  We consider a layered superconductor with a complex order parameter whose
phase switches sign from one layer to the next. This system is shown to exhibit
gapless superconductivity for sufficiently large interlayer pairing or
interlayer hopping. In addition, this description is consistent with
experiments finding signals of time-reversal symmetry breaking in
high-temperature superconductors only at the surface and not in the sample
bulk.
