Role of disorder in plasmon-assisted near-field heat transfer between two-dimensional metals

Abstract

We perform a theoretical study of the near-field heat transfer between two atomically thin metallic layers, isolated galvanically but coupled by the Coulomb interaction, within the framework of fluctuational electrodynamics in the Coulomb limit. We clarify the role of disorder and spatial dispersion, and identify several distinct regimes of the heat transfer. We find that the plasmon contribution to the heat current is suppressed in both the clean and diffusive limits, but dominates in a parametrically wide crossover region at sufficiently high temperatures.

Near field versus far field in radiative heat transfer between two-dimensional metals

“…Since λT = 7.6 μm at T = 300 K, in such structure the crossover to electrostatics occurs at a few nanometers. We note that in the (ld) regime, the heat transfer is mainly determined by rather small wave vectors [18], so that even at d = 1 nm, we obtain 1/k 100 nm, and the local response assumption should still be formally valid. However, at nanometric distances, other physical effects may come into play (electron or phonon tunneling, surface roughness, etc.…”

“…(3a)-(3d), with labels corresponding to lowtemperature plasmonic, high-temperature plasmonic, lowtemperature diffusive, and high-temperature diffusive, are the TM evanescent contributions that remain in the Coulomb limit and were calculated in Ref. [18]. Equations (3e) and (3f) (with labels corresponding to low-temperature traveling electric and high-temperature traveling electric) are the traveling TE contributions which dominate over the traveling TM contributions by the logarithmic factor ln(1/G).…”

“…In Eqs. (3), ζ (x) is the Riemann zeta function, and L(x) is a slow logarithmic function approximately given by [18] L(x) ≈…”

“…Equation ( 1) neglects (i) the spatial dispersion of the conductivity, and (ii) field variation over the layer thickness. For atomically thin materials, such as doped graphene or transition metal dichalcogenides, condition (ii) is irrelevant and condition (i) holds at distances d √ a 2D (a 2D and being the 2D screening radius and the electron mean free path, respectively) [18]. For thin but macroscopic layers of conventional metals, condition (ii) imposes that the thickness must be small compared both to the typical wavelength of the waves dominating the heat transfer (which may be rather short for evanescent waves) and to the skin depth at the typical frequency of these waves, while condition (i) requires the wavelength and the skin depth to be longer than the electron mean free path in the metal.…”

“…The importance of magnetic coupling in the near-field heat transfer between well-conducting metals has been emphasized [11,12]. In the extreme near-field limit, heat transfer due to the electrostatic Coulomb interaction has also been studied [13][14][15][16][17][18][19].…”