Phonon Transport in Surface-disordered Nanowires with Temperature Gradient

One idea to improve the efficiency of thermoelectric nano-devices is decreasing the heat current by using nanowires with surface disorder. However, the influence of surface disorder on phonon transport is still unclear. We start from an exact mapping from a nanowire with a rough surface to a nanowire with smooth surface with additional pseudo-potential and expand the pseudopotential term systematically. The terms generated are typically either a shift, a dilation, or both and lead to scattering of the propagating phonon from these surface-disorder generated frequency and momentum dependent anharmonic phonons. In addition, in a thermoelectric device, the wire is connected to hot and cold leads with fixed temperatures. We then go beyond the effects of surface disorder and develop a framework to study non-equilibrium thermal current in the presence of large temperature differences across the wire that leads to a temperature gradient within the wire. We apply another exact mapping from a nanowire with a temperature gradient to a nanowire with uniform temperature with additional pseudo-potential, which can also be described as various momentum and frequency dependent anharmonic phonons interacting with the propagating phonons across the wire in the standard field-theory language. There are unusual temperature-dependent contributions that do not exist in the current field-theory formulation.