  Thermal engineering of quantum devices has attracted much attention since the
discovery of quantized thermal conductance of phonons. Although easily
submerged in numerous excitations in macro-systems, quantum behaviors of
phonons manifest in nanoscale low-dimensional systems even at room temperature.
Especially in nano transport devices, phonons move quasi-ballistically when the
transport length is smaller than their bulk mean free paths. It has been shown
that phonon nonequilibrium Green's function method (NEGF) is effective for the
investigation of nanoscale quantum transport of phonons. In this tutorial
review two aspects of thermal engineering of quantum devices are discussed
using NEGF methods. One covers transport properties of pure phonons; the other
concerns the caloritronic effects, which manipulate other degrees of freedom,
such as charge, spin, and valley, via the temperature gradient. For each part,
we outline basic theoretical formalisms first, then provide a survey on related
investigations on models or realistic materials. Particular attention is given
to phonon topologies and a generalized phonon NEGF method. Finally, we conclude
our review and summarize with an outlook.
