Near-field radiative heat transfer in graphene plasmonic nanodisk dimers

Near-field thermal radiation mediated by surface plasmons in parallel graphene nanodisk dimers is studied using a semianalytical model under the electrostatic approximation. The radiative heat transfer between two disks as a function of the distance between them in coaxial and coplanar configurations is first considered. Three regimes are identified and their extents determined using nondimensional analysis. When the edge-to-edge separation is smaller than the disk diameter, near-field coupling and surface plasmon hybridization lead to an enhancement of the radiative heat transfer by up to four orders of magnitude compared to the Planck blackbody limit. A mismatch in the disk diameters affects the plasmonic mode hybridization and can either diminish or enhance the near-field radiation. Destructive interference between eigenmodes that emerge when the relative orientation between disks is varied can induce a twofold reduction in the radiative heat transfer. In all configurations, the radiative heat transfer properties can be controlled by tuning the disk size/orientation, the substrate optical properties, and graphene's doping concentration and electron mobility.

Figure 1

(a) Real part of the normalized electric-field intensity in the direction perpendicular to the plane of the disk, $E_z/{\left|E_z\right|}_{\text{max}}$, showing the surface charge distribution of the localized surface plasmon modes $(k,l)=(0,\pm 1),(0,\pm 2),(1,\pm 1)$, and $(1,\pm 2)$ in an isolated graphene disk $(D=100$ nm, $E_f=0.6$ eV). Hybrid surface plasmon resonant frequencies of two graphene nanodisks in (b) coaxial and (c) coplanar configurations as a function of the gap between them $(D=100$ nm, $E_f=0.6$ eV). A schematic diagram of the charge distribution of the lowest dipole mode, $(k,l)=(0,\pm 1)$, is drawn for each case, showing the form of the hybridized plasmon modes. Higher modes adopt similar hybridization behavior.

Figure 2

Near-field enhancement, $G_{\text{NF}}/G_{\text{BB}}$, of two coaxial graphene disks as a function of their separation $(D=100$ nm, $E_f=0.6$ eV). Inset: spectral radiative thermal conductance, $G_{\text{NF}}\left(\nu \right)$, showing the hybridization of the fundamental dipole mode $(k,l)=(0,\pm 1)$ at $\mathrm{\Delta }z/D=0.4$, 0.6, and 1.0.

Figure 3

(a) Near-field radiation enhancement between two coaxial graphene disks $(E_f=0.6$ eV) as a function of the distance $\mathrm{\Delta }z$ for disk diameters ranging from 50 to 500 nm. The blue line represents the near-field enhancement between two graphene sheets [17] with $E_f=0.6$ eV. (b) Near-field radiation enhancement between two coaxial graphene disks $(D=100$ nm) as a function of the distance $\mathrm{\Delta }z$ for Fermi levels ranging from 0.1 to 1.0 eV.

Figure 4

Nondimensional thermal conductance $G_{\text{NF}}/k_{\text{B}}{\omega }_R$ as a function of $\mathrm{\Delta }z/D$. The red dash-dotted lines mark the limits between the strong-coupling and transition regimes, ${(\mathrm{\Delta }z/D)}_{s\text{−}t}$, and between transition and weak-coupling regimes, ${(\mathrm{\Delta }z/D)}_{t\text{−}w}$. Here, ${(\mathrm{\Delta }z/D)}_{t\text{−}w}\approx 3.2$. In the inset, ${(\mathrm{\Delta }z/D)}_{s\text{−}t}$ is plotted as a function of $\hslash {\omega }_R/k_{\text{B}}T$, where the line serves as a guide to the eye.

Figure 5

Near-field enhancement for two coplanar graphene disks at different gaps $(D=100$ nm, $E_f=0.6$ eV). Inset: Spectral radiative thermal conductance showing the hybridization of the lowest dipole mode $(k,l)=(0,\pm 1)$ at $\mathrm{\Delta }x/D=1.1$, 1.2, and 1.5.

Figure 6

Effect of breaking symmetry in the disk diameters on the thermal conductance of the coaxial configuration. (a) Relative thermal conductance of a heterodimer with respect to that of a homodimer for $D_1=100$, $50<D_2<150$ nm. (b) Spectral thermal conductance of the heterodimer for selected cases.

Figure 7

Near-field enhancement, $G_{\text{NF}}/G_{\text{BB}}$, between two parallel graphene disks as a function of the positioning angle between centers $\theta$, for center-to-center separations, $\mathrm{\Delta }r$, of 105, 120, and 150 nm $(D=100$ nm, $E_f=0.6$ eV). (b) Spectral radiative thermal conductance at $\mathrm{\Delta }r=120$ nm showing the hybridization of the fundamental dipole mode, $(k,l)=(0,\pm 1)$, as a function of the angle.

Figure 8

Comparison of our electrostatic semianalytical model and BEM simulations for the flux spectrum of two graphene disks $(D=100$ nm, $E_f=0.6$ eV) in (a) a coaxial configuration with $\mathrm{\Delta }z=50$ nm, and (b) a coplanar configuration with $\mathrm{\Delta }x=110$ nm. The black line connecting the green circles serves as a guide to the eye.