Equations-of-motion method for triplet excitation operators in graphene

The particle-hole continuum in the Dirac sea of graphene has a unique window underneath, which in principle leaves room for bound state formation in the triplet particle-hole channel (Baskaran and Jafari 2002 Phys. Rev. Lett. 89 016402). In this work, we construct appropriate triplet particle-hole operators and, using a repulsive Hubbard-type effective interaction, we employ equations of motion to derive approximate eigenvalue equations for such triplet operators. While the secular equation for the spin density fluctuations gives rise to an equation which is second order in the strength of the short range interaction, the explicit construction of the triplet operators obtained here shows that, in terms of these operators, the second-order equation can be factorized to two first-order equations, one of which gives rise to a solution below the particle-hole continuum of Dirac electrons in undoped graphene.     

Excitation spectrum of one-dimensional extended ionic Hubbard model

We use perturbative continuous unitary transformations (PCUT) to study the one dimensional extended ionic Hubbard model (EIHM) at half-filling in the band insulator region. The extended ionic Hubbard model, in addition to the usual ionic Hubbard model, includes an inter-site nearest-neighbor (n.n.) repulsion, V. We consider the ionic potential as unperturbed part of the Hamiltonian, while the hopping and interaction (quartic) terms are treated as perturbation. We calculate total energy and ionicity in the ground state. Above the ground state, (i) we calculate the single particle excitation spectrum by adding an electron or a hole to the system; (ii) the coherence-length and spectrum of electron-hole excitation are obtained. Our calculations reveal that for V = 0, there are two triplet bound state modes and three singlet modes, two anti-bound states and one bound state, while for finite values of V there are four excitonic bound states corresponding to two singlet and two triplet modes. The major role of on-site Coulomb repulsion U is to split singlet and triplet collective excitation branches, while V tends to pull the singlet branches below the continuum to make them bound states.     

Interference of atomic levels and superfluid-Mott insulator phase transitions in a two-component Bose-Einstein condensate

The superfluid-Mott insulator phase transition in a Bose-Einstein condensate of neutral atoms with doubly degenerate internal ground states in an optical lattice is theoretically investigated. The optical lattice is created by two counterpropagating linearly polarized laser beams with the angle theta between the polarization vectors (lin-angle-lin configuration). The phase diagram of the system and the critical values of the parameters are worked out. It is shown that the sign of the detuning plays an important role and that there is a strong suppression of the Mott transition in the case of blue detuning. Varying the laser intensity and/or the angle theta one can manipulate the Mott insulator to superfluid quantum phase transition as well as prepare the condensate in physically distinguishable "ferromagnetic" and "antiferromagnetic" superfluid states.     

Spin singlet mott states and evidence for spin singlet quantum condensates of spin-one bosons in lattices

We have investigated spin singlet Mott states of spin-one bosons with antiferromagnetic interactions. These spin singlet states do not break rotational symmetry and exhibit remarkably different macroscopic properties compared with nematic Mott states of spin-one bosons. We demonstrate that the dynamics of spin singlet Mott states is fully characterized by even- or odd-class quantum dimer models. The difference between spin singlet Mott states for even and odd numbers of atoms per site can be attributed to a selection rule in the low energy sectors of on-site Hilbert spaces; alternatively, it can also be attributed to an effect of Berry’s phases on bosonic Mott states. We also discuss evidence for spin singlet quantum condensate of spin-one atoms. Our main finding is that in a projected spin singlet Hilbert space, the low energy physics of spin-one bosons is equivalent to that of a Bose-Hubbard model for spinless bosons interacting via Ising gauge fields. The other major finding is spin-charge separation in some one-dimensional Mott states. We propose charge-e spin singlet superfluid for an odd number of atoms per lattice site and charge-2e spin singlet superfluid for an even number of atoms per lattice site in one-dimensional lattices. All discussions in this article are limited to integer numbers of bosons per site.     

Gapless spin-1 neutral collective mode branch for graphite

Using the standard tight binding model of 2D graphite with short range electron repulsion, we predict a gapless spin-1, neutral collective mode branch below the particle-hole continuum with energy vanishing linearly with momenta at the Gamma and K points in the Brillouin zone. This spin-1 mode has a wide energy dispersion, 0 to approximately 2 eV, and is not Landau damped. The "Dirac cone spectrum" of electrons at the chemical potential of graphite generates our collective mode, so we call this "spin-1 zero sound" of the "Dirac sea." Epithermal neutron scattering experiments and spin polarized electron energy loss spectroscopy can be used to confirm and study our collective mode.     

Dynamical mean field study of the Dirac liquid

Renormalization is one of the basic notions of condensed matter physics. Based on the concept of renormalization, the Landau’s Fermi liquid theory has been able to explain, why despite the presence of Coulomb interactions, the free electron theory works so well for simple metals with extended Fermi surface (FS). The recent synthesis of graphene has provided the condensed matter physicists with a low energy laboratory of Dirac fermions where instead of a FS, one has two Fermi points. Many exciting phenomena in graphene can be successfully interpreted in terms of free Dirac electrons. In this paper, employing dynamical mean field theory (DMFT), we show that an interacting Dirac sea is essentially an effective free Dirac theory. This observation suggests the notion of Dirac liquid as a fixed point of interacting 2 + 1 dimensional Dirac fermions. We find one more fixed point at strong interactions describing a Mott insulating state, and address the nature of semi-metal to insulator (SMIT) transition in this system.     

Mottness

We review several of the normal state properties of the cuprates in an attempt to establish an organizing principle from which pseudogap phenomena, broad spectral features, T-linear resistivity, and spectral weight transfer emerge. We first show that standard field theories with a single critical length scale cannot capture the T-linear resistivity as long as the charge carriers are critical. What seems to be missing is an additional length scale, which may or may not be critical. Second, we prove a generalised version of Luttinger’s theorem for a Mott insulator. In particular, we show that for Mott insulators, regardless of the spatial dimension, the Fermi surface of the non-interacting system is converted into a surface of zeros of the single-particle Green function when the underlying band structure has particle-hole symmetry. Only in the presence of particle-hole symmetry does the volume of the surface of zeros equal the particle density. The surface of zeros persists at finite doping and is shown to provide a framework from which pseudogaps, broad spectral features, spectral weight transfer on the Mott gap scale, and the additional length scale required to capture T-linear resistivity can be understood.     

Spinfluctuations versus phonons: The case of Heavy-Fermion superconductivity

Superconductivity of Heavy-Fermions, with an emphasis on hexagonal UPt₃, is investigated microscopically on the basis of the LNCA-approximation for strongly correlated electrons in a Kondo lattice and of Eliashberg theory for anisotropic singlet and triplet superconducting order. The effective interaction kernel incorporates exchange of spin fluctuations carried by strongly renormalized particle-hole excitations as well as exchange of phonons generated by the breathing mechanism. Particular care is taken to include realistic anisotropies in band structure and couplings and to expand interaction kernel and order parameter in appropriate Fermi surface harmonics. Separate interactions and corresponding gap equations are used for pseudo-spin-singlet and -triplet channel, with a restriction to the case of weak spin-orbit coupling. Our main results include a detailed study of phonon- and spin-fluctuation mechanisms as a possible source for superconductivity and, in combination, their mutual influence and competition. Furthermore, the questions regarding singlet or triplet order, conventional or unconventional symmetry, order parameter zeros and phase transitions between different superconducting states are addressed. We propose a possible scenario of Heavy-Fermion superconductivity.     

Surface scattering via bulk continuum states in the 3D topological insulator Bi2Se3

We have performed scanning tunneling microscopy and differential tunneling conductance (dI/dV) mapping for the surface of the three-dimensional topological insulator Bi(2)Se(3). The fast Fourier transformation applied to the dI/dV image shows an electron interference pattern near Dirac node despite the general belief that the backscattering is well suppressed in the bulk energy gap region. The comparison of the present experimental result with theoretical surface and bulk band structures shows that the electron interference occurs through the scattering between the surface states near the Dirac node and the bulk continuum states.     

Diffusion of one- and two-electron vacancy centers in polar crystals

The change in the diffusion barrier for anion vacancies in polar crystals is calculated in the case where one electron (F centers) or two electrons (F′ centers) are captured. The lowest singlet and triplet states are considered for the two-electron system. It is shown that the capture of two electrons on the lowest metastable triplet state (which is possible under nonequilibrium conditions, for example, in the case of either exchange scattering of band electrons or thermal refilling of energy levels) leads to a decrease in the diffusion barrier for the system. However, for the two-electron center in the lowest singlet state, the potential barrier to migration, as a rule, is higher than that for a vacancy without electrons. Calculations are carried out for Gaussian functions with the inclusion of the effects of interelectron correlations and electron-phonon interactions.     

Spinor bosonic atoms in optical lattices: symmetry breaking and fractionalization

We study superfluid and Mott insulator phases of cold spin-1 Bose atoms with antiferromagnetic interactions in an optical lattice, including a usual polar condensate phase, a condensate of singlet pairs, a crystal spin nematic phase, and a spin singlet crystal phase. We suggest a possibility of exotic fractionalized phases of spinor Bose-Einstein condensates and discuss them in the language of Z2 lattice gauge theory.     

Single-particle spectral function of the Hubbard chain: frustration induced

The one-electron spectral function of a frustrated Hubbard chain is computed by making use of the cluster perturbation theory. The spectral weight we found turns out to be strongly dependent on the frustrating next-nearest-neighbor hopping t'. A frustration induced pseudogap arises when the system evolves from a gapful Mott insulator to a gapless conductor for an intermediate value of the frustration parameter |t'|. Furthermore, the opening of a pseudogap in the density of states already in the metallic side leads to a continuous opening of the true gap in the insulator. For the hole-doped case, the pseudogap is pinned at the Fermi energy, while the Mott gap is shifted in energy with increasing Hubbard interaction U. The separation of the pseudogap and Mott gap in the hole-doped system demonstrates the validity of the existence of a pseudogap.     

Effective area and expansion energy of trapped Bose gas in a combined magnetic-optical potential

In this Letter a conventional method of statistical physics and quantum mechanics is used to calculate the effective area and the expansion energy for trapped Bose gas in a combined optical-magnetic potential. Correction due to the finite number of particles, interatomic interaction and the deepness of the lattice potential are given simultaneously. It is found that the system possess two different phases which are superfluid phase and Mott insulator phase. The critical temperature which separate these two phases is calculated. In the superfluid phase both the effective area and expansion energy is sensitive to the variation of temperature and lattice depth. Mott insulator phase is characterized by vanishing of the condensed fraction and freezing of the effective area at the value which corresponding to BEC transition temperature. So these parameters can serve as a practical thermometer for such system. The expansion energy shows that the lack of expansion in any direction is due to the strong anisotropy of the trapping potential in this direction. The obtained results provide a solid theoretical foundation for the current experiments.     

Phase coherence of an atomic Mott insulator

We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle-hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible kinks are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator.     

Competition between weak localization and antilocalization in topological surface states

A magnetoconductivity formula is presented for the surface states of a magnetically doped topological insulator. It reveals a competing effect of weak localization and weak antilocalization in quantum transport when an energy gap is opened at the Dirac point by magnetic doping. It is found that, while random magnetic scattering always drives the system from the symplectic to the unitary class, the gap could induce a crossover from weak antilocalization to weak localization, tunable by the Fermi energy or the gap. This crossover presents a unique feature characterizing the surface states of a topological insulator with the gap opened at the Dirac point in the quantum diffusion regime.     

The tunneling density-of-states of interacting massless Dirac fermions

We calculate the tunneling density-of-states (DOS) of a disorder-free two-dimensional interacting electron system with a massless-Dirac band Hamiltonian. The DOS exhibits two main features: (i) linear growth at large energies with a slope that is suppressed by quasiparticle velocity enhancement, and (ii) a rich structure of plasmaron peaks which appear at negative bias voltages in an n-doped sample and at positive bias voltages in a p-doped sample. We predict that the DOS at the Dirac point is non-zero even in the absence of disorder because of electron–electron interactions, and that it is then accurately proportional to the Fermi energy. The finite background DOS observed at the Dirac point of graphene sheets and topological insulator surfaces can therefore be an interaction effect rather than a disorder effect.     

Breakdown of Luttinger's theorem in two-orbital Mott insulators

An analysis of Luttinger's theorem shows that – contrary to recent claims – it is not valid for a generic Mott insulator. For a two-orbital Hubbard model with two electrons per site the crossover from a non-magnetic correlated insulating phase (Mott or Kondo insulator) to a band insulator is investigated. Mott insulating phases are characterized by poles of the self-energy and corresponding zeros in the Greens functions defining a “Luttinger surface” which is absent for band insulators. Nevertheless, the ground states of such insulators with two electrons per unit cell are adiabatically connected.     

Energy Spectrum of Two-Component Bose-Einstein Condensates in Optical Lattices

With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We find that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.     

Doped Mott insulators are insulators: hole localization in the cuprates

We demonstrate that a Mott insulator lightly doped with holes is still an insulator at low temperature even without disorder. Hole localization obtains because the chemical potential lies in a pseudogap which has a vanishing density of states at zero temperature. The energy scale for the pseudogap is set by the nearest-neighbor singlet-triplet splitting. As this energy scale vanishes if transitions, virtual or otherwise, to the upper Hubbard band are not permitted, the fundamental length scale in the pseudogap regime is the average distance between doubly occupied sites. Consequently, the pseudogap is tied to the noncommutativity of the two limits U-->infinity (U the on-site Coulomb repulsion) and L -->infinity (the system size).     

Spin anisotropy for excitation in collisions between two one-electron atoms

The singlet and triplet contributions of excitation cross sections are studied theoretically for collisions between various two one-electron atoms. The spin anisotropy is shown to have a general behavior in the important impact energy range. At low energies triplet cross sections dominate completely over the singlet ones while the opposite is true when the active electron and projectile velocities are comparable. Beyond the matching velocity regime singlet and triplet contributions become identical. We propose a general dynamical interpretation based on the analysis of the time dependency of the electron probability density and probability current density.