Post deadline Session on MgB₂

Introduction, Talks 1 - 19

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Table of Contents
	Talks:   1-19     20-39     40-59      60-79
Intro	Introduction
Talk 01	Prof. Jun Akimitsu
Talk 02	Boron Isotope Effect in Superconducting MgB2
Talk 03	Mg and B Isotope Effects in MgB2
Talk 04	Resistivity, specific heat, and boron isotope effect in MgB2
Talk 05	Phonon Density-of-States in MgB2
Talk 06	Lattice Dynamics and Structure of MgB2
Talk 07	Electronic Structure and Electron-phonon Coupling in MgB2
Talk 08	Electronic and Transport Properties of MgB2
Talk 09	Anisotropic, Anharmonic, and Nonlinear Electron-phonon Coupling in MgB2
Talk 10	Superconductivity of MgB2 from Hole-Doped Covalent bonds
Talk 11	Nature of bonding and electronic properties of MgB2, a boron intercalation superconductor
Talk 12	Ab Initio calculations of the phonon frequencies, Grüneisen constants and electron phonon coupling in MgB2
Talk 13	Tight-binding description of MgB2 and related compounds
Talk 14	Anharmonic Lattice Dynamics and Nonlinear Electron-phonon Coupling in MgB2
Talk 15	A New Method of Probing the Phonon Mechanism in Superconductors including MgB2
Talk 16	Acoustic Plasmons in MgB2
Talk 17	Hole Superconductivity in MgB2:a high Tc cuprate without Cu
Talk 18	Hole superconductivity in MgB2: superconducting properties
Talk 19	Thermoelectric Power and High Pressure Effects on Tc of MgB2

 

 

 

Introduction

Introduction

 

Talk 01

Prof. Jun Akimitsu                                                      8 minutes

Aoyama-Gakuin University, Tokyo, Japan

 

The following talks are limited to 2 minutes, followed by 1 minute for questions and changing speakers.   The limit will be strictly enforced.

 

Isotope Effect

 

Talk 02

Boron Isotope Effect in Superconducting MgB₂ .

S. L. Bud'ko, G. Lapertot, C. Petrovic, C. E . Cunningham, N. Anderson, and P. C. Canfield, Ames Laboratory and Dept. of Physics and Astronomy, Iowa State University.

We report the preparation method of, and boron isotope effect for MgB₂, a new binary intermetallic superconductor with a remarkably high superconducting transition temperature T_c(¹⁰B) = 40.2 K. Measurements of both temperature dependent magnetization and specific heat reveal a 1.0 K shift in T_c between Mg¹¹B₂ and Mg¹⁰B₂. Whereas such a high transition temperature might imply exotic coupling mechanisms, the boron isotope effect in MgB₂ is consistent with the material being a phonon-mediated BCS superconductor. In addition, an analysis of the specific heat data gives Q _D = 750 ± 30 K, g = 3 ± 1 mJ/mol K, and D C_p/ g T_c near unity.

Talk 03

Mg   and B Isotope Effects in MgB₂,

D. G. H inks, H. CLAUS, and J. D. JORGENSEN, Materials Science Division, Argonne National Laboratory, Argonne, IL 60439.    

We have determined the Mg and B isotope effects in MgB₂ using the six combinations of ²⁴Mg, ²⁶Mg, natural-abundance Mg, ¹⁰B, and ¹¹B.   The isotope effect coefficients are a_Mg=0.02(1) and a_B=0.30(1 ).   The very small isotope effect for Mg shows that frequency changes of phonons with significant contributions from Mg do not affect T_c; rather, B vibrations are most strongly coupled to the carriers that give rise to superconductivity.   The failure of a_Mg and a_B to sum to 1/2 shows that simple models for explaining the total isotope effect are inadequate.

 

Talk 04

Resistivity, specific heat, and boron isotope effect in MgB₂

D.D. Lawrie, J. P. Franck, Guanwen Zhang, Department of Physics, University of Alberta, C. Marcenat, and A. Pautrat, CEA, Grenoble

Measurements were performed on sintered pieces of MgB₂ synthesized using amorphous B powder. The resistive transition in zero field has a width of about 0.25 K. Resistivity measurements up to 5.5 T show no magnetoresistance in the normal state. Specific heat data have been obtained in fields up to 3 T. The onset of the C_p anomaly coincides with the R = 0 point, the magnetic T_c lies close to the specific heat maximum. The samples show strong pinning due to remaining unreacted boron. Isotopic comparison pairs (¹⁰B-¹¹B) were obtained with zero field cooled magnetic transitions of 39 K (¹¹B) and 40 K (¹⁰B), confirming the isotope effect observed by Bud’ko et al.

 

Talk 05

Phonon Density-of-States in MgB₂

RAY OSBORN, EUGENE GOREMYCHKIN, ALEXANDER KOLESNIKOV,

DAVID HINKS, Argonne National Laboratory

We report inelastic neutron scattering measurements of the phonon density-of-states in Mg¹¹B₂, which has superconducting transition at 39.2 K. The acoustic phonons extend in energy to 36 meV, and there are highly dispersive optic branches peaking at 54, 78, 89 and 97 meV. A simple Born-von Karman model reproduces the mode energies, and provides an estimate of the electron-phonon coupling of l ~ 0.9. Furthermore, the estimated boron and magnesium contributions to the isotope effect are in qualitative agreement with experiment. The data confirm that a conventional phonon mechanism, with moderately strong electron-phonon coupling, can explain the observed superconductivity.

 

Talk 06

Lattice Dynamics and Structure of MgB₂

J. W. LYNN, C. M. BROWN, T. J. UDOVIC, Q. HUANG, NIST Center for Neutron Research, NIST, Gaithersburg, MD 20899 and University of Maryland, College Park, MD 20742, N. ROGADO, K.A. REGAN, M.A. HAYWARD, J.S. SLUSKY, T. HE, M.K. HAAS, P. KHALIFAH, K. INUMARU, and R.J. CAVA, Department of Chemistry and Princeton Materials Institute, Princeton University, Princeton, NJ 08544.  

We have carried out neutron diffraction and inelastic scattering measurements on polycrystalline Mg⁽¹¹⁾B₂ from 7 K to 325 K.   The lattice parameters decrease smoothly with decreasing temperature, while the mean square displacements are quite anisotropic, indicative of the layered nature of the crystal structure.   The complete generalized phonon density of states has been measured, which shows considerable structure, and has a cutoff at ~100 meV.   The data are in excellent agreement with first-principles calculations of the lattice dynamics.   The nature of the lattice dynamics and its relation to the strong electron-phonon coupling in this system will be discussed.

 

Talk 07

Electronic Structure and Electron-phonon Coupling in MgB₂

J. KORTUS, I.I. MAZIN, Naval Research Laboratory, V.P. ANTROPOV, K.D. BELASHCHENKO, Ames Lab, L.L. BOYER, NRL

We report full potential LAPW band structure calculations for MgB₂. We observe four Fermi surfaces, formed by bonding and antibonding states of B p_z orbitals, and by bonding states of B p_x and p_y orbitals. The latter are highly 2D, while the former are fairly isotropic. The average plasma frequency is about 7 eV and isotropic. The role of Mg, apart from donating electrons, is assisting B p_z hopping between the planes. Borons form a hexagonal lattice with strong covalent bonding in-plane and metallic bonding between the plane. The bonding between the boron sublattice and Mg atoms is mostly ionic. Strong bonding and light mass provides high-frequency phonons that couple with electrons, while metallic character of the B sublattice ensures reasonable density of states (comparable to Al metal). We estimate electron-phonon coupling using the rigid muffin tin approximation. Although this approximation is questionable for MgB₂, it indicates qualitatively that the coupling is indeed strong. We also computed phonon frequencies for all 4 allowed zone center modes, using frozen-phonons technique. There is one Raman and two infrared modes, which can be, in principle, observed experimentally.

  

Talk 08

Electronic and Transport Properties of MgB₂

I.I. MAZIN, J. KORTUS, Naval Research Laboratory, E. PAVARINI, INFM, Pavia, Italy

In order to facilitate the digesting of the experimental information available for MgB₂, we computed various electronic properties of this compound using the full-potential LAPW method, and, in some cases, ASA-LMTO method. We will analyze the temperature-dependent resistivity and will show that the observed power-law like behavior can be explained by the Bloch-Grueneisen formula with a soft and a hard phonon mode, the latter coupled much stronger with the electrons than the former. Calculations of the Hall conductivity result in a rather larger (due to strong cancellation of the hole and the electron pocket contributions) effective hole concentration. We will also report calculations of the NMR relaxation rate, including dipolar component (which needs to be taken into account because of the predominantly p-character of the states of the Fermi level). Since electronic properties of the two different set of bands near the Fermi surface differ greatly, we will show how different bands contribute into the calculated density of states, plasma frequency, penetration depth, etc. We will also present a tight-binding description of the four bands crossing the Fermi level and analytical expressions for the band dispersions.

 

Talk 09

Anisotropic, Anharmonic , and Nonlinear Electron-phonon Coupling in MgB₂

A.Y. LIU, J. KORTUS, Naval Research Laboratory and Georgetown University, I.I. MAZIN, NRL

We calculated the standard harmonic linear electron-phonon coupling (EPC) for MgB₂, using the linear response method in framework of the local density functional theory. 96 different phonons at 12 inequivalent points in the Brillouin zone were included. We found a total EPC constant of ~ 1, and the BCS prefactor w _log ~ 700 K. Most of the EPC comes from the interaction of the in-plane B p_x;y states with the near-zone-center honeycomb-contorting B_x;y modes; these states form quasi-2D bands and account for ~ 1/3 of the total density of states. Of the four Fermi surfaces, the two 2D pockets interact with the phonons much stronger than the two 3D ones (p_z-derived). This suggests a possibility of two different order parameters in the two sets of bands, in accord with reports of different tunneling gaps (we expect the larger gap to be visible only in in-plane tunneling), and nontrivial thermodynamic properties at D ₁ < T < D ₂ . Since most of the EPC is coming from one (doubly degenerate at the zone center) phonon, we concentrated on this mode and performed frozen-phonon calculations. We found this mode to be extremely anharmonic (590 vs. 515 cm^-1 in the harmonic approximation). Moreover, it interacts with the electrons highly nonlinearly. Although more calculations are needed, it seems two-phonon processes induce a stronger pairing than one-phonon exchange. This should modify the isotope effect and lead to other interesting physics.

 

Talk 10

Superconductivity of MgB₂ from Hole-Doped Covalent bonds ¹  

J.M . AN, W. E. PICKETT, UC Davis

Although a first look suggests that MgB₂ is a standard three dimensional conductor, we have taken the viewpoint that its remarkable superconducting properties (T_c ~ 40 K) requires a very specific microscopic cause, and we have identified it. A series of calculations on MgB₂ and related isoelectronic systems, undistorted and with frozen-in phonons, reveals that:

·         Although the Mg²⁺ ions indeed donate their electrons to the B layers, they are not bystanders. Their attractive potential lowers the non bonding B p (p_z) bands relative to the bonding s (sp_xp_y) bands, causing s -> p charge transfer. The resulting s band doping is 0.13 holes/cell.

·         Due to their two dimensionality, the s bands contribute strongly to the Fermi level density of states, almost independently of doping level.

·         Calculated deformation potentials of G point phonons identify the B bond stretching modes as dominating the electron-phonon coupling. This deformation potential may be the largest ever observed in a metal.

·         We estimate an electron-phonon coupling strength l ~ 1 due to coupling of the bond stretching modes (E_2g at G ) to only the two hole bands. This value approaches the value necessary to produce T_c ~ 40 K.

·         Superconductivity driven by s band holes is consistent with the report of destruction of superconductivity by electron doping with Al.

 

Talk 11

Nature of bonding and electronic properties of MgB₂, a boron intercalation superconductor

V.P. ANTROPOV, K.D. BELASHCHENKO, Ames Laboratory, M. VAN SCHILFGAARDE, Sandia National Laboratories, S.N. RASHKEEV, Vanderbilt University.

Chemical bonding and electronic structure of MgB₂ are studied using self-consistent band structure techniques. Analysis of the transformation of the band structure for the hypothetical series of graphite – primitive graphite – primitive graphite-like boron – intercalated boron, shows that the band structure of MgB₂ is graphite-like, with p bands falling deeper than in ordinary graphite. These bands possess a typically delocalized and metallic, as opposed to covalent, character. The in-plane s bands retain their 2D covalent character, but exhibit metallic hole-type conductivity. The coexistence of 2D covalent in-plane and 3D metallic-type interlayer conducting bands is a peculiar feature of MgB₂. We analyze the 2D and 3D features of the band structure of MgB₂ and related compounds, and their contributions to conductivity. Using the non-spherical rigid muffin tin approximation, we sort out the contributions to the Hopfield parameter h from different sheets of the Fermi surface, as well as for in-plane and out-of-plane vibrations, and discuss the behavior of h in the Mg_xAl_1-xB₂ system. Further, a significant hardening of the in-plane E_2g phonon mode in AlB₂ compared to MgB₂ contributes to the suppression of superconductivity. We also use the band structure to analyse the optical conductivity in a wide energy range.

 

Talk 12

Ab Initio calculations of the phonon frequencies, Grüneisen constants and electron phonon coupling in MgB₂

DAVID ROUNDY, HYOUNG JOON CHOI, HONG SUN*, STEVEN G. LOUIE,

MARVIN L. COHEN, Dept. of Physics, Univ. of California Berkeley and Lawrence

Berkeley National Laboratory.

We will present results for ab initio   pseudopotential density functional calculations for MgB₂, beginning with calculations of the elastic constants showing the elastic anisotropy of MgB₂, along with calculations of the phonon frequencies and dispersion relation. We will then present results on the Grüneisen constants, and a discussion of the effect of pressure on the vibrational properties of MgB₂. Finally, we will show the result of our calculation of the electron-phonon coupling interaction in MgB₂.

 

Talk 13

Tight-binding description of MgB₂ and related compounds

D. A. PAPACONSTANTOPOULOS, M. J. MEHL, Center for Computational Materials Science, Naval Research Laboratory

We will describe a tight-binding fit to all-electron full-potential LAPW calculations for MgB₂. The TB parameters follow the NRL-TB scheme¹ and reproduce the total energy as well as the electronic energy bands and the densities of states. The resulting Hamiltonian may be suitable for deriving transport and other properties of this material. We will also present a search for possible higher transition temperatures in related diboride compounds using an evaluation of the electron-phonon coupling in the rigid muffin-tin approximation.

 

Talk 14

Anharmonic Lattice Dynamics and Nonlinear Electron-phonon Coupling in MgB₂ ,

T. YILDIRIM and O. GULSEREN , NIST Center for Neutron Research, NIST, Gaithersburg, MD.  

We report first-principles calculations of the electronic band structure and lattice dynamics of MgB₂[1]. The dynamical matrix is obtained by direct-force method using the periodically repeated supercells. We found an excellent agreement between the calculated phonon dispersion curves and the phonon density of states with the inelastic neutron scattering measurements.   Frozen-phonon calculations [2] indicated that while most of the phonons are harmonic, the in-plane boron phonons (E_2g) near the zone-center are very anharmonic (i.e. E(u)=A₂u²+A₄u⁴ where A₄/A₂²~8). This anharmonicity enhances the E_2g mode energy by about 25% from its harmonic value.   We also calculated the deformation energy within frozen-phonon approach and found that the anharmonic B-modes strongly and non-linearly couples to the partially occupied planer boron sigma bands near the Fermi level. The very anharmonic in-plane B modes and their strong non-linear electron-phonon couplings are essential to explain the high T_C in MgB₂[1].

[1] “Giant Anharmonicity and Non-linear Electron-Phonon Coupling in MgB₂: Frist-principles calculations and Inelastic Neutron Scattering Study”,

T. Yildirim   et al (Submitted).

[2] Various nice animations of the phonons in MgB₂ and their effects on the band structure can be found at http://www.ncnr.nist.gov/staff/taner/mgb2

 

Talk 15

A New Method of Probing the Phonon Mechanism in Superconductors including MgB₂,

Yong-Jihn Kim (Bilkent University)

Weak localization has a strong influence on both the normal and superconducting properties of metals. S ince weak localization leads to the decoupling of electrons and phonons, the temperature dependence of resistance is decreasing with increasing disorder , as manifested by Mooij's empirical rule. In addit i on, the universal correlation of T_c and the resistance ratio follows. This understanding provides a new powerful means to probe the phonon mechanism in superconductors including MgB₂. The merit of this method is its wide applicability and reliability because McMillan's electron-phonon coupling constant changes in a broad range due to weak localization.

 

Talk16

Acoustic Plasmons in MgB₂

K. Voelker ¹, V. I. Anisimov ^1,2, and T. M. Rice ¹

¹ Theoretische Physik, ETH Hönggerberg, CH-8093 Zürich, Switzerland

² Institute of Metal Physics, Russian Academy of Sciences, Ekaterinburg, Russia

We present evidence for the existence of an acoustic plasmon mode, that is, a quadrupolar charge collective mode with linear dispersion, in MgB₂.   This collective mode arises from the interplay between quasi two-dimensional and three-dimensional carriers.   It leads to an attractive retarded contribution to the Coulomb interaction, which will modify the repulsive Coulomb pseudopotential.   Y. Kong et al. [cond-mat/0102499]   find relatively strong coupling to a high frequency phonon mode in MgB₂,   but could obtain the observed T_c = 39.5K only by assuming that the Coulomb pseudopotential takes an anomalously small value m ^* » 0.02 - a value roughly seven times smaller than for usual s-p superconductors.   We propose that the acoustic plasmon mode may be responsible for this unusually small value.

 

Talk17

Hole Superconductivity in MgB₂ : a high T_c cuprate without Cu

J. E. Hirsch, Department of Physics, University of California, San Diego, La Jolla, CA 92093-0319

The theory of hole superconductivity(1) explains high temperature superconductivity incuprates as driven by pairing of hole carriers in oxygen planar p- p orbitals in the highly negatively charged Cu-O planes. The pairing mechanism is hole undressing and is Coulomb-interaction driven. We propose that the planes of B atoms in MgB₂ are akin to the Cu-O planes without Cu, and that the recently observed high temperature superconductivity in MgB₂ arises similarly from undressing of hole carriers in the planar boron p_{x,y} orbitals in the negatively charged B^- planes. Doping MgB₂ with electrons and with holes should mirror the behavior of underdoped and overdoped high T_c cuprates respectively. We discuss possible ways to achieve higher transition temperatures in boron compounds based on this theory.

 

Talk18

Hole superconductivity in MgB₂: superconducting properties

F. Marsiglio¹ and J.E. Hirsch²

¹ University of Alberta, ²University of California, San Diego

The model of hole superconductivity predicts that superconductivity will arise when the Fermi level is near the top of a band, driven by lowering of kinetic energy induced by Coulomb interactions. We estimate parameters for the model based on reported band structure calculations and experimental measurements on MgB₂, and report results for various observables. In particular, Tc, energy gap, specific heat, tunneling, coherence length, London penetration depth and pressure effect are presented versus temperature and doping for a two-dimensional model as well as a three-dimensional anisotropic

structure. Where available, comparison with experiment will be made.

 

Talk19

Thermoelectric Power and High Pressure Effects on T_c of MgB₂

B. LORENZ, R. L. MENG, C. W. CHU^*, TCSUH, University of Houston

The thermoelectric power, S, and hydrostatic pressure effects on the newly discovered superconductor MgB₂ have been determined. S is positive, relatively small and decreases linearly with temperature below 150 K, as is expected for a metal with hole-type carriers. The transition temperature T_c was found to decrease linearly with pressure at a large rate of -1.6 K/GPa, consistent with the suggestion that electron-phonon interaction may play a significant role in the superconductivity of the compound. The relative pressure coefficient, dlnT_c/dp, for MgB₂ lies between the known values for sp- and d-superconductors. However, it should be noted that the proposition of the “universal” mechanism for the observed superconductivity in MgB₂ cannot be ruled out at this moment.