Electronic heat tunneling between two metals beyond the WKB approximation

Abstract

Two metals at different temperatures separated by large gaps exchange heat under the form of electromagnetic radiation. When the separation distance is reduced and they approach contact (nanometer and sub-nanometer gaps), electrons and phonons can tunnel between the bodies, competing and eventually going beyond the flux mediated by thermal photons. In this transition regime the accurate modeling of electronic current and heat flux is of major importance. Here we show that, in order to quantitatively model this transfer, a careful description of the tunneling barrier between two metals is needed and going beyond the traditional WKB approximation is also essential. We employ analytical and numerical approaches to model the electronic potential between two semi-infinite jellium planar substrates separated by a vacuum gap in order to calculate the electronic heat flow and compare it with its radiative counterpart described by near-field radiative heat transfer. We demonstrate that the results for heat flux and electronic current density are extremely sensitive to both the shape and height of the barrier, as well as the calculation scheme for the tunneling probability, with variations up to several orders of magnitude. Using the proximity force approximation, we also provide estimates for tip-plane geometries. The present work provides realistic models to describe the electronic heat flux, in the scanning-thermal-microscopy experiments.

arXiv comment12 pages, 10 figures

References in corpus (14)

• A real-space grid implementation of the Projector Augmented Wave method
• Surface Electromagnetic Waves Thermally Excited: Radiative Heat Transfer, Coherence Properties and Casimir Forces Revisited in the Near Field
• Near-field heat transfer in a scanning thermal microscope
• Towards a black body for near-field thermal radiation
• Near-field Radiative Heat Transfer in Many-Body Systems
• A mesoscopic description of radiative heat transfer at the nanoscale
• Effects of spatial dispersion in near-field radiative heat transfer between two parallel metallic surfaces
• Fundamental limits for non-contact transfers between two bodies
• Extreme Near-Field Heat Transfer Between Gold Surfaces
• Atomistic simulation of phonon heat transport across metallic nanogaps
• Contribution of the acoustic waves to near-field heat transfer
• First-principles calculations of phonon transport across a vacuum gap
• Role of Nottingham effect in the heat transfer in extreme near-field regime
• Atomistic modeling of extreme near-field heat transport across nanogaps between two polar dielectric materials

Cited by in corpus (2)

• Extreme near-field heat transfer between silica surfaces
• Electron tunneling induced thermoelectric effects