Multiband Model Research Articles

Comment on “Isotope Effect in Multi-Band and Multi-Channel Attractive Systems and Inverse Isotope Effect in Iron-Based Superconductors”

In a recent paper Yanagisawa et al. [1] claim from a theoretical analysis of a multi-channel multi-band superconductor model that an inverse isotope exponent on the superconducting transition temperature Tc can be realized in iron-based superconductors. Simultaneously, a subgroup of the authors of Ref. 1 performed the corresponding isotope effect experiment on (Ba, K)Fe2As2 by investigating the iron isotope exchange effect on Tc [2]. In accordance with their theoretical analysis they indeed report an unusually large sign reversed isotope exponent of {\alpha} \simeq -0.18(3) which is in strong contrast to previous experiments on the nominally same system with the same composition in Ba, K content, namely Ba0.6K0.4Fe2As2 [3], where the exponent was determined to be {\alpha} \simeq 0.37(3). This conflict remains unsolved until now with the exception of Ref. 4 where the iron isotope exponent has been determined for FeSe. In accordance with the results of Ref. 3 a large positive isotope exponent has been seen thus questioning the outcome of Ref. 1 and implicitly the findings of Ref. 2. Here, we do not comment on the controversial experimental situation but address the theoretical analysis of Ref. 1, where a variety of misleading assumptions have led to the conclusion that a sign reversed isotope exponent can be realized in a multi-band and multi-channel attractive model for iron based superconductors.

Tight-binding theory of the spin-orbit coupling in graphene

The spin-orbit coupling in graphene induces spectral gaps at the high-symmetry points. The relevant gap at the $\ensuremath{\Gamma}$ point is similar to the splitting of the $p$ orbitals in the carbon atom, being roughly 8.5 meV. The splitting at the $\mathrm{K}$ point is orders of magnitude smaller. Earlier tight-binding theories indicated the value of this intrinsic gap of $1\text{ }\ensuremath{\mu}\text{eV}$, based on the $\ensuremath{\sigma}\text{\ensuremath{-}}\ensuremath{\pi}$ coupling. All-electron first-principles calculations give much higher values, between 25 and $50\text{ }\ensuremath{\mu}\text{eV}$, due to the presence of the orbitals of the $d$ symmetry in the Bloch states at $\mathrm{K}$. A realistic multiband tight-binding model is presented to explain the effects the $d$ orbitals play in the spin-orbit coupling at $\mathrm{K}$. The $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\sigma}$ coupling is found irrelevant to the value of the intrinsic spin-orbit-induced gap. On the other hand, the extrinsic spin-orbit coupling (of the Bychkov-Rashba type), appearing in the presence of a transverse electric field, is dominated by the $\ensuremath{\pi}\text{\ensuremath{-}}\ensuremath{\sigma}$ hybridization, in agreement with previous theories. Tight-binding parameters are obtained by fitting to first-principles calculations, which also provide qualitative support for the model when considering the trends in the spin-orbit-induced gap in graphene under strain. Finally, an effective single-orbital next-nearest-neighbor hopping model accounting for the spin-orbit effects is derived.

Effect of Short Antiferromagnetic Correlations on the Normal and Superconducting Properties in Copper Oxides

The abnormal “normal” state and origin of high temperature superconductivity in cuprates are still not clear [1, 2]. The strong electron correlations (SEC) are known to be one of the main difficulties for the theory of high- cuprates. The conventional LDA (local density approximation) approach to the band structure fails in the regime of SEC. Various realistic multiband models of a layer at low energy result in the effective Hubbard or models [3 7]. The hybrid LDA+GTB scheme [8] generates the low-energy effective model with all parameters calculated ab initio.

Limb-darkening measurements for a cool red giant in microlensing event OGLE 2004-BLG-482

Aims: We present a detailed analysis of OGLE 2004-BLG-482, a relatively high-magnification single-lens microlensing event which exhibits clear extended-source effects. These events are relatively rare, but they potentially contain unique information on the stellar atmosphere properties of their source star, as shown in this study. Methods: Our dense photometric coverage of the overall light curve and a proper microlensing modelling allow us to derive measurements of the OGLE 2004-BLG-482 source star's linear limb-darkening coefficients in three bands, including standard Johnson-Cousins I and R, as well as in a broad clear filter. In particular, we discuss in detail the problems of multi-band and multi-site modelling on the expected precision of our results. We also obtained high-resolution UVES spectra as part of a ToO programme at ESO VLT from which we derive the source star's precise fundamental parameters. Results: From the high-resolution UVES spectra, we find that OGLE 2004-BLG-482's source star is a red giant of MK type a bit later than M3, with Teff = 3667 +/- 150 K, log g = 2.1 +/- 1.0 and an assumed solar metallicity. This is confirmed by an OGLE calibrated colour-magnitude diagram. We then obtain from a detailed microlensing modelling of the light curve linear limb-darkening coefficients that we compare to model-atmosphere predictions available in the literature, and find a very good agreement for the I and R bands. In addition, we perform a similar analysis using an alternative description of limb darkening based on a principal component analysis of ATLAS limb-darkening profiles, and also find a very good agreement between measurements and model predictions.

Characterization of spin-state tuning in thermally annealed semiconductor quantum dots

We report a systematic study of magneto-optical properties in CdZnSe/ZnSe semiconductor quantum dots (QDs) subjected to postgrowth thermal annealing. The theoretical and experimental characterizations are combined in order to understand the evolution of Zeeman splitting and the blueshift as well as redshift of the magnetic subcomponents with magnetic field strength of excitons confined in annealed QDs as a function of different annealing times. A combination of a multiband model as well as parameter interpolation supported by ab initio calculations is presented and points toward an inversion of the light-hole-heavy-hole states due to annealing. The band mixing of exciton states explains besides the variation in the Zeeman splitting for differently annealed QD excitons, the evolution of the diamagnetic blueshift into a paramagnetic redshift of the magnetic subcomponents. A discussion of the effects associated to the Coulomb interaction on the polarized excitonic recombinations modulated by magnetic field is given.

Resonant two‐magnon Raman scattering in high‐Tc cuprates

AbstractResonance enhancement of one‐phonon, two‐phonon, and two‐magnon Raman scattering in a general, exactly solvable, multiband model is explained in a way that is in accordance with the general analytical properties of the total optical conductivity tensor. Using this approach, the charge‐transfer limit of the Emery three‐band model is examined to explain resonance enhancement of the two‐magnon Raman spectra of high‐Tc cuprates, which is found in experiments to be of 3 orders of magnitude. While previous Raman and optical conductivity analyzes of the cuprates, based on the single‐band Hubbard model, are found to be consistent with the picture where one hole per one CuO2 unit is localized on the Cu ion, the present three‐band approach allows the study of the opposite, strong copper‐oxygen hybridization limit, which is found to be in agreement with the results of nuclear magnetic resonance (NMR) and one‐phonon Raman scattering experiments. Copyright © 2010 John Wiley & Sons, Ltd.

Reversed polarized emission in highly straineda-plane GaN/AlN multiple quantum wells

The polarization of the emission from a set of highly strained $a$-plane GaN/AlN multiple quantum wells of varying well widths has been studied. A single photoluminescence peak is observed that shifts to higher energies as the quantum well thickness decreases due to quantum confinement. The emitted light is linearly polarized. For the thinnest samples the preferential polarization direction is perpendicular to the wurtzite $c$ axis with a degree of polarization that decreases with increasing well width. However, for the thickest well the preferred polarization direction is parallel to the $c$ axis. Raman scattering, x-ray diffraction, and transmission electron microscopy studies have been performed to determine the three components of the strain tensor in the active region. Moreover, the experimental results have been compared with the strain values computed by means of a model based on the elastic continuum theory. A high anisotropic compressive in-plane strain has been found, namely, $\ensuremath{-}0.6\mathrm{%}$ and $\ensuremath{-}2.8\mathrm{%}$ along the in-plane directions $[1\overline{1}00]$ and [0001], respectively, for the thickest quantum well. The oscillator strength of the lowest optical transition has been calculated within the framework of a multiband envelope function model for various quantum well widths and strain values. The influence of confinement and strain on the degree of polarization is discussed and compared with experiment considering various sets of material parameters.

Multi-band nature of superconducting anisotropy in PrFeAsO1−δ single crystal

We investigated the magnetic torque of superconducting PrFeAsO1−δ single crystal using the torque magnetometer at temperatures from 2K to 200K in magnetic field of 30kG. The torque curve tends to have a singular shape compared to other superconductors. The analyses of the PrFeAsO1−δ torque curves by the single-band and the multi-band Kogan model yield 3<γλ<5 in 30kG. With the aid of the multi-band Kogan model, however, we obtain γξ=0.79±0.01 and γλ=19±3 in 30kG at 20.5K. The smallness of γξ(<1) thus obtained is due to the multi-band nature of the iron pnictide.

Multi‐band theory of magnetoexcitons in ZnO/ZnMnO quantum wells

AbstractWe present a multiband magnetoexciton absorption model in ZnO/ZnMnO quantum wells which takes into account the details of the valence band structure. In our model we incorporate the k·p as well as the Coulomb coupling between valence sub‐bands. The s,p‐d interaction between the carriers and the magnetic ions in the barrier is taken into account within the mean field approximation.The effect of the electric field is accounted for using proper potential profile of the quantum well. As a result we obtain electric and magnetic field dependent excitonic absorption spectra from which the exciton binding energies and life‐times as well as the overlap with the magnetic barrier material may be deduced (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Small jump of specific heat and small gap in iron pnictide superconductors

We demonstrate that a realistic multi-band model consistently explains the specific heat of typical iron-based superconductor. With density of states of each band obtained by first principle calculations, we evaluate multiple full-gap amplitudes from the angle resolved photoemission spectroscopy and successfully reproduce the specific heat. Consequently, it is found that the specific heat strongly depends density of states. In addition, the present calculations reveal that superconducting states of the iron-based pnictide are mainly characterized by two factors. One is an amplitude difference between large and small gaps, and the other is the distribution of their gap amplitudes.

A common thread

The structures, the phase diagrams, and the appearance of a neutron resonance in the superconducting state provide phenomenological evidence which relate the heavy fermion, cuprate and Fe superconductors. Single- and multi-band Hubbard models have been found to describe a number of the observed properties of these materials so that it is reasonable to examine the origin of the pairing interaction in these models. Here based on the experimental phenomenology and studies of the momentum and frequency dependence of the pairing interaction for Hubbard-like models, we suggest that spin-fluctuation mediated pairing is the common thread linking this broad class of superconducting materials.

Multiband model of the valence-band electronic structure in cylindrical GaAs nanowires

We compute the hole states in the GaAs free-standing nanowires, and in the GaAs/(Al,Ga)As core-shell nanowires of type I-s, which are grown along the [100] direction. The hole states are extracted from the 4-band Luttinger-Kohn Hamiltonian, which explicitly takes into account mixing between the light and heavy holes. The axial aproximation is adopted, which allowed classification of states according to the total angular monentum (fz when expressed in units of the Planck constant). The envelope functions are expanded in Bessel functions of the first kind. The dispersion relations of the subbands E(kz) obtained by the devised method do not resemble parabolas, which is otherwise a feature of the dispersion relations of the conduction subbands. Furthermore, the energy levels of holes whose total orbital momentum is fz=1/2 are shown to cross for a free-standing wire. The low energy fz=1/2 states are found to anticross, but these anticrossings turn into crossings when the ratio of the inner and outer radius of the core-shell wire takes a certain value. The influence of the geometric parameters on the dispersion relations is considered for both free standing and core-shell nanowires.

Electronic structure and magnetic properties ofLi2ZrCuO4: A spin-12Heisenberg system close to a quantum critical point

Based on density functional calculations, we present a detailed theoretical study of the electronic structure and the magnetic properties of the quasi-one dimensional chain cuprate Li_2ZrCuO_4 (Li_2CuZrO_4). For the relevant ratio of the next-nearest neighbor exchange J_2 to the nearest neighbor exchange J_1 we find alpha = -J_2/J_1 = 0.22\pm0.02 which is very close to the critical point at 1/4. Owing this vicinity to a ferromagnetic-helical critical point, we study in detail the influence of structural peculiarities such as the reported Li disorder and the non-planar chain geometry on the magnetic interactions combining the results of LDA based tight-binding models with LDA+U derived exchange parameters. Our investigation is complemented by an exact diagonalization study of a multi-band Hubbard model for finite clusters predicting a strong temperature dependence of the optical conductivity for Li_2ZrCuO_4.

Three-bands±Eliashberg theory and the superconducting gaps of iron pnictides

Superconductivity in iron pnictides has been recently proposed to be due to spin-fluctuation mediated coupling between hole and electron bands with order parameters of opposite sign. BCS multiband models give qualitative predictions but cannot simultaneously reproduce the experimental values of critical temperature and energy gaps. We show, instead, that a three-band strong-coupling Eliashberg model can quantitatively reproduce the gaps and their temperature dependence in both the 1111 and 122 families. We also show that this requires small typical boson energies (in agreement with experiments) and high values of the electron-boson coupling constants.

Floquet projections of a Gaussian Wigner function in a Kronig-Penney potential

In this contribution, we apply the multiband model developed in [1] to a Kronig-Penney potential and calculate the Floquet projections of a Gaussian Wigner function in phase space. The Bloch functions are calculated numerically and then used in the expressions of the Wigner projections.

Collectived-wave exciton modes in the calculated Raman spectrum of Fe-based superconductors

Calculations of the pairing interaction in multi-band models of the Fe superconductors show that it is attractive in both the $A_{1g}$ (s-wave) and $B_{1g}$ (d-wave) channels. This raises the possibility that these materials may have collective excitonic modes. Here, assuming an s-wave groundstate, we investigate the d-wave collective excitonic mode and its coupling to the Raman scattering.

Nodal superconductivity and antinodal pseudogap in cuprate superconductors

According to recent experimental findings the leading pairing resides in the nodal (FS arcs) momentum region of hole doped cuprates. The pseudogap is an antinodal feature. A corresponding multiband model of the electronic background evolving with doping serves the usually presented phase diagram. The pairing is due by the pair-transfer between overlapping nodal defect (polaron) band and the itinerant band. A bare gap vanishing with extended doping between the antinodal defect subband and the itinerant band top leads to the formation of the pseudogap as a perturbative band-structure effect. The calculated behaviour of two superconducting gaps and of the pseudogap on the whole doping scale is in qualitative agreement with the observations. Arguments to include cuprates into the class of multiband–multigap superconductors are given by these results.

Theory of unconventional metamagnetic electron states in orbital band systems

We extend the study of the Fermi surface instability of the Pomeranchuk type into systems with orbital band structures, which are common features in transition metal oxides. Band hybridization significantly shifts the spectral weight of the Landau interactions from the conventional $s$-wave channel to unconventional non-$s$-wave channels, which results in anisotropic (nematic) Fermi surface distortions even with ordinary interactions in solids. The Ginzburg-Landau free energy is constructed by coupling the charge-nematic, spin-nematic, and ferromagnetic order parameters together, which shows that nematic electron states can be induced by metamagnetism. The connection between this mechanism and the anisotropic metamagnetc states observed in ${\text{Sr}}_{3}{\text{Ru}}_{2}{\text{O}}_{7}$ at high magnetic fields is studied in a multiband Hubbard model with the hybridized quasi-one-dimensional ${d}_{xz}$ and ${d}_{yz}$ bands.

Effects of fermions on the superfluid-insulator phase diagram of the Bose-Hubbard model

Building on the work of Fisher et al. [Phys. Rev. B 40, 546 (1989)], we develop the perturbation theory for the Bose-Hubbard model and apply it to calculate the effects of a degenerate gas of spin-polarized fermions interacting by contact interactions with the constituent bosons. For the single-band Bose-Hubbard model, we find that the net effect of the screening of the boson on-site interaction by the fermions is to suppress the Mott-insulating lobes in the Bose-Hubbard phase diagram. For the more general multiband model, we find that, in addition to the fermion screening effects, the virtual excitations of the bosons to the higher Bloch bands, coupled with the contact interactions with the fermions, result in an effective increase (decrease) of the boson on-site repulsion (hopping parameter). If the higher-band renormalization of the boson parameters is dominant over the fermion screening of the interaction, the Mott-insulating lobes in the Bose-Hubbard phase diagram are enhanced for either sign of the Bose-Fermi interactions, consistent with the recent experiments.

Multiphoton avalanche generation of free carriers in a multiband crystal

A new mechanism for generating nonequilibrium electron-hole pairs in transparent wide-gap crystals under high-power picosecond light pulses of prebreakdown intensity is considered. The kinetics of free carrier generation is investigated by the numerical solution of the system of balance equations for particle concentrations within the multiband model of electron energy spectrum of the crystal. It is shown that in the intensity range of 1010–1012 W/cm2 the proposed way of nonequilibrium carrier generation is more effective in the case of picosecond pulses than the conventional multiphoton absorption. It is shown that the nonequilibrium carrier generation considered here may initiate a multiphoton avalanche.