  We calculate the collective mode spectrum in models of superconductors with
attractive interactions in s-and d channels as a function of their relative
strength, across a phase diagram that includes transition between s, s+id, and
d-wave ground states. For one-band systems, we recover the largely known
results for the phase, amplitude, and Bardasis-Schrieffer modes of pure s or
d-states, and show how the well-defined Bardasis-Schrieffer mode softens near
the s + id phase boundary and evolves in a characteristic manner through the s
+ id phase as a mixed symmetry mode. For two-band systems, we consider a model
of hole-doped Fe-based superconductors, and find in the case of an s-wave
ground state a well-defined Bardasis-Schrieffer mode below the lowest gap edge,
as well as a second, damped mode of this type between the two gap energies.
Both modes soften as the s + id phase is approached, and only a single
"mixed-symmetry Bardasis-Schrieffer mode" below the pairbreaking continuum
propagates in the s + id phase itself. These modes coexist with a damped
Leggett mode with collective frequency between the two gap scales. In the pure
d-state, no Bardasis-Schrieffer type s excitonic mode exists at low T. We
briefly discuss Raman scattering experiments and how they can be used to
identify an s + id state, and to track the evolution of competing s- and d-
interactions in these systems.
