Nonlinearities and Noise-Signal Relations in Electronic Heat Transport via Molecules

We examine the electronic heat transport phenomena in nanoscale junctions composed of organic molecules coupled to two metallic reservoirs of different temperatures. The electronic heat flux and its dynamical noise properties are calculated within the scattering (Landauer) formalism with the transmission probability determined by using non-equilibrium Green's functions (NEGF technique). The method based on Taylor series expansion is used to determine nonlinear corrections to the electronic heat flux and its noise power spectral density with up to the second order terms with respect to the temperature difference. Our results show only limited applicability of ballistic Fourier's law and fluctuation-dissipation theorem to heat transport in molecular systems. We derived and tested numerically several signal-signal, noise-signal, and noise-noise relations applicable to nanoscale heat flow carried by electrons at strongly non-equilibrium conditions (similar formulas are expected for phonons and photons). Importantly, the special treatment proposed by us may be extended to higher order terms in order to address a variety of problems related to nonlinear thermal and electro-thermal effects which may occur at nanoscale.