  I report that thermal single-barrier (TSB) and thermal double-barrier (TDB)
structures (formed, for example, by inserting one or two regions of a few Ge
monolayers in Si) provide both a suppression of the phonon transport as well as
a resonant-thermal-transport effect. I show that high-frequency phonons can
experience a traditional double-barrier resonant tunneling in the TDB
structures while the formation of Fabry-Perot resonances (at lower frequencies)
causes quantum oscillations in the temperature variation of both the TSB and
TDB thermal conductances $\sigma_{\text{TSB}}$ and $\sigma_{\text{TDB}}$.
