Generalized first-principles method to study near-field heat transfer mediated by Coulomb interaction

We present a general microscopic first-principles method to study the Coulomb-interaction-mediated heat transfer in the near field. Using the nonequilibrium Green's function formalism, we derive Caroli formulas for heat transfers between materials with translational invariance. The central physical quantities are the screened Coulomb potential and the spectrum function of polarizability. Within the random phase approximation, we calculate the polarizability using the linear response density functional theory and obtain the screened Coulomb potential from a retarded Dyson equation. We show that the heat transfer mediated by the Coulomb interaction is consistent with that of the $p$-polarized evanescent waves which dominate the heat transfer in the near field. We adopt single-layer graphene as an example to calculate heat transfers between two parallel sheets separated by a vacuum gap $d$. Our results show a saturation of heat flux at the extreme near field which is different from the reported $1/d$ dependence for local response functions. The calculated heat flux is up to $5\times {10}^4$ times more than the blackbody limit, and a $1/d^2$ dependence is shown at large separations. From the spectrum of energy current density, we infer that the near-field enhancement of heat transfer stems from electron transitions around the Fermi energy. With a uniform strain, the heat flux increases for most of the distances, while a negative correlation is shown at the moderate field. Our method is valid for inhomogeneous materials in which the macroscopic response function used in conventional theory of fluctuational electrodynamics would fail at the subnanometer scale.

Figure 1

Sketch of the unit simulation box of two parallel plates with a vacuum gap of $d$. Each of the plates is in its own internal thermal equilibrium state; that is, plate 1 has temperature $T_1$, and plate 2 has temperature $T_2$. $a$, $b$, and $c$ are lattice constants of the $x$, $y$, and $z$ directions, respectively.

Figure 2

Distance dependence of the near-field heat flux ratio between two parallel graphene sheets. The temperature is fixed at $T_1=1000$ K and $T_2=300$ K. The red solid curve shows results obtained from ab initio first-principles calculation, and the blue solid curve represents results obtained from a local response function of graphene in the Dirac model. The red and blue dashed lines show the asymptotic $1/d^2$ and $1/d$ dependence of heat flux at small and large separations, respectively.

Figure 3

The Coulomb (solid curve, left axis, $d=100$ nm) and blackbody radiative (dashed curve, right axis) energy current density of graphene with different temperatures. The left and right axes have the same scale of ticks but differ by 4 orders of magnitude.

Figure 4

Strain effect on the Coulomb heat flux between two parallel single-layer graphene sheets with different gap sizes. The horizontal axis is the magnitude of strain in percent, and the vertical axis is the percentage change of heat flux after strain is applied.