Phonon imaging in superconducting Pb crystals: Absence of large gap anisotropy and spin-density waves

摘要: We show that anisotropies in the electronic structure of a superconducting metal can be probed with ballistic acoustic phonons at low temperatures. were motivated by possibility Pb has narrow valleys lowered gap, possibly caused spin-density wave (SDW) postulated Overhauser and Daemen [Phys. Rev. Lett. 61, 1885 (1988)]. Our experiments analysis on crystals different thickness, plus results phonon-frequency filter, do not support their idea deep gap parameter. For spherical Fermi surface, phonon scattering would isotropic but for highly anisotropic surface Pb, rate depends direction vector, $\mathbf{q}$. To observe this anisotropy, we perform phonon-imaging high-purity cooled between 1.45 2.1 K. At temperature mean-free path extend to millimeter distances if its energy is less than $2{\ensuremath{\Delta}}_{o}$. In regime, are absorbed thermally excited quasiparticles surface. Phonon images striking pattern absorption becomes stronger as raised. The anisotropy explained calculation actual without recourse SDWs. preliminary dependences reported paper, which assumes doing equilibrium lattice temperature, much weaker low-temperature form $\text{exp}(\ensuremath{-}{\ensuremath{\Delta}}_{o}/{k}_{B}T)$ predicted BCS theory superconductivity. Even accounting inherent from isotopes crystal, find path-length dependence phonon-absorption coefficient inconsistent SDW valleys. A filter experiment designed attenuate eject such clearly supports conclusion. resolution anomalous sample-length dependences, measurement phonon-imaging, following paper.