  We explore the physics of thermal impedance matching at the interface between
two dissimilar materials by controlling the properties of a single atomic mass
or bond. The maximum thermal current is transmitted between the materials when
we are able to decompose the entire heterostructure solely in terms of
primitive building blocks of the individual materials. Using this approach, we
show that the minimum interfacial thermal resistance arises when the
interfacial atomic mass is the arithmetic mean, while the interfacial spring
constant is the harmonic mean of its neighbors. The contact induced broadening
matrix for the local vibronic spectrum, obtained from the self-energy matrices,
generalizes the concept of acoustic impedance to the nonlinear phonon
dispersion or the short-wavelength (atomic) limit.
