reconstruct the dispersion relation in the high energy bands using a single Bragg excitation with a fixed momentum transfer.

Collective Magnetic Excitations in the Spin LadderSr14Cu24O41Measured Using High-Resolution Resonant Inelastic X-Ray Scattering

We investigate magnetic excitations in the spin-ladder compound Sr_{14}Cu_{24}O_{41} using high-resolution Cu L_{3} edge resonant inelastic x-ray scattering (RIXS). Our findings demonstrate that RIXS couples to two-triplon collective excitations. In contrast to inelastic neutron scattering, the RIXS cross section changes only moderately over the entire Brillouin zone, revealing high sensitivity also at small momentum transfers, allowing determination of the two-triplon energy gap as 100 +/- 30 meV. Our results are backed by calculations within an effective Hubbard model for a finite-size cluster, and confirm that optical selection rules are obeyed for excitations from this spherically symmetric quantum spin-liquid ground state.

Spin waves and magnetic exchange interactions in CaFe2As2

Antiferromagnetism is relevant to high-temperature (high-Tc) superconductivity because copper oxide and iron arsenide superconductors arise from electron- or hole-doping of their antiferromagnetic parent compounds1,2,3,4,5,6. There are two broad classes of explanation for antiferromagnetism: in the ‘local moment’ picture, appropriate for the insulating copper oxides1, antiferromagnetic interactions are well described by a Heisenberg Hamiltonian7,8; whereas in the ‘itinerant model’, suitable for metallic chromium, antiferromagnetic order arises from quasiparticle excitations of a nested Fermi surface9,10. There has been contradictory evidence regarding the microscopic origin of the antiferromagnetic order in iron arsenide materials5,6, with some favouring a localized picture11,12,13,14,15 and others supporting an itinerant point of view16,17,18,19,20. More importantly, there has not even been agreement about the simplest effective ground-state Hamiltonian necessary to describe the antiferromagnetic order21,22,23,24,25. Here, we use inelastic neutron scattering to map spin-wave excitations in CaFe2As2 (refs 26, 27), a parent compound of the iron arsenide family of superconductors. We find that the spin waves in the entire Brillouin zone can be described by an effective three-dimensional local-moment Heisenberg Hamiltonian, but the large in-plane anisotropy cannot. Therefore, magnetism in the parent compounds of iron arsenide superconductors is neither purely local nor purely itinerant, rather it is a complicated mix of the two.

Entanglement perturbation theory for the elementary excitation in one dimension

The entanglement perturbation theory is developed to calculate the excitation spectrum in one dimension. Applied to the spin- 1 2 antiferromagnetic Heisenberg model, it reproduces the des Cloiseaux–Pearson Bethe ansatz result. As for spin-1, the spin-triplet magnon spectrum has been determined for the first time for the entire Brillouin zone, including the Haldane gap at k = π .

Spin polarization and relativistic electronic structure of the 1×1 H/W(110) surface

We present an analysis of the relativistic electronic structure of the 1×1 H/W(110) surface. Our calculations reproduce in detail the experimentally determined Fermi surface and spin polarization of the surface electron states. A projected spin-polarized density of states is defined in order to simulate the photoemission spectra exhibiting very good agreement with existing spin-resolved measurements. Our calculations confirm that the spin-split states, S1 and S2, are approximately circularly spin polarized with respect to the high-symmetry point . Moreover, we present the precise shape and magnitude of the spin polarization of the spin–orbit split S1 and S2 states, through the entire Brillouin zone.

Numerical study on the anisotropic triangular-lattice Hubbard model at quarter filling: Charge fluctuations with three-fold periodicity

We study the extended Hubbard model at quarter filling defined on the anisotropic triangular lattices. We use the density-matrix renormalization group (DMRG) method to determine the ground-state phase diagram and the dynamical DMRG and Lanczos exact-diagonalization methods to calculate the excitation spectra. We find that the charge fluctuation with the three-fold periodicity, as well as the vertical and diagonal charge stripes, appears in realistic parameter ranges. We also find that, in the charge excitation spectra, there appear the low-energy collective modes in the entire Brillouin zone, together with the low-energy Drude-like peak separated from the high-energy broad features in the optical conductivity spectra, indicating the presence of the anomalous charge excitations in the state with the three-fold charge fluctuations.

Px,y-orbital counterpart of graphene: Cold atoms in the honeycomb optical lattice

We study the ground-state properties of the interacting spinless fermions in the ${p}_{x,y}$-orbital bands in the two-dimensional honeycomb optical lattice, which exhibit different features from those in the ${p}_{z}$-orbital system of graphene. In addition to two dispersive bands with Dirac cones, the tight-binding band structure exhibits another two completely flat bands over the entire Brillouin zone. With the realistic sinusoidal optical potential, the flat bands acquire a finite but much smaller bandwidth compared to the dispersive bands. The band flatness dramatically enhanced interaction effects giving rise to various charge and bond ordered states at commensurate fillings of $n=\frac{i}{6}(i=1--6)$. At $n=\frac{1}{6}$, the many-body ground states can be exactly solved as the close-packed hexagon states which can be stabilized even in the weakly interacting regime. The dimerization of bonding strength occurs at both $n=\frac{1}{2}$ and $\frac{5}{6}$, and the latter case is accompanied with the charge-density wave of holes. The trimerization of bonding strength and charge inhomogeneity appear at $n=\frac{1}{3},\frac{2}{3}$. These crystalline orders exhibit themselves in the noise correlations of the time-of-flight spectra.

Extracting the spectral function of the cuprates by a full two-dimensional analysis: Angle-resolved photoemission spectra ofBi2Sr2CuO6

Recently, angle-resolved photoemission spectroscopy (ARPES) has revealed a dispersion anomaly at high binding energy near $0.3--0.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ in various families of the high-temperature superconductors. For further studies of this anomaly, we present a new two-dimensional fitting scheme and apply it to high-statistics ARPES data of the strongly overdoped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Cu}{\mathrm{O}}_{6}$ cuprate superconductor. The procedure allows us to extract the self-energy in an extended energy and momentum range. It is found that the spectral function of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Cu}{\mathrm{O}}_{6}$ can be parametrized using a small set of tight-binding parameters and a weakly momentum-dependent self-energy up to $0.7\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ in binding energy and over the entire first Brillouin zone. Moreover, the analysis gives an estimate of the momentum dependence of the matrix element, a quantity, which is often neglected in ARPES analyses.

Band structure built from oligomer calculations

A method to build accurate band structures of polymers from oligomer calculations has been developed. This method relies on systematic procedures for (i) assigning k values, (2) eliminating strongly localized molecular orbitals, and (iii) connecting bands across the entire Brillouin zone. Illustrative calculations are carried out at the HF/STO-3G level for trans-polyacetylene (PA), poly(para-phenylene) (PPP), and water chains. More stringent tests at several different levels are reported for polydiacetylene/polybutatriene.

DILUTED FERROMAGNETIC SEMICONDUCTORS — ORIGIN OF MAGNETIC ORDERING AND SPIN-TRANSPORT PROPERTIES

In the first hour of the lecture the present understanding of the origin of exchange interaction and mechanisms leading to ferromagnetic order in diluted magnetic semiconductors will be presented.1 The lecture will start by discussing energy positions of relevant open magnetic shells, including the correlation energy and excitations within the magnetic ions. The origin and magnitude of sp–d exchange interactions will then be described. This will be followed by presenting the physics of indirect exchange interactions between localized spins contrasting magnetic characteristics in the absence and in the presence of free carriers. The Zener and RKKY models of ferromagnetism will be introduced and the role of confinement, dimensionality, and spin-orbit interaction in determining properties of the ferromagnetic phase will be outlined. The second lecture will be devoted to theory of spin transport in layered structures of diluted ferromagnetic semiconductors, emphasizing the issues important for perspective spintronics devices. A recently developed theory,2 which combines a multi-orbital empirical tight-binding approach with a Landauer–Büttiker formalism will be presented. In contrast to the standard kp method, this theory describes properly the interfaces and inversion symmetry breaking as well as the band dispersion in the entire Brillouin zone, so that the essential for the spin-dependent transport Rashba and Dresselhaus terms as well as the tunneling via k points away from the zone center are taken into account. The applicability of this model for the description of tunneling magnetoresistance (TMR), resonant tunneling spectra, spin-current polarization in Esaki-Zener diodes, and domain-wall resistance will be presented. Note from Publisher: This article contains the abstract only.

Lattice dynamics and the phase transition from the cubic phase to the tetragonal phase in the LaMnO3 crystal within the polarizable-ion model

The paper reports on the results of ab initio calculations of the static and dynamic properties of the LaMnO3 crystal with a perovskite structure in the cubic, rhombohedral, and orthorhombic phases. The calculations are performed within the ionic crystal model, which takes into account the deformability and polarizability of the ions. It is revealed that the spectrum of lattice vibrations in the cubic phase contains unstable vibrational modes, which occupy the phase space in the entire Brillouin zone. The eigenvectors of the softest mode at the boundary point R of the Brillouin zone are associated with the displacements of the oxygen ions and correspond to the “rotation” of the MnO6 octahedron. The condensation of one, two, and three components of this mode leads to the tetragonal, orthorhombic, and rhombohedral distortions of the structure. The structural phase transition is described in terms of the local mode approximation with the use of the double perovskite unit cell, in which the MnO6 octahedron is explicitly separated. The parameters of the model Hamiltonian are determined. The static properties are investigated by the Monte Carlo method. The calculated temperature of the phase transition from the cubic phase (9800 K) is considerably higher than the melting temperature of the crystal under investigation. The calculated frequencies of long-wavelength lattice vibrations in the experimentally observed orthorhombic and rhombohedral phases are in reasonable agreement with experimental data.

The model of self-compensation and pinning of the Fermi level in irradiated semiconductors

A model is developed to analyze numerically the electrical properties and the steady-state (limiting) position of the Fermi level (Flim) in tetrahedral semiconductors irradiated with high-energy particles. It is shown that an irradiated semiconductor represents a highly compensated material, in which Flim is identical to 〈EG〉/2, where 〈EG〉 is the average energy gap between the conduction band and valence band within the entire Brillouin zone of the crystal. The experimental values of Flim, the calculated values of 〈EG〉/2, and the data on the electrical properties of irradiated semiconductors are presented. The chemical trends controlling the variation in the quantity Flim in groups of semiconductors with the similar types of chemical bonding are analyzed.

Dynamics of quantum spin liquid and spin solid phases inIPA−CuCl3under an applied magnetic field studied with neutron scattering

Inelastic and elastic neutron scattering is used to study spin correlations in the quasi-one-dimensional quantum antiferromagnet IPA-CuCl3 in strong applied magnetic fields. A condensation of magnons and commensurate transverse long-range ordering is observe at a critical field Hc=9.5 T. The field dependencies of the energies and polarizations of all magnon branches are investigated both below and above the transition point. Their dispersion is measured across the entire one-dimensional Brillouin zone in magnetic fields up to 14 T. The critical wave vector of magnon spectrum truncation Masuda et al., Phys. Rev. Lett. 96, 047210 2006 is found to shift from hc0,35 at HHC to hc=0.25 for HHC. A drastic reduction of magnon bandwidths in the ordered phase Garlea et al., Phys. Rev. Lett. 98, 167202 2007 is observed and studied in detail. New features of the spectrum, presumably related to this bandwidth collapse, are observed just above the transition field.

Anomalous phonon behavior in the high-temperature shape-memory alloyTi50Pd50−xCrx

${\mathrm{Ti}}_{50}{\mathrm{Pd}}_{50\ensuremath{-}x}{\mathrm{Cr}}_{x}$ is a high-temperature shape-memory alloy with a martensitic transformation temperature strongly dependent on the Cr composition. Prior to the transformation, a premartensitic phase is present with an incommensurate modulated cubic lattice with wave vector of ${q}_{0}=(0.22,0.22,0)$. The temperature dependence of the diffuse scattering in the cubic phase is measured as a function temperature for $x=6.5$, 8.5, and $10\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$. The lattice dynamics has been studied and reveals anomalous temperature and $q$ dependences of the $[110]\text{\ensuremath{-}}{\mathrm{TA}}_{2}$ transverse phonon branch. The phonon linewidth is broad over the entire Brillouin zone and increases with decreasing temperature, contrary to the behavior expected for anharmonicity. No anomaly is observed at ${q}_{0}$. The results are compared with first principles calculation of the phonon structure.

Effects of time reversal symmetry on phonons in sapphire substrate for ZnO and GaN

Vibrational states in a crystal are classified according to the irreducible representations (irreps) of the corresponding factor group G0k/T. The wave vector k runs over the entire Brillouin zone (BZ). For trigonal BZs, the factor groups are determined by the symmetry points Γ, F, L, T, and the symmetry lines Λ, Σ, Y. When the irreps are complex, the time reversal symmetry has to be taken into account. Using the Frobenuis–Schur criterion adapted to space groups with real and complex irreps, we have investigated high symmetry points and lines of the phonons in trigonal crystals: Cr2O3,Fe2O3,Ti2O3,V 2O3,FeCO3,CaCO3,CdCO3,MgCO3,MnCO3,NaCO3 and ZnCO3, with the common space group D3d6(R3c). We have found several phonons which are influenced by the time reversal symmetry. Therefore, an extra degeneracy of phonons arises. The theoretical results are also compared with available experimental data.

Canalization for subwavelength focusing by a slab of dielectric photonic crystal

A rectangular lattice of high dielectric rectangular rods in air is used to achieve canalization for subwavelength focusing. At the working frequency, the equifrequency curve of the dielectric photonic crystal is split into two very straight parallel lines in the entire first Brillouin zone. To increase greatly the transmission, the size of the rods on the interface layers is adjusted appropriately, while the thickness of the slab can be arbitrary. A slab of such a photonic crystal can transfer subwavelength focusing to a far distance even if moderate material loss exists.

Inelastic neutron scattering and lattice dynamical calculation of negative thermal expansion compoundsCu2OandAg2O

Negative thermal expansion (NTE) is known in ${\mathrm{Cu}}_{2}\mathrm{O}$ below $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and in ${\mathrm{Ag}}_{2}\mathrm{O}$ up to its decomposition temperature of about $500\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Inelastic neutron scattering measurements in ${\mathrm{Cu}}_{2}\mathrm{O}$ and lattice dynamics calculations of NTE in both ${\mathrm{Cu}}_{2}\mathrm{O}$ and ${\mathrm{Ag}}_{2}\mathrm{O}$ are reported. The phonon density of states from a polycrystalline sample of ${\mathrm{Cu}}_{2}\mathrm{O}$ is measured using the triple-axis spectrometer at Trombay. A lattice dynamical model is used for the calculations of phonon frequencies and their pressure dependence in the entire Brillouin zone. The experimental phonon spectrum is in fair agreement with calculations. The calculated Gr\uneisen parameters for ${\mathrm{Cu}}_{2}\mathrm{O}$ have lower negative values in comparison with ${\mathrm{Ag}}_{2}\mathrm{O}$. This results in a smaller value of negative thermal expansion coefficient in ${\mathrm{Cu}}_{2}\mathrm{O}$, in fair agreement with the experimental data from the literature. An important librational mode is identified that is related to NTE. Variance of bond lengths $(⟨{u}_{\mathit{\text{bond}}}^{2}⟩)$ and their temperature dependence have been calculated and compared with extended x-ray absorption fine structure data that illustrates the nature of the $M\text{\ensuremath{-}}\mathrm{O}$ and $M\text{\ensuremath{-}}M$ $(M=\mathrm{Cu},\mathrm{Ag})$ bonds in these compounds.