Spectroscopy of phonons in dirty superconducting contacts

The nonlinearities of current-voltage characteristics (IVC) of superconducting niobium point contacts for voltages of the order of the characteristic phonon frequencies are investigated. It is shown that in limiting by dirty contacts ${{l}_{1}}\ll d$ , (${{l}_{1}}$ is the momentum mean-free path of electrons), features are observed on the IVC corresponding to maxima in the first or second derivatives and are situated at energies close to the characteristic phonon energies. These features are due to the energy dependence of the excess current, since the nonlinearity of the IVC in the normal state is several times smaller in absolute magnitude, and its second derivative is monotonic. For a contact diameter $d$ of the order of several tens of angstroms (the contact resistance is of the order of 100 $\Omega $), the thermal effects can be neglected. It is assumed that in the region of the constriction, the characteristic lengths of the system satisfy the relation $\xi \gtrsim d>{{\Lambda }_{\varepsilon }}$ (${{\Lambda }_{\varepsilon }}$ is the diffusion length for energy relaxation of the electrons, $\xi$ is the coherence length) which makes possible inelastic transitions of electrons between pair chemical potentials differing in energy by an account $eV$ ($V$ is the voltage drop across the contact)
Comment: 8 pages, 4 figures