Near-field thermal radiation transfer controlled by plasmons in graphene

It is shown that thermally excited plasmon-polariton modes can strongly mediate, enhance, and tune the near-field radiation transfer between two closely separated graphene sheets. The dependence of near-field heat exchange on doping and electron relaxation time is analyzed in the near infrared within the framework of fluctuational electrodynamics. The dominant contribution to heat transfer can be controlled to arise from either interband or intraband processes. We predict maximum transfer at low doping and for plasmons in two graphene sheets in resonance, with orders-of-magnitude enhancement (e.g., ${10}^2$ to ${10}^3$ for separations between 0.1 $\mu \text{m}$ and 10 nm) over the Stefan-Boltzmann law, known as the far-field limit. Strong, tunable, near-field transfer offers the promise of an externally controllable thermal switch as well as a novel hybrid graphene-graphene thermoelectric/thermophotovoltaic energy conversion platform.

Figure 1

(a) Schematic diagram of the radiation transfer problem: a suspended sheet of graphene at temperature $T_1$ is radiating to another suspended graphene sheet at temperature $T_2$ and distance $D$ away. k-vector components are $q$,$\gamma$, for the parallel and perpendicular component, respectively. (b) Real and imaginary parts of graphene $p$-polarization reflection coefficient for $\mu =0.5$ eV, $T=300$ K, and $\tau ={10}^{-13}$ s. Dashed line is the vacuum plasmon dispersion relation (4) for the graphene sheet. Insets show the real and imaginary part of reflectivity at $q\approx 50\text{eV}/\hslash c$ as a function of $\omega$.

Figure 2

Contour plot of the integrand (a.u.) in $f_p\left(\omega \right)$ from Eq. (2), for two graphene sheets at $T_{1,2}=300$ K, separated by $D=10$ nm. Chemical potentials are ${\mu }_1=0.5$ eV, while ${\mu }_2$ is different for each plot. Dashed lines correspond to the vacuum plasmon dispersion relations for the bottom (1) and the top (2) graphene sheet.

Figure 3

(a) Spectral transfer function $f_p\left(\omega \right)$ from Eq. (2), for plasmons in two graphene sheets at resonance, ${\mu }_{1,2}=\mu$, ${\tau }_{1,2}=\tau$; $T_{1,2}=300$ K, $D=10$ nm. Solid green line corresponds to the ${\mu }_{1\left(2\right)}=0.3\left(0.5\right)$ eV, ${\tau }_{1\left(2\right)}={10}^{-13}\left({10}^{-14}\right)$ s case. (b) Contour plot of the integrated ratio of the near-field transfer between two graphene sheets, $H_{gg}^{nf}$, and the far-field transfer between two blackbodies, $H_{BB}^{ff}$ for plasmons in resonance (left, ${\mu }_{1,2}=0.1$ eV) and out of resonance [right, ${\mu }_{1\left(2\right)}=0.1\left(0.3\right)$ eV]. Here, $T_2=300\text{K}\text{and}{\tau }_{1,2}={10}^{-13}\text{s}$.