Single-particle Excitation Spectrum Research Articles

Asymmetric Two-Component Fermion Systems in Strong Coupling

We study the phase structure of a dilute two-component Fermi system with attractive interactions as a function of the coupling and a finite number asymmetry or polarization. In weak coupling, a number asymmetry results in phase separation. A mixed phase containing symmetric superfluid matter and an asymmetric normal phase is favored. For strong coupling we show that the stress on the superfluid phase to accommodate a number asymmetry increases. Near the infinite-scattering length, we calculate the single-particle excitation spectrum and the ground-state energy. A picture of weakly interacting quasiparticles emerges for modest polarizations. In this regime a homogeneous phase with a finite population of quasiparticle states characterized by a gapless spectrum is favored over the phase separated state. These states may be realized in cold atom experiments.

Frustrated Antiferromagnets at High Fields: Bose-Einstein Condensation in Degenerate Spectra

Quantum phase transition at the saturation field is studied for a class of frustrated quantum antiferromagnets. The considered models include (i) the ${J}_{1}\mathrm{\text{\ensuremath{-}}}{J}_{2}$ frustrated square-lattice antiferromagnet with ${J}_{2}=\frac{1}{2}{J}_{1}$ and (ii) the nearest-neighbor Heisenberg antiferromagnet on a face centered cubic lattice. In the fully saturated phase the magnon spectra for the two models have lines of degenerate minima. Transition into a partially magnetized state is treated via a mapping to a dilute gas of hard-core bosons and by complementary spin-wave calculations. Momentum dependence of the exact four-point boson vertex removes the degeneracy of the single-particle excitation spectra and selects the ordering wave vectors at $(\ensuremath{\pi},\ensuremath{\pi})$ and $(\ensuremath{\pi},0,0)$ for the two models. We predict a unique form for the magnetization curve $\ensuremath{\Delta}M=S\ensuremath{-}M\ensuremath{\simeq}{\ensuremath{\mu}}^{(d\ensuremath{-}1)/2}(\mathrm{log}\ensuremath{\mu}{)}^{(d\ensuremath{-}1)}$, where $\ensuremath{\mu}$ is a distance from the quantum critical point.

Alkali and alkali-earth ions inHe4systems

We study with variational Monte Carlo simulations a single ion impurity in nanodroplets and in liquid $^{4}\mathrm{He}$. Within the shadow wave function (SWF) approach we have studied alkali-earth ion doped $^{4}\mathrm{He}$ systems (${\mathrm{Be}}^{+}$ and ${\mathrm{Mg}}^{+}$) and we have also improved our previous variational results for alkali ion impurities (${\mathrm{Na}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{Cs}}^{+}$). The new $\mathrm{SWF}$ allows for anisotropic correlations between $^{4}\mathrm{He}$ atoms and the ion. The first shell of $^{4}\mathrm{He}$ atoms around the ions has always a well defined solidlike structure, which is remarkably different for each ion but it does not depend on the $^{4}\mathrm{He}$ system (bulk liquid or cluster). We also give results for the chemical potential, the single particle excitation spectrum, and the effective mass of the ions in the bulk.

Evolution of spin susceptibility from the Pauli to Curie-Weiss type in strongly correlated Fermi systems

The magnetic properties of strongly correlated Fermi systems are studied within the framework of the fermioncondensation model—phase transition associated with the rearrangement of the Landau quasiparticle distribution, resulting in the appearance of a plateau at T=0 exactly in the Fermi surface of the single-particle excitation spectrum. It is shown that the Curie-Weiss term ∼T −1 appears in the expression for the spin susceptibility χac(T) of the system after the transition point at finite temperatures. The behavior of χac(T, H) as a function of temperature and static magnetic field H in the region where the critical fermion-condensation temperature T f is close to zero is discussed. The results are compared with the available experimental data.

Quasiparticle energies, excitonic effects and optical absorption spectra of small-diameter single-walled carbon nanotubes

We present a first-principles study of the effects of many-electron interactions on the optical properties of single-walled carbon nanotubes. Motivated by recent experiments, we have carried out ab initio calculations on the single-walled carbon nanotubes (3, 3), (5, 0) and (8, 0). The calculations are based on a many-body Green’s function approach in which both the quasiparticle (single-particle) excitation spectrum and the optical (electron–hole excitation) spectrum are determined. We show that the optical spectrum of both the semiconducting and metallic nanotubes studied exhibits important excitonic effects due to their quasi-one-dimensional nature. Binding energies for excitonic states range from zero for the metallic (5, 0) tube to nearly 1 eV for the semiconducting (8, 0) tube. Moreover, the metallic (3, 3) tube possesses exciton states bound by nearly 100 meV. Our calculated spectra explain quantitatively the observed features found in the measured spectra.

Electron correlation effects on SiC(111) and SiC(0001) surfaces

The possibility is discussed that, independent of the polytype, large electronic correlationeffects give rise to semiconducting SiC surfaces with [111] or [0001] orientations. The mostimportant surface translational symmetries and 3 × 3 are considered. The discussion is based on the detailed knowledge of the surfaceatomic geometries and the electronic structures derived for these geometries usinga local density approximation for exchange and correlation. It is argued thatthe resulting half-filled, weakly dispersive dangling-bond bands within thefundamental gaps are split according to a Hubbard interaction parameterU, and that the surface systems undergo a Mott–Hubbard transition. Such a physical pictureprovides a qualitatively correct account of the single-particle excitation spectra eitherinferred from angle-resolved photoemission and inverse photoemission experiments orobtained from scanning tunnelling spectroscopy. The gap opening and hence the HubbardU parameter are discussed in terms of their dependence on the surface reconstruction as wellas the SiC polytype.

Self-consistent projection operator method for the single-particle excitation spectrum

A new projection operator method combined with the coherent potential approximation is presented. The theory interpolates between the strong- and the weak-Coulomb interaction limits, and allows us to calculate the momentum dependence of the self-energy. Numerical results for the case of infinite dimensions indicate that it can describe quantitatively the quasi-particle properties of a system.

Coherent potential approximation and projection operators for interacting electrons

A theory of the single-particle excitation spectrum is presented on the basis of the projection operator method combined with the many-body coherent-potential approximation (CPA). The theory describes the dynamics of the excitations by means of an energy-dependent Liouville operator accompanied by a coherent potential which is determined by the self-consistent CPA condition. It is shown that the present theory is essentially equivalent to the dynamical CPA and the dynamical mean-field theory. The Hubbard III approximation and the modified perturbation theory are rederived from the theory. A renormalized perturbation scheme for the Green function is developed on the basis of a general formula for the memory function. It interpolates between the weak- and strong-Coulomb interaction limits, and yields the metal-insulator transition for half-filled bands. Numerical calculations have been performed for the Gutzwiller-Hubbard model on a hypercubic lattice in infinite dimensions. The results show that the theory describes quantitatively the quasiparticle weight vs Coulomb interaction curve, yielding a reasonable critical Coulomb interaction for the metal-insulator transition. It produces the overall features of the excitation spectra and the momentum distributions for various Coulomb interaction strengths.

Collective excitations in double quantum wells with strong tunnel coupling

Spectra of collective and magnetic excitations in symmetric double quantum wells with strong tunnel coupling were studied by inelastic scattering. Gaps in the spectrum of collective and single-particle excitations associated with tunnel interwell splitting were measured. New excitation modes, namely, tunnel Bernstein modes, were detected in a magnetic field. Based on the dispersion and magnetic-field dependences of the energies of inelastic light scattering lines, a classification of excitations and magnetic excitations was given.

Spin degrees of freedom and flattening of the spectra of single-particle excitations in strongly correlated Fermi systems

The impact of long-range spin-spin correlations on the structure of a flat portion in single-particle spectra $\xi(p)$, which emerges beyond the point, where the Landau state loses its stability, is studied. We supplement the well-known Nozieres model of a Fermi system with limited scalar long-range forces by a similar long-range spin-dependent term and calculate the spectra versus its strength $g$. It is found that Nozieres results hold as long as $g>0$. However, with $g$ changing its sign, the spontaneous magnetization is shown to arise at any nonzero $g$. The increase of the strength $|g|$ is demonstrated to result in shrinkage of the domain in momentum space, occupied by the flat portion of $\xi(p)$, and, eventually, in its vanishing.

Wave vector dependent inter-Landau-level transitions in modulation-doped quantum wells

Inter-Landau-level transitions in two-dimensional electron gases under small magnetic field are observed by electronic Raman scattering due to finite wave-vector relaxation of the Δn=0 selection rule. The spectrum of single-particle excitations becomes discretized as soon as the cyclotron energy overcomes the homogeneous broadening of the transitions. We have discovered that, at smaller fields, Landau quantization still strongly modifies the Raman response. Strong envelope oscillations are shown to result from overlap variations between Landau eigenfunctions at different wave vectors which persist at magnetic fields where the individual levels can no longer be energy resolved.

Electron and phonon dynamics in copper oxides

We examine the phonon and electron dynamics in the strongly correlated electron systems coupled with phonons by using the numerically exact diagonalization techniques. The total number of phonons in the model is truncated to treat the phonon Hilbert space with finite dimensions. We calculate the phonon excitation spectra and the single-particle excitation spectra in one-dimensional half-filled Hubbard model coupled with phonons. We find that the phonon excitation is strongly influenced by the electron–phonon interaction via hopping of electrons, compared with that via density of electrons. We also find that the character of the spin-charge separation is destroyed by phonons in the single-particle excitation spectra.

Density Functional Theory versus the Hartree–Fock Method: Comparative Assessment

We compare two different approaches to investigations of many-electron systems. The first is the Hartree–Fock (HF) method and the second is the Density Functional Theory (DFT). Overview of the main features and peculiar properties of the HF method are presented. A way to realize the HF method within the Kohn–Sham (KS) approach of the DFT is discussed. We show that this is impossible without including a specific correlation energy, which is defined by the difference between the sum of the kinetic and exchange energies of a system considered within KS and HF, respectively. It is the nonlocal exchange potential entering the HF equations that generates this correlation energy. We show that the total correlation energy of a finite electron system, which has to include this correlation energy, cannot be obtained from considerations of uniform electron systems. The single-particle excitation spectrum of many-electron systems is related to the eigenvalues of the corresponding KS equations. We demonstrate that this spectrum does not coincide in general with the eigenvalues of KS or HF equations.

Collective and single-particle excitations in coupled quantum wires in magnetic fields

The full spectra of magnetoplasmons and single-particle excitations are obtained of coupled one-dimensional electron gases in parallel semiconductor quantum wires with tunneling. We show the effects of the interwire Coulomb interaction and the tunneling, as well as the magnetic-field-induced localization on the elementary excitations in symmetric and asymmetric coulped quantum wire structures. The interacton and resonance between the plasmon and the intersubband single-particle excitations are found in magnetic fields.

Many-body properties of a spherical two-dimensional electron gas

We investigate the many-body properties of a two-dimensional electron gas constrained to the surface of a sphere, a system which is physically realized in, for example, multielectron bubbles in liquid helium. A second-quantization formalism, suited for the treatment of a spherical two-dimensional electron gas (S2DEG), is introduced. Within this formalism, the dielectric response properties of the S2DEG are derived, and we identify both collective excitations and a spectrum of single-particle excitations. We find that the single-particle excitations are constrained to a well-defined region in the angular-momentum--energy plane. The collective excitations differ in two important aspects from those of a flat 2DEG: on a sphere, the ``spherical plasmons'' have a discrete frequency spectrum and the lowest frequency is nonzero.

Dynamical nature of chaos in electron systems of high-T c superconductors

A model of the fermion-condensation phase transition forming a plateau in the spectrum of single-particle excitations near the Fermi surface at T=0 is used to analyze those features of the spectral functions of normal states of high-T c superconductors which are inherent in a marginal Fermi liquid contaminated by impurities. With this model, such a behavior is shown to be due to the fermion condensate, which acts as an impurity subsystem because its energy spectrum at T=0 is dispersionless. The influence of the anisotropy of condensate distribution in the Brillouin zone on the spectral functions is discussed.

Dynamical Cluster Approximation for the Periodic Anderson Model: Competition between Local and Non-local Correlations

The single particle excitation spectrum of the periodic Anderson model in two dimensions is calculated by using the dynamical cluster approximation (DCA). The DCA method is an extention of the dyna...

Dynamical Cluster Approximation for Study of Non-Local Correlations in the Periodic Anderson Model

The single particle excitation spectrum of the periodic Anderson model in two dimensions is calculated by using the dynamical cluster approximation (DCA). The DCA method restores the short ranged inter-site correlations which are neglected in the dynamical mean field approximation. For the half filling model the resoance peak at the Fermi level is suppressed due to the anti-feromagnetic RKKY-like interaction. When the filling of the conduction electron band is small, there is a sharp coherence peak. It can be explaind that the effect of the RKKY-like interaction is weaker than that for the half filling model. For the intermediate filling model the intensity of the coherence peak becomes very small.

Effect of non-local correlations in the periodic Anderson model studied by the dynamical cluster approximation

The single particle excitation spectrum of the periodic Anderson model for the half filling case in two dimensions is calculated by using the dynamical cluster approximation (DCA). The DCA method restores the short-ranged inter-site correlations which are neglected in the dynamical mean field approximation (DMFA). A comparison between the results by DCA and DMFA shows that the resonance peak in low energies is suppressed due to the non-local correlations.

Cooperon propagator description of high-temperature superconductivity

A phenomenological description of the high- T c superconductors based on the Cooperon propagator is presented. This model allows one to study the effects of local pairing correlations and long-range phase fluctuations on the same footing, both above and below T c. Based on numerical calculations, it is shown that the two types of correlations contribute to the gap/pseudogap in the single-particle excitation spectra. The concourse of these two effects can induce low energy states, which should be observable in underdoped materials at very low temperature.