Detection of collective modes in unconventional superconductors using tunneling spectroscopy

We propose using tunneling spectroscopy with a superconducting electrode to probe the collective modes of unconventional superconductors. The modes are predicted to appear as peaks in $dI/dV$ at voltages given by $eV={\ensuremath{\omega}}_{i}/2$ where ${\ensuremath{\omega}}_{i}$ denotes the mode frequencies. This may prove to be a powerful tool to investigate the pairing symmetry of unconventional superconductors. The peaks associated with the collective modes appear at fourth order in the single-particle tunneling-matrix element. At the same fourth order, multiple Andreev reflection (MAR) leads to peaks at voltage equal to the energy gaps, which, in BCS superconductors, coincides with the expected position of the amplitude (Higgs) mode. The peaks stemming from the collective modes of unconventional superconductors do not suffer from this coincidence. For scanning tunneling microscopes, we estimate that the magnitude of the collective mode contribution is smaller than the MAR contribution by the ratio of the energy gap to the Fermi energy. Moreover, there is no access to the mode dispersion. Conversely, for planar tunnel junctions the collective mode peak is expected to dominate over the MAR peak, and the mode dispersion can be measured. We discuss systems where the search for such collective modes is promising.