Exponential suppression of thermal conductance using coherent transport and heterostructures

Coherent thermal transport, using thermal channels with length smaller than the mean-free path of the thermal carriers, is important for fundamental study of thermal processes and for new device opportunities in thermal management.1–11 In this Brief Report, we consider a coherent thermal channel formed by cascading a series of nonidentical photonic crystals. We show that its thermal conductance can be suppressed exponentially with respect to the channel length l. This is fundamentally different from the incoherent process, where the conductance typically decreases as 1 / l.12 We therefore demonstrate that coherent processes can be very effective in suppressing thermal conductance. This result also indicates that an aperiodic coherent thermal channel is qualitatively different from all previously considered coherent thermal channels1–10 including periodic multilayer photonic crystals as we previously considered,9,10 where the intrinsic thermal conductance of the channels were all independent of the channel length l. As a concrete implementation, we utilize the concept of photonic crystal heterostructure,13–15 and consider multilayer systems consisting of a total of N different photonic crystals, as illustrated in Fig. 1 a . All crystals consist of alternate periodic layers of vacuum and dielectric. The use of vacuum ensures that heat transfer is carried only by photons. The dielectric can be silicon n=nSi=3.42 . For photon frequencies within the blackbody spectrum at room temperature, silicon has very little dispersion and dissipation, with typical attenuation length exceeding millimeter.16 Consequently photonic thermal transport should be coherent across the entire structure.9,10 For the structure shown in Fig. 1 a , we assume that all crystals have the same period a. The mth crystal has a dielectric layer thickness dsm and a vacuum layer thickness dvm. At either ends of the structure, we have two semiinfinite photonic crystals. In between these two ends, there can be a series of crystals cascaded together, each having the same number of periods NP and hence the same total thickness. Thus the length of the channel is proportional to N−2. We also assume that the two crystals at the ends are maintained at temperatures of T and T+dT, respectively. The three-dimensional 3D thermal conductance per unit area is then defined as G3D T =dQ T /dT, where dQ T is the heat flux per unit area. In such multilayer structures, each photon state is characterized by three parameters: frequency , wave number k in the direction parallel to the layers, and polarization =s , p. The s and p polarizations have electric and magnetic fields parallel to the layers, respectively.17 Summing over all photon states, we have10