Construction of Wannier functions from localized atomic-like orbitals

The problem of construction of the Wannier functions (WFs) in a restricted Hilbert space of eigenstates of the one-electron Hamiltonian $\hat{H}$ (forming the so-called low-energy part of the spectrum) can be formulated in several different ways. One possibility is to use the projector-operator techniques, which pick up a set of trial atomic orbitals and project them onto the given Hilbert space. Another possibility is to employ the downfolding method, which eliminates the high-energy part of the spectrum and incorporates all related to it properties into the energy-dependence of an effective Hamiltonian. We show that by modifying the high-energy part of the spectrum of the original Hamiltonian $\hat{H}$, which is rather irrelevant to the construction of WFs in the low-energy part of the spectrum, these two methods can be formulated in an absolutely exact and identical form, so that the main difference between them is reduced to the choice of the trial orbitals. Concerning the latter part of the problem, we argue that an optimal choice for trial orbitals can be based on the maximization of the site-diagonal part of the density matrix. The main idea is illustrated for a simple toy model, consisting of only two bands, as well as for a more realistic example of $t_{2g}$ bands in V$_2$O$_3$. An analogy with the search of the ground state of a many-electron system is also discussed.Comment: 13 pages, 6 figure

First-principle Wannier functions and effective lattice fermion models for narrow-band compounds

We propose a systematic procedure for constructing effective lattice fermion models for narrow-band compounds on the basis of first-principles electronic structure calculations. The method is illustrated for the series of transition-metal (TM) oxides: SrVO$_3$, YTiO$_3$, V$_2$O$_3$, and Y$_2$Mo$_2$O$_7$. It consists of three parts, starting from LDA. (i) construction of the kinetic energy Hamiltonian using downfolding method. (ii) solution of an inverse problem and construction of the Wannier functions (WFs) for the given kinetic energy Hamiltonian. (iii) calculation of screened Coulomb interactions in the basis of \textit{auxiliary} WFs, for which the kinetic-energy term is set to be zero. The last step is necessary in order to avoid the double counting of the kinetic-energy term, which is included explicitly into the model. The screened Coulomb interactions are calculated in a hybrid scheme. First, we evaluate the screening caused by the change of occupation numbers and the relaxation of the LMTO basis functions, using the conventional constraint-LDA approach, where all matrix elements of hybridization involving the TM $d$ orbitals are set to be zero. Then, we switch on the hybridization and evaluate the screening associated with the change of this hybridization in RPA. The second channel of screening is very important, and results in a relatively small value of the effective Coulomb interaction for isolated $t_{2g}$ bands. We discuss details of this screening and consider its band-filling dependence, frequency dependence, influence of the lattice distortion, proximity of other bands, and the dimensionality of the model Hamiltonian.Comment: 35 pages, 25 figure

Fingerprints of Spin-Orbital Physics in Crystalline O2_2

The alkali hyperoxide KO$_2$ is a molecular analog of strongly-correlated systems, comprising of orbitally degenerate magnetic O$_2^-$ ions. Using first-principles electronic structure calculations, we set up an effective spin-orbital model for the low-energy \textit{molecular} orbitals and argue that many anomalous properties of KO$_2$ replicate the status of its orbital system in various temperature regimes.Comment: 4 pages, 2 figures, 1 tabl

Lattice Distortion and Magnetism of 3d-t2gt_{2g} Perovskite Oxides

Several puzzling aspects of interplay of the experimental lattice distortion and the the magnetic properties of four narrow $t_{2g}$-band perovskite oxides (YTiO$_3$, LaTiO$_3$, YVO$_3$, and LaVO$_3$) are clarified using results of first-principles electronic structure calculations. First, we derive parameters of the effective Hubbard-type Hamiltonian for the isolated $t_{2g}$ bands using newly developed downfolding method for the kinetic-energy part and a hybrid approach, based on the combination of the random-phase approximation and the constraint local-density approximation, for the screened Coulomb interaction part. Then, we solve the obtained Hamiltonian using a number of techniques, including the mean-field Hartree-Fock (HF) approximation, the second-order perturbation theory for the correlation energy, and a variational superexchange theory. Even though the crystal-field splitting is not particularly large to quench the orbital degrees of freedom, the crystal distortion imposes a severe constraint on the form of the possible orbital states, which favor the formation of the experimentally observed magnetic structures in YTiO$_3$, YVO_, and LaVO$_3$ even at the HF level. Beyond the HF approximation, the correlations effects systematically improve the agreement with the experimental data. Using the same type of approximations we could not reproduce the correct magnetic ground state of LaTiO$_3$. However, we expect that the situation may change by systematically improving the level of approximations for dealing with the correlation effects.Comment: 30 pages, 17 figures, 8 tables, high-quality figures are available via e-mai

Non-Ground-State Bose-Einstein Condensates of Trapped Atoms

The possibility of creating a Bose condensate of trapped atoms in a non-ground state is suggested. Such a nonequilibrium Bose condensate can be formed if one, first, obtains the conventional Bose condensate in the ground state and then transfers the condensed atoms to a non-ground state by means of a resonance pumping. The properties of ground and non-ground states are compared and plausible applications of such nonequilibrium condensates are discussed.Comment: 1 file, 16 pages, RevTe

Late-Time Circumstellar Interaction in a Spitzer Selected Sample of Type IIn Supernovae

Type IIn supernovae (SNe IIn) are a rare (< 10%) subclass of core-collapse SNe that exhibit relatively narrow emission lines from a dense, pre-existing circumstellar medium (CSM). In 2009, a warm Spitzer survey observed 30 SNe IIn discovered in 2003 - 2008 and detected 10 SNe at distances out to 175 Mpc with unreported late-time infrared emission, in some cases more than 5 years post-discovery. For this single epoch of data, the warm-dust parameters suggest the presence of a radiative heating source consisting of optical/X-ray emission continuously generated by ongoing CSM interaction. Here we present multi-wavelength follow-up observations of this sample of 10 SNe IIn and the well-studied Type IIn SN 2010jl. A recent epoch of Spitzer observations reveals ongoing mid-infrared emission from nine of the SNe in this sample. We also detect three of the SNe in archival WISE data, in addition to SNe 1987A, 2004dj, and 2008iy. For at least five of the SNe in the sample, optical and/or X-ray emission confirms the presence of radiative emission from ongoing CSM interaction. The two Spitzer nondetections are consistent with the forward shock overrunning and destroying the dust shell, a result that places upper limits on the dust-shell size. The optical and infrared observations confirm the radiative heating model and constrain a number of model parameters, including progenitor mass-loss characteristics. All of the SNe in this sample experienced an outburst on the order of tens to hundreds of years prior to the SN explosion followed by periods of less intense mass loss. Although all evidence points to massive progenitors, the variation in the data highlights the diversity in SN IIn progenitor evolution. While these observations do not identify a particular progenitor system, they demonstrate that future, coordinated, multi-wavelength campaigns can constrain theoretical mass-loss models.Comment: 10 pages, 6 figures, accepted to AJ (with comments

Constraining the Progenitor Companion of the Nearby Type Ia SN 2011fe with a Nebular Spectrum at +981 Days

We present an optical nebular spectrum of the nearby Type Ia supernova 2011fe, obtained 981 days after explosion. SN 2011fe exhibits little evolution since the +593 day optical spectrum, but there are several curious aspects in this new extremely late-time regime. We suggest that the persistence of the $\sim5800$~\AA\ feature is due to Na I D, and that a new emission feature at $\sim7300$~\AA\ may be [Ca II]. Also, we discuss whether the new emission feature at $\sim6400$~\AA\ might be [Fe I] or the high-velocity hydrogen predicted by Mazzali et al. The nebular feature at 5200~\AA\ exhibits a linear velocity evolution of $\sim350$ $\rm km\ s^{-1}$ per 100 days from at least +220 to +980 days, but the line's shape also changes in this time, suggesting that line blending contributes to the evolution. At $\sim 1000$ days after explosion, flux from the SN has declined to a point where contribution from a luminous secondary could be detected. In this work we make the first observational tests for a post-impact remnant star and constrain its temperature and luminosity to $T \gtrsim 10^4$ $\rm K$ and $L \lesssim 10^4$ $\rm L_{\odot}$. Additionally, we do not see any evidence for narrow H$\alpha$ emission in our spectrum. We conclude that observations continue to strongly exclude many single-degenerate scenarios for SN 2011fe.Comment: 11 pages, 10 figures, published by MNRA

Variability of Fe II Emission Features in the Seyfert 1 Galaxy NGC 5548

We study the low-contrast Fe II emission blends in the ultraviolet (1250--2200A) and optical (4000--6000A) spectra of the Seyfert 1 galaxy NGC 5548 and show that these features vary in flux and that these variations are correlated with those of the optical continuum. The amplitude of variability of the optical Fe II emission is 50% - 75% that of Hbeta and the ultraviolet Fe II emission varies with an even larger amplitude than Hbeta. However, accurate measurement of the flux in these blends proves to be very difficult even using excellent Fe II templates to fit the spectra. We are able to constrain only weakly the optical Fe II emission-line response timescale to a value less than several weeks; this upper limit exceeds all the reliably measured emission-line lags in this source so it is not particularly meaningful. Nevertheless, the fact that the optical Fe II and continuum flux variations are correlated indicates that line fluorescence in a photoionized plasma, rather than collisional excitation, is responsible for the Fe II emission. The iron emission templates are available upon request.Comment: 34 pages including 12 figures and 2 tables. Accepted for publication by ApJ (tentatively in vol. 626 June 10, 2005

Crossover from hydrodynamic to acoustic drag on quartz tuning forks in normal and superfluid 4He

We present measurements of the drag forces on quartz tuning forks oscillating at low velocities in normal and superfluid 4He. We have investigated the dissipative drag over a wide range of frequencies, from 6.5 to 600 kHz, by using arrays of forks with varying prong lengths and by exciting the forks in their fundamental and first overtone modes. At low frequencies the behavior is dominated by laminar hydrodynamic drag, governed by the fluid viscosity. At higher frequencies acoustic drag is dominant and is described well by a three-dimensional model of sound emission

Observation of vortex dipoles in an oblate Bose-Einstein condensate

We report experimental observations and numerical simulations of the formation, dynamics, and lifetimes of single and multiply charged quantized vortex dipoles in highly oblate dilute-gas Bose-Einstein condensates (BECs). We nucleate pairs of vortices of opposite charge (vortex dipoles) by forcing superfluid flow around a repulsive gaussian obstacle within the BEC. By controlling the flow velocity we determine the critical velocity for the nucleation of a single vortex dipole, with excellent agreement between experimental and numerical results. We present measurements of vortex dipole dynamics, finding that the vortex cores of opposite charge can exist for many seconds and that annihilation is inhibited in our highly oblate trap geometry. For sufficiently rapid flow velocities we find that clusters of like-charge vortices aggregate into long-lived dipolar flow structures.Comment: 4 pages, 4 figures, 1 EPAPS fil