Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session B32: Focus Session: Superconductivity: Theory and Computation I |
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Sponsoring Units: DCOMP DCMP Chair: Jens Kortus, IPCMS Room: LACC 507 |
Monday, March 21, 2005 11:15AM - 11:27AM |
B32.00001: Electron – lattice coupling in HTSC cuprates: Evidence for polaron formation from unconventional isotope and strain effects Annette Bussmann-Holder, Hugo Keller, Alan R. Bishop, Arndt Simon, Roman Micnas, K.A. M\"uller Motivated by recent Andreev reflection experiments we use a two- component scenario to study lattice effects on the superconducting transition temperature T$_{c}$, the isotope exponent and strain effects in high temperature superconducting copper oxides. We find that the polaronic renormalization of the single particle energies substantially enhances T$_{c}$, can explain the strain induced enhancement of T$_{c}$ and yields the unconventional isotope effect on the London penetration depth $\lambda _{L}$. The lattice distortion which causes these effects is identified as the Q$_{2}$-type Jahn-Teller mode. [Preview Abstract] |
Monday, March 21, 2005 11:27AM - 11:39AM |
B32.00002: Bethe -Salpeter Equation and Isotope Effect in Superconductivity Yuriy Malozovsky, J.D. Fan We evaluate the temperature of superconducting phase transition in terms of the Bethe-Salpeter equation for the many-body system. We consider the case when both electron-phonon interaction and strong Coulomb interaction coexist. To remove the artificial cutoff at high energy we solve the Bethe-Salpeter equation in terms of the two-particle vacuum scattering amplitude. We show that such an approach leads to the conclusion that the so-called Coulomb pseudopotential appears only due to artificial cutoff and does not exist at all in terms of the Bethe-Salpeter equation. [Preview Abstract] |
Monday, March 21, 2005 11:39AM - 11:51AM |
B32.00003: On the Isotope Effect in Superconductivity J.D. Fan, Yuriy Malozovsky The cutoff frequency \textit{$\omega $}$_{D}$ introduced in the BCS theory leads to the well-known 0.5 isotope effect exponent, but conflicts with the 0, non-one-half or even negative exponents observed in high- temperature superconductors. In the framework of the repulsive Coulomb interaction and collective excitations, no cutoff is needed and allowed. We show that the contributions from Coulomb interaction, collective excitations and the contribution from phonons co-exist and compete leading to compensation. Depending on the structure of a superconductor and elements made of, the net contribution to the component $\alpha $ can be positive, negative or zero. It seems that the term that is called ``dangerous'' and dropped off in Bogolyubov's Hamiltonian corresponds to the collective excitations in the field theory and should make a negative contribution to the isotope effect exponent $\alpha $. [Preview Abstract] |
Monday, March 21, 2005 11:51AM - 12:27PM |
B32.00004: Denstity Functional Theory of Superconductivity Invited Speaker: A novel density-functional approach to the description of phonon-mediated superconductivity is presented. The theory is formulated in terms of three quantities: the ordinary electron density, the superconducting order parameter, and the nuclear N-body density. These three ``densities'' are determined by a set of Bogoliubov-type Kohn-Sham equations representing the electronic degrees of freedom, and a Schr{\"o}dinger equation with an N-body interaction describing the nuclear motion. These equations are coupled to each other via exchange-correlation (xc) potentials which are universal functionals of the three densities. The formalism can be viewed either as a strong-coupling generalization of the weak-coupling DFT for superconductors [1] or as a superconducting generalization of the multi-component DFT [2] for electrons and nuclei. Approximations of the universal xc functionals will be derived on the basis of many-body perturbation theory [3,4]. In this way, a true ab-initio description is achieved which does not contain any empirical parameters. Numerical results for the critical temperature and the gap will be presented for simple metals [5], for MgB$_2$ [6], and for Li and Al under pressure. In particular, for MgB$_2$, the two gaps and the specific heat as function of temperature are in very good agreement with experimental data. Moreover, our calculations show clearly, how the Coulomb interaction acts differently on $\sigma$ and $\pi$ states, thereby stabilizing the observed superconducting phase. For Li and Al under pressure the calculations explain why these two metals behave very differently, leading to a strong enhancement of superconductivity for Li and to a clear suppression for Al with increasing pressure. \newcounter{fig} \begin{list}{[\arabic{fig}]}{\usecounter{fig} \itemsep -1.7mm} \item L.N. Oliveira, E.K.U. Gross, W. Kohn, PRL {\bf 60}, 2430 (1988). \item T. Kreibich, E.K.U. Gross, PRL {\bf86}, 2984 (2001). \item S. Kurth, M. Marques, M. L\"{u}ders, E.K.U. Gross, PRL {\bf 83}, 2628 (1999). \item M. L\"uders et al, cond-mat/0408685 (2004). \item M. Marques et al, cond-mat/0408686 (2004). \item A. Floris et al, PRL (2004, in press). \end{list} [Preview Abstract] |
Monday, March 21, 2005 12:27PM - 12:39PM |
B32.00005: Cooper Pairs in a spherical 2D electron system Jacques Tempere, Vladimir Gladilin, Isaac F. Silvera, Jozef T. Devreese We investigate the pairing properties of electrons on a spherical surface. In particular, we consider multielectron bubbles in liquid helium. These are typically micron-sized cavities in helium containing electrons that form a nanometer thin film anchored to the inner surface of the bubble. The bubble is forced open by the Coulomb repulsion between the electrons, balanced by the surface tension of the helium. The electrons in the spherical two-dimensional layer interact with the ripplons, quantized modes of oscillation of the helium bubble surface. This interaction leads to an attractive effective interaction between the electrons, allowing for a Cooper pairing scenario. The paired state is investigated with the Richardson model (more commonly used to study superconductivity in small nanograins). We present results for the ground state properties and the density of states, and highlight differences between the pairing ground state on a spherical surface and that in a bulk (2D or 3D) superconductor. [Preview Abstract] |
Monday, March 21, 2005 12:39PM - 12:51PM |
B32.00006: Giant magnetization of superconductor - two-dimensional electron gas - superconductor structure. Eduard Bogachek, Igor Romanovsky, Uzi Landman, Ilya Krive Superconductivity-induced phase-controlled mesoscopic magnetic effects in two-dimensional semiconductor quantum wires bridged between two superconductors are considered. Giant paramagnetic response of the contact to the applied magnetic field at certain resonant values of the phase difference of the order parameter is predicted. This resonant behavior of the magnetization is a result of the change in the population of the $2N_{\perp}$-fold degenerate Andreev levels near the Fermi energy ( $N_{\perp}$ is the number of transverse modes in the quantum wire). The magnetic response at the resonances at low temperatures is proportional to the number of transverse modes and, if the the number of transverse modes is large, the total magnetization of the junction may achieve values large enough to be experimentally detectable. [Preview Abstract] |
Monday, March 21, 2005 12:51PM - 1:03PM |
B32.00007: On the magnetization of two-dimensional superconductors Vadim Oganesyan, David Huse, Shivaji Sondhi We calculate the magnetization of a two-dimensional superconductor in a perpendicular magnetic field near its Kosterlitz-Thouless transition and in the low temperature algebraically ordered phase. We find that the critical behavior is more complex than assumed in the literature and that, in particular, the critical magnetization is {\it not} field independent as naive scaling predicts. We compare our analysis with the data on the cuprates. [Preview Abstract] |
Monday, March 21, 2005 1:03PM - 1:39PM |
B32.00008: Harmonic and anharmonic phonons in MgB$_2$ Invited Speaker: The discovery \footnote{ J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Nature (London) {\bf 410}, 63 (2001).} of a $39$ K critical superconducting temperature in MgB$_2$ has challenged our understanding of electron-phonon mediated superconductivity. Several mechanisms have been proposed to explain the large critical temperature, including a double gap structure and anharmonic effects. Much attention has been devoted to the study of the E$_{2g}$ phonon mode, an anti-phase vibration of the two boron atoms parallel to the hexagonal plane. In Raman spectra \footnote{J. W. Quilty, S. Lee, A. Yamamoto, and S. Tajima, Phys. Rev. Lett. {\bf 88}, 087001 (2002)} an E$_{2g}$ symmetry feature, commonly attributed to the E$_{2g}$ phonon mode, is strongly damped, an effect which has been ascribed to large electron-phonon coupling and large anharmonic effects of the E$_{2g}$ mode. The interpretation of the magnitude of each effect is, however, very controversial, mostly because accurate phonon dispersion measurements by neutron spectroscopy are not yet available due to the small size of MgB$_{2}$ single crystals.\\ In this talk we show how the magnitude of anharmonic effects can be determined using a joined experimental and theoretical approach. We measure, for the first time, the phonon dispersion and lifetime in MgB$_{2}$ single crystals with inelastic X-ray scattering \footnote{A. Shukla, M. Calandra, M. d'Astuto, M. Lazzeri, F. Mauri, C. Bellin, M. Krisch, J. Karpinski, S. M. Kazakov, J. Jun, D. Daghero, and K. Parlinski, Phys. Rev. Lett. {\bf 90}, 095506 (2003)}. This experimental technique allows accurate determination of phonon spectra even in the case of small single crystals. By using first principles calculations we obtain the harmonic phonon dispersion in MgB$_2$ (in agreement with previous calculations \footnote{Y. Kong, O. V. Dolgov, O. Jepsen, and O. K. Andersen, Phys. Rev. B 64, 020501(R) (2001)}). We evaluate the magnitude of anharmonic effects by calculating the anharmonic contributions to the phonon self-energy. We consider all the lowest order terms from three- and four-phonon vertices. The scattering between different phonon modes at different k-points in the Brillouin zone are included. We use density functional theory and the (2n+1) theorem to evaluate the three- and four-phonon vertices. The inclusion of these terms is found to be crucial in determining the anharmonic contribution to the phonon self-energy. From the real and imaginary part of the phonon self energy we extract anharmonic phonon frequency shifts and linewidths (the inverses of the lifetime) at the special k- points $\Gamma$, A, M. We find the anharmonic linewidth of the E$_{2g}$ mode to be negligible compared to that due to electron-phonon coupling. Thus the measurement of the phonon linewidth of the E2g mode allows the experimental determination of the electron-phonon coupling. For the anharmonic phonon frequency shift of the E$_{2g}$ mode we find a cancellation between the contributions of the three- and four-phonon vertices \footnote{M. Lazzeri, M. Calandra and F. Mauri, Phys. Rev. B 68, 220509(R) (2003).}. The total anharmonic shift of the E$_{2g}$ mode at Gamma is $+3.5$ meV, corresponding to a relative frequency shift of $+5.4\%$. The resulting anharmonic phonon frequencies are in good agreement with the phonon dispersion measured with inelastic X-ray scattering. [Preview Abstract] |
Monday, March 21, 2005 1:39PM - 1:51PM |
B32.00009: Superconductivity with Unconventional Pair Symmetry in a 2D System with Inherent Gap Renyuan Liao, Khandker Quader We study superconductivity in a 2D system with ``inherent'' gap; semiconducting gap is chosen as a prototypical case. We consider s and d wave pair symmetries, and carry out a mean-field study of the evolution of the order parameter and critical temperature, $T_c$, with varying interaction strength, doping and the inherent gap magnitude. The model 2D system exhibits a rich variety of transition and crossover behavior, including a ``pseudogap-like'' feature. To better understand pair-breaking, we also study phase fluctuations, and compare our calculated Kosterlitz-Thouless temperature, $T_c^{KT}$ with our mean-field $T_c$. [Preview Abstract] |
Monday, March 21, 2005 1:51PM - 2:03PM |
B32.00010: A superconductor to superfluid phase transition in liquid metallic hydrogen Egor Babaev, Asle Sudbo, Neil Ashcroft A superconductor to superfluid phase transition in liquid metallic hydrogen. Babaev (1,2), A. Sudbo (2), N. W. Ashcroft (1) (1) Cornell U. and (2) NTNU Trondheim,hydrogen is the simplest of atoms, it does not form the simplest of solids or liquids. Recent studies of the melting curve of hydrogen indicate that at high (but experimentally accessible) pressures, compressed hydrogen will adopt a liquid state, even at low temperatures. In reaching this phase, hydrogen is also projected to pass through an insulator-to-metal transition. This raises the possibility of new state of matter: a near ground-state liquid metal, and its ordered states in the quantum domain. Ordered quantum fluids are traditionally categorized as superconductors or superfluids; these respective systems feature dissipationless electrical currents or mass flow. Here we report an analysis based on topological arguments of the projected phase of liquid metallic hydrogen, finding that it may represent a new type of ordered quantum fluid. Specifically, we show that liquid metallic hydrogen cannot be categorized exclusively as a sperconductor or superfluid. We predict that, in the presence of a magnetic field, liquid metallic hydrogen will exhibit several phase transitions to ordered states, ranging from superconductors to superfluids. [Preview Abstract] |
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B32.00011: Particle-Hole Excitations and the BCS Ground State J.D. Fan, Yuriy Malozovsky We show that the well-known BCS Hamiltonian in terms of the BCS ground state represents, in fact, the generator of the particle-hole pairs and that the BCS ground state describes both the particle-hole excitations as well as the pairing condensate of Cooper's pairs. We calculate the contribution of particle-hole excitations to the ground state energy. We show that the particle-hole pairs in the case of attractive interaction significantly lower the ground state energy, which means that the BCS ground state is not really the ground state. In contrast, for the repulsive interaction the particle-hole excitations just renormalize the ground state energy. In the case of the repulsive interaction the condensate of bound pairs would lead to the real ground state of the system as shown. [Preview Abstract] |
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