Session Z39: Focus Session: Superconductivity-Theory and Computations (Mostly Phonons)

Apical oxygen electron-phonon coupling and poor screening in the cuprates

A theory of the effect of screening in anisotropic planar materials on the electron-phonon coupling for phonon vibrations out of the plane is presented. Specifically it is shown that the poor ability of electrons to propagate along the c-axis has consequences on the screened electron-phonon interaction. A theory for the coupling of charge-transfer excitations to apical oxygen phonons in the cuprates is presented, and strong doping dependence of the magnitude and anisotropy of the electron-phonon coupling is demonstrated.   

Interaction of Zhang-Rice singlets with the buckling phonons in Cuprates

Starting from a fully interacting three-band model we derive an effective single-band Hamiltonian which describes the interaction of Zhang-Rice (ZR) singlets[1] with the buckling phonons. Our approach is based on exact diagonalization of small clusters which contain both Cu and O atoms[2]. We study the parametric dependence of the electron-phonon coupling. The coupling to the phonon mode with $B_{1g}$ symmetry is one order of magnitude stronger than the coupling to the $A_{1g}$ phonon mode and there is an anisotropy in the interaction. For the $B_{1g}$ phonon, the antinodes contribute to the interaction more than the nodes, in agreement with weak coupling approaches[3]. By increasing the O-O hopping, the coupling amplitude becomes smaller in antinodal points. We also find that a simpler model, which considers the modulation of the ZR hopping by the corresponding bond phonons, captures the symmetry of the electron-phonon interaction. Reference: [1] F. C. Zhang and T. M. Rice, PRB {\bf 37}, 3759 (1988) [2] H. Eskes {\em et.al.}, Physica C {\bf 160}, 424 (1989) [3] T. P. Devereaux {\em et.al.}, PRL {\bf 93}, 117004 (2004)   

Anisotropic electron-phonon coupling in Bi2212 and Bi2223

In this talk we present calculations of self energy effects due to anisotropic electron-phonon coupling in the Bi-family of cuprates. The specific anisotropy of a number of phonon modes yields momentum-dependent signatures in the spectral function and renormalizations in the tunneling density of states both above and below Tc. The spectral functions are compared to angle-resolved photoemission and SIS break junction measurements and renormalizations at specific wavevectors and energies are in accordance with coupling primarily to the B1g phonon. Self-consistent treatment of the electron-phonon interaction is shown to display band renormalizations at energies well above that of the characteristic phonon energy.   

Numerical study of the isotope effect of underdoped high-temperature superconductors

We present a numerical study of the isotope effect on the angle resolved photoemission spectra (ARPES) in the undoped cuprates. By the systematic-error-free Diagrammatic Monte Carlo method, the Lehman spectral function of a single hole in the $tt't''-J$ model in the regime of intermediate and strong couplings to optical phonons is calculated for normal and isotope substituted systems. We found that the isotope effect is strongly energy-momentum dependent, and is anomalously enhanced in the intermediate coupling regime while it approaches to that of the localized hole model in the strong coupling regime. We predict the strengths of effect as well as the fine details of the ARPES lineshape change. Implications to the doped case are also discussed.   

Polaronic effect in lightly doped high-Tc cuprates

The effect of in-plane oxygen phonons is investigated by numerical exact diagonalizations of the t-J Holstein model.[1] The present study indicates that the breathing vibration mode gives rise to a polaronic effect which yields a broadening of the single hole quasiparticle spectrum and a shift from the chemical potential, as the one observed in angle-resolved photoemission spectroscopy.[2] [1] T. Sakai, D.Poilblanc and D.J.Scalapino, Phys. Rev. B 55 (1997) 8445. [2] K. M. Shen et al., Phys. Rev. Lett. 93 (2004) 267002.   

Transport and thermodynamic properties of cuprate superconductors: E(k) dispersion, pseudogap and isotope effects.

We have calculated the thermoelectric power, susceptibility and entropy of Bi-2212 and Bi-2201 using the ARPES-derived energy dispersion, a model scattering rate and including a normal-state pseudogap. The doping and temperature dependence is found to closely mimic the experimentally measured data. We have used this approach to examine isotope effects and in particular note that the kink in the dispersion near E$_{F}$ (including its isotope effect) can be probed through the high temperature thermoelectric power.   

Renormalization Group Study of the Electron-phonon Interaction in High $T_c$ Cuprates

We apply a numerical renormalization group scheme to study the phonon-mediated retarded interactions in the high $T_c$ cuprates. We find that three sets of phonon-mediated retarded quasiparticle scatterings grow under RG flow. These scatterings share the following common features: 1) the initial and final quasiparticle momenta are in the antinodal regions, and 2) the scattering amplitudes have a $x^2-y^2$ symmetry. All three sets of retarded interactions are driven to strong coupling by the magnetic fluctuations around $(\pi,\pi)$. After growing strong, these retarded interactions can trigger density wave orders with d-wave symmetry. However, due to the d-wave form factor they will leave the nodal quasiparticle unaffected. We conclude that the main effect of electron-phonon coupling in the cuprates is to promote these density wave orders.   

Phonon renormalization reflecting dynamic charge inhomogeneity in copper-oxide superconductors

Our inelastic neutron scattering measurements show that there is a strong anomaly in the Cu-O bond-stretching phonon in cuprate superconductors La$_{2-x}$Sr$_{x}$CuO$_{4}$ (x=0.07,0.15). This behavior also appears in superconducting YBa$_{2}$Cu$_{3}$O$_{6+x}$, however it is completely absent in undoped and overdoped LSCO.$^{ }$In La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ and La$_{1.48}$Nd$_{0.4}$Sr$_{0.12}$CuO$_{4}$, compounds that exhibit spatially modulated charge and magnetic order, often called stripe order, the anomaly occurs at a wave vector corresponding to the charge order. The results suggest that this giant electron-phonon anomaly, which is absent in LDA calculations, is associated with charge inhomogeneity induced by strong electronic correlations. It follows that electron-phonon coupling may be important to understanding the superconductivity although its contribution to the mechanism is probably non-BCS-like.   

Is room-temperature superconductivity with phonons possible?

By recognizing the vital importance of two-hole Cooper pairs in addition to the usual two-electron ones in a strongly-interacting many-electron system, the concept of Cooper pairing was re-examined with striking conclusions, namely gapped and linearly-dispersive resonances with a finite lifetime. Based on this, Bose-Einstein condensation (BEC) theory has been generalized to include not boson-boson interactions (also neglected in BCS theory) but rather boson-fermion interaction vertices reminiscent of the Froehlich electron-phonon interaction in metals. Instead of phonons, the bosons in the generalized BEC (GBEC) theory are now both particle and hole Cooper pairs. Each kind is responsible for half the condensation energy. The GBEC reduces to all the old known statistical theories as special cases---including the so-called ``BCS-Bose crossover'' picture which in turn generalizes BCS theory. With no adjustable parameters, the GBEC theory yields superconducting transition temperatures substantially higher than the BCS limitation of around 45K [including room-temperature superconductivity (RTSC)] without relying on non-phononic dynamics involving excitons, plasmons, magnons or otherwise purely-electronic mechanisms. The results are expected to shed light in the experimental search for RTSCs.   

Duality and normal modes in a Cooper pair Wigner crystal

A duality transformation from a phase fluctuating d-wave superconductor to a condensed state of vortices shows that Cooper pairs may form a Wigner crystal once the phase fluctuations destroy the superconducting long range order [1]. The lattice constant and the basis of this crystal are consistent with the charge modulations seen by the STM experiments in strongly underdoped cuprates [2]. Based on this vortex-boson duality we suggest a theoretical picture to relate the charge modulations seen by STM and the mysterious increase in the thermal conductivity [3] recently observed in the underdoped non-superconducting state. This addition to the thermal conductivity has bosonic temperature dependence and is attributed within our picture to the vibrational modes of the pair Wigner crystal. We analyze the spectrum of these modes and find it qualitatively consistent with the experimental observations. \\ 1. Z. Tesanovic, Phys. Rev. Lett. 93, 217004 (2004).\\ 2. J. E. Hoffman et al., Science 295, 466 (2002).\\ 3. L. Taillefer (unpublished).   

Cooper-Pair Molasses: Cooling a nanomechanical resonator with quantum backaction

We have measured the back-action of a superconducting single electron transistor using a radio frequency nanomechanical resonator. The backaction forces are a factor of 15 above the intensity required by the Heisenberg uncertainty principle: $ \sqrt{S_x S_f}=15\frac{\hbar}{2} $. This system has also shown a record position and force sensitivity of $0.4fm/\sqrt{Hz}$ and $0.5aN/\sqrt{Hz}$, and the closest approach to the quantum ground state of a mechanical system (N=25) (1). In addition, we have discovered a novel cooling mechanism, analogous to optical molasses, which is a result of resonant Josephson effects in the transistor (2,3). Using devices of similar design and performance, we are anticipating the observation of squeezed, superposition, and entangled states of a mechanical device.\\ \\ 1. M.LaHaye, O. Buu, B. Camarota, K. Schwab, Science 304, 74 (2004). \\ 2. M. P. Blencowe, J. Imbers and A. D. Armour, xxx.lanl.gov/ cond-mat/0507645.\\ 3. A. A. Clerk, S. Bennett, xxx.lanl.gov/ cond-mat/0507646. \\   

Real-Space Picture of the Cooper Pair

The Cooper pair is generally analyzed in momentum space, but its real-space structure also follows directly from the BCS theory. From this viewpoint [1], a Cooper pair consists of a spherical quasi-atomic wavefunction of radius $\sim \pi \xi _{0}$ for both electrons, with radial nodes separated by $\pi $/$k_{F}$. An induced commensurate quasi-static charge modulation in the underlying lattice provides the interaction potential, similar to that in the simple BCS approximation, which leads to a bound state. This picture can be generalized for alternative pairing symmetries (p or d-wave) as well as alternative pairing mechanisms (excitonic or spin-based) and extended to disordered superconductors. While it does not derive essentially new physics, this real-space approach may provide a more heuristic picture for developing and understanding new phenomena in superconductivity. [1] A.M. Kadin, http://www.arxiv.org/abs/cond-mat/0510279   

Cooper pairs on a spherical surface

Superconductivity has been widely studied for flat, two-dimensional electron systems, such as electrons in copper-oxide planes or electron films on helium. In this contribution, we investigate how Cooper pairing is affected by curvature. In particular we investigate the pairing correlations of a spherical, two-dimensional electron gas. This system is realized in for example multielectron bubbles, and in metallic nanoshells. For the case of multielectron bubbles, the pairing Hamiltonian can be solved exactly using Richardson's method. This reveals not only the structure of the ground state, but also the density of states of the excited states. We find that in the ground state, a redistribution of the electrons over the angular momentum levels occur, and that in the density of states a pseudogap appears. These results are put in the context of multielectron bubbles in helium, and compared to those for a flat 2D electron system.   

Cooper Pair Wavefunction Approach to the AC Josephson Effect

Recently, we have proposed Cooper pair wavefunction approach to the DC Josephson effect, which shows the threshold resistance of SIS Josephson junctions (in the high tunneling resistance regime). In the MgB$_{2 }$case, since the threshold resistance is so small for the big gap, MgB$_{2 }$break junctions and SIS tunnel junctions display the Josephson supercurrent only for the small gap. We apply this approach to the AC Josephson effect. The amplitude of the oscillating supercurrent in the presence of the electric field is calculated, using the Cooper pair wavefunctions formed by the Airy functions. We also discuss the sign problem of the pair-quasi-particle interference term.