[Paper Review] Nonlinearities and Noise-Signal Relations in Electronic Heat Transport via Molecules

Arthur Luniewski, Rita Aghjayan+1 more|arXiv (Cornell University)|Jan 25, 2016

Thermal properties of materials4 references3 citations

TL;DR

This paper investigates nonlinear heat transport and noise-signal relations in molecular junctions under strong non-equilibrium conditions using the non-equilibrium Green's function (NEGF) and scattering formalism. It derives second-order nonlinear corrections to electronic heat flux and noise power spectral density, revealing limited validity of ballistic Fourier's law and fluctuation-dissipation theorem in molecular systems, and establishes generalized signal-signal, noise-signal, and noise-noise relations applicable to nanoscale electron-mediated heat flow.

ABSTRACT

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.

Motivation & Objective

• To analyze electronic heat transport in molecular junctions under strong non-equilibrium conditions due to large temperature differences between reservoirs.
• To investigate the breakdown of linear response theories such as ballistic Fourier's law and the fluctuation-dissipation theorem in molecular-scale systems.
• To develop a systematic method for computing nonlinear corrections to heat flux and noise power spectral density up to second order in temperature difference.
• To derive and test generalized signal-signal, noise-signal, and noise-noise relations applicable to electron-mediated heat transport in nanoscale systems.

Proposed method

• Employing the non-equilibrium Green's function (NEGF) technique to calculate the transmission probability in molecular junctions coupled to metallic reservoirs.
• Using the scattering (Landauer) formalism to compute electronic heat flux and its dynamical noise properties.
• Applying a Taylor series expansion method to derive second-order nonlinear corrections to heat flux and noise power spectral density with respect to temperature difference.
• Deriving generalized relations between heat flux (signal), noise power spectral density, and their cross-correlations under strongly non-equilibrium conditions.
• Validating the derived relations numerically for model molecular junctions under varying temperature gradients.
• Extending the formalism to higher-order terms for future studies of complex nonlinear thermal and electro-thermal effects.

Experimental results

Research questions

• RQ1 To what extent does the ballistic Fourier's law hold in molecular junctions under large temperature differences?
• RQ2 How do nonlinear corrections to the electronic heat flux and its noise power spectral density scale with temperature difference in molecular systems?
• RQ3 What are the generalized signal-signal, noise-signal, and noise-noise relations in electron-mediated heat transport under strong non-equilibrium conditions?
• RQ4 Can the fluctuation-dissipation theorem be reliably applied to electronic heat transport in molecular nanostructures?
• RQ5 How can higher-order nonlinear effects in thermal transport be systematically modeled and computed in nanoscale systems?

Key findings

• The ballistic Fourier's law shows limited applicability in molecular junctions due to strong nonlinearities arising from large temperature gradients.
• The fluctuation-dissipation theorem breaks down under strongly non-equilibrium conditions in molecular systems, invalidating standard linear-response noise assumptions.
• Second-order nonlinear corrections to heat flux and noise power spectral density are significant and must be included for accurate modeling of nanoscale thermal transport.
• Generalized signal-signal, noise-signal, and noise-noise relations are derived and numerically validated, extending known linear relations to nonlinear regimes.
• The proposed method based on Taylor expansion of the transmission probability enables systematic computation of higher-order nonlinear effects in thermal transport.
• The formalism is extendable to higher-order terms, offering a pathway to model complex nonlinear thermal and electro-thermal phenomena in molecular electronics.