Coherent lattice vibrations in superconductors

A recent analysis has shown that the pair wavefunction within the BCS theory may be represented in real-space as a spherical electronic orbital (on the scale of the coherence length ξ0ξ0) coupled to a standing-wave lattice vibration with wavevector 2kF2kF and a near-resonant phonon frequency. The present paper extends this picture to a coherent pattern of phonon standing-waves on the macroscopic scale, with electrons forming Bloch waves and an energy gap much like those in the classic band theory of crystals. These parallel planes form a diffractive waveguide permitting electron waves to traveling parallel to the planes, corresponding to lossless supercurrent. A similar picture may be extended to unconventional superconductors such as the cuprates, with an array of standing spin waves rather than phonons. Such coherent lattice vibrations should be universal indicators of the superconducting state, and should be observable below TcTc using X-ray and neutron diffraction techniques. Further implications of this picture are discussed.