  Clock-comparison experiments are among the sharpest existing tests of Lorentz
symmetry in matter. We characterize signals in these experiments arising from
modifications to electron or nucleon propagators and involving Lorentz- and
CPT-violating operators of arbitrary mass dimension. The spectral frequencies
of the atoms or ions used as clocks exhibit perturbative shifts that can depend
on the constituent-particle properties and can display sidereal and annual
variations in time. Adopting an independent-particle model for the electronic
structure and the Schmidt model for the nucleus, we determine observables for a
variety of clock-comparison experiments involving fountain clocks,
comagnetometers, ion traps, lattice clocks, entangled states, and antimatter.
The treatment demonstrates the complementarity of sensitivities to Lorentz and
CPT violation among these different experimental techniques. It also permits
the interpretation of some prior results in terms of bounds on nonminimal
coefficients for Lorentz violation, including first constraints on nonminimal
coefficients in the neutron sector. Estimates of attainable sensitivities in
future analyses are provided. Two technical appendices collect relationships
between spherical and cartesian coefficients for Lorentz violation and provide
explicit transformations converting cartesian coefficients in a laboratory
frame to the canonical Sun-centered frame.
