Role of confined phonons in thin film superconductivity

We calculate the critical temperature $T_c$ and the superconducting energy gaps $\Delta_n$ of a thin film superconductor system, where $\Delta_n$ is the superconducting energy gap of the $n$-th subband. Since the quantization of both the electron energy and phonon spectrum arises due to dimensional confinement in one direction, the effective electron-electron interaction mediated by the quantized confined phonons is different from that mediated by the bulk phonon, leading to the modification of $T_c$ in the thin film system. We investigate the dependence of $T_c$ and $\Delta_n$ on the film thickness $d$ with this modified interaction.Comment: 4 pages, 2 figure

Extracting the electron--boson spectral function α2\alpha^2F(ω\omega) from infrared and photoemission data using inverse theory

We present a new method of extracting electron-boson spectral function $\alpha^2$F($\omega$) from infrared and photoemission data. This procedure is based on inverse theory and will be shown to be superior to previous techniques. Numerical implementation of the algorithm is presented in detail and then used to accurately determine the doping and temperature dependence of the spectral function in several families of high-T$_c$ superconductors. Principal limitations of extracting $\alpha^2$F($\omega$) from experimental data will be pointed out. We directly compare the IR and ARPES $\alpha^2$F($\omega$) and discuss the resonance structure in the spectra in terms of existing theoretical models

Scaling of the superfluid density in high-temperature superconductors

A scaling relation \rho_s \simeq 35\sigma_{dc}T_c has been observed in the copper-oxide superconductors, where \rho_s is the strength of the superconducting condensate, T_c is the critical temperature, and \sigma_{dc} is the normal-state dc conductivity close to T_c. This scaling relation is examined within the context of a clean and dirty-limit BCS superconductor. These limits are well established for an isotropic BCS gap 2\Delta and a normal-state scattering rate 1/\tau; in the clean limit 1/\tau \ll 2\Delta, and in the dirty limit 1/\tau > 2\Delta. The dirty limit may also be defined operationally as the regime where \rho_s varies with 1/\tau. It is shown that the scaling relation \rho_s \propto \sigma_{dc}T_c is the hallmark of a BCS system in the dirty-limit. While the gap in the copper-oxide superconductors is considered to be d-wave with nodes and a gap maximum \Delta_0, if 1/\tau > 2\Delta_0 then the dirty-limit case is preserved. The scaling relation implies that the copper-oxide superconductors are likely to be in the dirty limit, and that as a result the energy scale associated with the formation of the condensate is scaling linearly with T_c. The a-b planes and the c axis also follow the same scaling relation. It is observed that the scaling behavior for the dirty limit and the Josephson effect (assuming a BCS formalism) are essentially identical, suggesting that in some regime these two effects may be viewed as equivalent. This raises the possibility that electronic inhomogeneities in the copper-oxygen planes may play an important role in the nature of the superconductivity in the copper-oxide materials.Comment: 8 pages with 5 figures and 1 tabl

Infrared Studies of the Onset of Conductivity in Ultra-Thin Pb Films

In this paper we report the first experimental measurement of the infrared conductivity of ultra-thin quenched-condensed Pb films. For dc sheet resistances such that $\omega \tau \ll 1$ the ac conductance increases with frequency but is in disagreement with the predictions of weak localization. We attribute this behavior to the effects of an inhomogeneous granular structure of these films, which is manifested at the very small probing scale of infrared measurements. Our data are consistent with predictions of two-dimensional percolation theory.Comment: Submitted to Physical Review Letter

Absence of a Zero Temperature Vortex Solid Phase in Strongly Disordered Superconducting Bi Films

We present low temperature measurements of the resistance in magnetic field of superconducting ultrathin amorphous Bi films with normal state sheet resistances, $R_N$, near the resistance quantum, $R_Q={\hbar\over {e^2}}$. For $R_N<R_Q$, the tails of the resistive transitions show the thermally activated flux flow signature characteristic of defect motion in a vortex solid with a finite correlation length. When $R_N$ exceeds $R_Q$, the tails become non-activated. We conclude that in films where $R_N>R_Q$ there is no vortex solid and, hence, no zero resistance state in magnetic field. We describe how disorder induced quantum and/or mesoscopic fluctuations can eliminate the vortex solid and also discuss implications for the magnetic-field-tuned superconductor-insulator transition.Comment: REVTEX, 4 pages, 3 figure

Phenomenological Determination of the Beauty Meson Decay Parameter fBf_B and the CP-Violating Angle δ\delta

We fit the ${\cal CKM}$-matrix to all recent data with the following free parameters: three mixing angles, the CP-violating angle $\delta$ in the Maiani parametrisation, the top quark mass $m_t$, and the product f_B{\cal B}_{\B}^{1/2}, where $f_B$ is the $B$-meson decay parameter and {\cal B}_{\B} is the bag parameter. Our fits span a contiguous region in the (f_B{\cal B}_{\B}^{1/2},\ \cos\delta)--plane, limited by 0.117\lsim f_B{\cal B}_{\B}^{1/2}/{\rm GeV}\lsim 0.231 and --0.95 \lsim $\cos\delta$ \lsim 0.70. The parameters f_B{\cal B}_{\B}^{1/2} and $\cos\delta$ are strongly positively correlated.Comment: 9 pages + 1 figure available upon request, HU-TFT-94-3

Effect of granularity on the insulator-superconductor transition in ultrathin Bi films

We have studied the insulator-superconductor transition (IST) by tuning the thickness in quench-condensed $Bi$ films. The resistive transitions of the superconducting films are smooth and can be considered to represent "homogeneous" films. The observation of an IST very close to the quantum resistance for pairs, $R_{\Box}^N \sim h/4e^2$ on several substrates supports this idea. The relevant length scales here are the localization length, and the coherence length. However, at the transition, the localization length is much higher than the superconducting coherence length, contrary to expectation for a "homogeneous" transition. This suggests the invalidity of a purely fermionic model for the transition. Furthermore, the current-voltage characteristics of the superconducting films are hysteretic, and show the films to be granular. The relevant energy scales here are the Josephson coupling energy and the charging energy. However, Josephson coupling energies ($E_J$) and the charging energies ($E_c$) at the IST, they are found to obey the relation $E_J < E_c$. This is again contrary to expectation, for the IST in a granular or inhomogeneous, system. Hence, a purely bosonic picture of the transition is also inconsistent with our observations. We conclude that the IST observed in our experiments may be either an intermediate case between the fermioinc and bosonic mechanisms, or in a regime of charge and vortex dynamics for which a quantitative analysis has not yet been done.Comment: accepted in Physical Review