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Register a new userOn the Question of Coincidence Between Energy Gaps and Kohn Anomalies
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Recently, neutron scattering spin echo measurements have provided high resolution data on the temperature dependence of the linewidth $Gamma({bf q},T)$ of acoustic phonons in conventional superconductors Pb and Nb. [P. Aynajian, et al, Science 319, 1509 (2008)]. At low temperatures the merging of the $2Delta(T)$ structure in the linewidth with a peak associated with a low lying $hbaromega_{bf q_{KA}}$ Kohn anomaly suggested a coincidence between $2Delta(0)$ and $hbaromega_{bf q_{KA}}$ in Pb and Nb. Here we carry out a standard BCS calculation of the phonon linewidth to examine its temperature evolution and explore how close $2Delta(0)/hbaromega_{bf q_{KA}}$ must be to unity in order to be consistent with the neutron data.
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The momentum and temperature dependence of the lifetimes of acoustic phonons in the elemental superconductors Pb and Nb was determined by resonant spin-echo spectroscopy with neutrons. In both elements, the superconducting energy gap extracted from these measurements was found to converge with sharp anomalies originating from Fermi-surface nesting (Kohn anomalies) at low temperatures. The results indicate electron many-body correlations beyond the standard theoretical framework for conventional superconductivity. A possible mechanism is the interplay between superconductivity and spin- or charge-density-wave fluctuations, which may induce dynamical nesting of the Fermi surface.
A comparison between the single particle spectrum of the discrete Bardeen-Cooper-Schrieffer (BCS) model, used for small superconducting grains, and the spectrum of a paradigmatic model of Single Excitation Superradiance (SES) is presented. They are both characterized by an equally spaced energy spectrum (Picket Fence) where all the levels are coupled between each other by a constant coupling which is real for the BCS model and purely imaginary for the SES model. While the former corresponds to the discrete BCS-model describing the coupling of Cooper pairs in momentum space and it induces a Superconductive regime, the latter describes the coupling of single particle energy levels to a common decay channel and it induces a Superradiant transition. We show that the transition to a Superradiant regime can be connected to the emergence of an imaginary energy gap, similarly to the transition to a Superconductive regime where a real energy gap emerges. Despite their different physical origin, it is possible to show that both the Superradiant and the Superconducting gaps have the same magnitude in the large gap limit. Nevertheless, some differences appear: while the critical coupling at which the Superradiant gap appears is independent of the system size $N$, for the Superconductivity gap it scales as $(ln N)^{-1}$. The presence of a gap in the imaginary energy axis between the Superradiant and the Subradiant states shares many similarities with the standard gap on the real energy axis: the superradiant state is protected against disorder from the imaginary gap as well as the superconducting ground state is protected by the real energy gap. Moreover we connect the origin of the gapped phase to the long-range nature of the coupling between the energy levels.
The anomalous high-energy dispersion of the conductance band in the high-Tc superconductor Pb-Bi2212 has been extensively mapped by angle-resolved photoemission (ARPES) as a function of excitation energy in the range from 34 to 116 eV. Two distinctive types of dispersion behavior are observed around 0.6 eV binding energy, which alternate as a function of photon energy. The continuous transitions observed between the two kinds of behavior near 50, 70, and 90 eV photon energies allow to exclude the possibility that they originate from the interplay between the bonding and antibonding bands. The effects of three-dimensionality can also be excluded as a possible origin of the excitation energy dependence, as the large period of the alterations is inconsistent with the lattice constant in this material. We therefore confirm that the strong photon energy dependence of the high-energy dispersion in cuprates originates mainly from the photoemission matrix element that suppresses the photocurrent in the center of the Brillouin zone.
We examine experiments on energy gaps in high temperature superconductors (HTSC) in terms of experimental probes that utilize momentum, position, or neither. Experiments on very high quality mechanical tunnel junctions show a sharp energy gap with a maximum anisotropy of ~ 10%, while ultrahigh precision ARPES experiments show 100% anisotropy (d-wave pairing). We resolve this conbflict by showing that the latter result is caused by the momentum-projective nature of ARPES and glassy orthorhombic dopant correlations. The latter appear to be a universal feature of the intermediate phase tha is responsible for HTSC. Apparent large inconsistencies between position-projective STM gap data and tunnel junction data on severely underdoped BSCCO are also resolved.
I present the detailed behavior of phonon dispersion curves near momenta which span the electronic Fermi sea in a superconductor. I demonstrate that an anomaly, similar to the metallic Kohn anomaly, exists in a superconductors dispersion curves when the frequency of the phonon spanning the Fermi sea exceeds twice the superconducting energy gap. This anomaly occurs at approximately the same momentum but is {it stronger} than the normal-state Kohn anomaly. It also survives at finite temperature, unlike the metallic anomaly. Determination of Fermi surface diameters from the location of these anomalies, therefore, may be more successful in the superconducting phase than in the normal state. However, the superconductors anomaly fades rapidly with increased phonon frequency and becomes unobservable when the phonon frequency greatly exceeds the gap. This constraint makes these anomalies useful only in high-temperature superconductors such as $rm La_{1.85}Sr_{.15}CuO_4$.
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