Plasmonic thermal transport in graphene nanodisk waveguides

The thermal radiation properties of guided surface plasmons in one-dimensional co-planar graphene nanodisk arrays are predicted using a semi-analytical electrostatic model. The plasmonic band structure contains nonlocalized dispersion bands that are well-described by the electrostatic model for disk diameters smaller than 200 nm. A nondimensional model is proposed that enables systematic analysis of the waveguiding properties based on scaling laws. The thermal transport is dominated by the lowest-order radial modes and can be controlled by tuning the disk size, the substrate optical properties, and graphene's doping concentration and electron mobility. The maximum predicted thermal conductivity and thermal diffusivity are 4.$5{\mathrm{W}\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ and $1.3\times {10}^{-3}{\mathrm{m}}^2$/s, orders of magnitude larger than predictions of thermal transport by guided surface plasmon- or phonon-polaritons in other materials. The results suggest that graphene surface plasmons, which can be thermally-activated at room temperature, are a suitable platform for tunable and fast thermal transport, with potential application as photon-based thermotronic interconnects.

Figure 1

(a) Dispersion relation and (b) decay lengths of the lowest radial modes $\left(k=0\right)$ for a one-dimensional periodic co-planar array of graphene disks $(E_f=1.0$ eV, $D=100$ nm, and $\mathrm{\Delta }x=110$ nm). The dispersion for EM-waves propagating in vacuum $\left({\varepsilon }_1=1.0\right)$ and in a dielectric substrate $\left({\varepsilon }_2=2.4\right)$ are included in (a) as a reference, where $c_0$ is the speed of light in vacuum. The inset of (b) shows the decay length in terms of number of cycles completed, $L_p/{\lambda }_{sp}$, for the fundamental dipole modes, $(k,l)=(0,\pm 1)$.

Figure 2

Surface plasmon dispersion relations and decay lengths of the fundamental dipole modes $\left[\right(k,l)=(0,\pm 1\left)\right]$ for an array of graphene nanodisks in vacuum with $\mathrm{\Delta }x/D=1.1,E_f=1.0$ eV, ${\varepsilon }_1={\varepsilon }_2=1$, and (a) $D=100$ and (b) 500 nm. The lines correspond to the full dipole-dipole interaction model from Eq. (S18) and the open circles correspond to the electrostatic model from Eq. (S8).

Figure 3

Nondimensional (a) dispersion and (b) decay lengths for an array of co-planar graphene disks $\left(\mathrm{\Delta }x/D=1.1\right)$ for the fundamental dipole modes, $(k,l)=(0,\pm 1)$, considering different disk diameters and carrier concentrations. The value of ${\chi }_T\equiv \hslash {\omega }_R{k}_{\text{B}}T/E_f^2$ is provided in the lower right-hand corner of (a) for each case.

Figure 4

(a) Heat capacity and (b) thermal conductivity of co-planar disk arrays for different diameters and separations obtained from the electrostatic (ES) model. The data in open circles in (b) correspond to thermal conductivity predictions that consider radiation damping effects (Rad. damp.). $T=300$ K, $E_f=1.0$ eV, and ${\varepsilon }_2=2.4$ for all calculations.

Figure 5

Frequency-dependent thermal conductivity accumulation, $k_t\left(\omega \right)$, for $\mathrm{\Delta }x/D=1.1,E_f=1.0$ eV, ${\varepsilon }_2=2.4$, and (a) $D=100$ and (b) 500 nm. The contribution from each band is labeled by its angular index $l$.

Figure 6

(a) Thermal conductivity and (b) thermal diffusivity as a function of the Fermi level in a graphene disk array with $\mathrm{\Delta }x/D=1.1$ and disk diameters of 100, 500, and 1000 nm on a dielectric substrate $\left({\varepsilon }_2=2.4\right)$.

Figure 7

(a) Nondimensional dispersion relations of the fundamental dipole modes. The dispersion bands obtained from our electrostatic model are indicated by the circles, where open and filled correspond to longitudinal and transverse modes. The continuous lines are the bands obtained from fitting to Eq. (A1). (b) Fitting constants for the model of Eq. (A2).