Active Temporal Control of Radiative Heat Transfer with Graphene Nanodisks

The ability to dynamically control the radiative transfer of heat at the nanoscale holds the key to the development of a diverse number of technologies, ranging from nanoscale thermal-management systems to improved thermophotovoltaic devices. Recently, graphene has emerged as an ideal material to achieve this goal, since it can be electrically doped to support surface plasmons, collective oscillations of the conduction electrons. These resonances produce large and spectrally narrow optical cross sections, which dictate the emission and absorption properties of the graphene nanostructure and, thus, the heat that it radiatively exchanges with other objects and the environment. For attainable levels of doping, the plasmons supported by graphene nanostructures naturally lie in the midinfrared part of the spectrum, which is the most relevant wavelength range for radiative heat transfer under realistic temperatures. Furthermore, these resonances are actively tunable, thus providing full dynamic control over the heat transfer. Motivated by this great potential, we present a comprehensive analysis of the temporal evolution of the radiative heat transfer between arrangements of graphene nanodisks, showing that it is possible to exploit the tunability of these structures to obtain actively controlled heat transfer scenarios not possible with conventional passive nanostructures. The results of this work provide a framework for achieving fully dynamical control over nanoscale radiative heat transfer and thus provide fundamental insights into this process.

Figure 1

Radiative heat transfer between two graphene nanodisks. (a) Schematics of the system under consideration, consisting of two graphene nanodisks of equal radius $R=15\mathrm{nm}$, separated by a distance $a=4R$. One disk has temperature $T_1=400\mathrm{K}$ and Fermi level $E_{F1}$, while the other is at $T_2=300\mathrm{K}$ with $E_{F2}$. The environment is held at $T_0=300\mathrm{K}$. (b) Power absorbed by disk $2$ at a time $t=0\mathrm{s}$ as a function of $E_{F1}$ and $E_{F2}$. (c) Line cuts from panel (b) for $E_{F1}=E_{F2}$ (black solid curve), $E_{F1}=0.28\mathrm{eV}$ (blue dashed curve), and $E_{F2}=0.28\mathrm{eV}$ (yellow dotted curve).

Figure 2

Directed heat transfer. (a) Temporal evolution of the temperatures of two nanodisks of radius $R=15\mathrm{nm}$ and center-to-center separation $a=4R$, as depicted in the upper schematics. One disk (red) begins at temperature $T_1=400\mathrm{K}$ and has $E_{F1}=0.28\mathrm{eV}$, while the other disk (blue) begins at $T_2=300\mathrm{K}$ with $E_{F2}$. The dashed curves correspond to the case in which $E_{F2}=0.28\mathrm{eV}$, while the solid ones show the temporal evolution when $E_{F2}=1.0\mathrm{eV}$. (b) Evolution of the temperatures for a chain of three nanodisks of the same size and separations as in (a), as shown by the schematics. The outer disks begin at a temperature $T_1=T_3=300\mathrm{K}$, whereas the center one starts at $T_2=400\mathrm{K}$. One outer disk (yellow), and the center one (red) have Fermi levels $E_{F1}=E_{F2}=0.28\mathrm{eV}$, while the other outer disk (blue) has Fermi level $E_{F3}=1.0\mathrm{eV}$.

Figure 3

Active control of heat propagation. (a) Schematics of the system under consideration, consisting of a chain of seven nanodisks of uniform radius $R=15\mathrm{nm}$, center-to-center separation $a=4R$, and doping level $E_F=0.28\mathrm{eV}$. On the left end of the chain, there is a heat source (red) that is held at $T=400\mathrm{K}$ and, on the right one, a heat sink (blue) held at $T=300\mathrm{K}$. The environment is at $T_0=300\mathrm{K}$. (b) Fermi levels of the heat source (red curve) and heat sink (blue curve) as a function of time. (c) Temporal evolution of the temperatures of disks 1–7. The colored curves match the corresponding labels of the disks that they represent from panel (a).

Figure 4

Thermal isolation of a hot nanodisk. (a) Schematics of the system under consideration, consisting of a chain of five nanodisks of uniform radius $R=15\mathrm{nm}$ and center-to-center separation $a=4R$. On both sides of the chain, there is a heat source (red) that is held at $T=400\mathrm{K}$ and a heat sink (blue) held at $T=300\mathrm{K}$, while the environment is held at $T_0=300\mathrm{K}$. Both the heat source and sink are a distance of $4R$ from the closest disk in the chain. (b),(c) Temporal evolution of the Fermi levels of the heat sources and sinks (b) and the different disks in the chain (c). The colors of the different curves are matched with the colors of the disks in the schematics. (d) Temporal evolution of the temperature of each disk in the chain.

Figure 5

Specific heat of graphene. The red dots correspond to measured data from Ref. [75], while the blue solid curve represents a polynomial fit to the data.

Figure 6

Power absorbed by disk $2$ at time $t=0\mathrm{s}$ in a pair of nanodisks of equal radius $R$ separated from center to center by a distance $a$. Disk $1$ has Fermi level $E_{F1}$ and is at temperature $T_1=400\mathrm{K}$, while disk $2$ has Fermi level $E_{F2}$ and is at $T_2=300\mathrm{K}$. The environment is vacuum at temperature $300\mathrm{K}$. The middle panel corresponds to the same values of $R$ and $a$ as in Fig. 1. In all panels, the Fermi level $E_{F1}=E_{F2}$ for which the power is maximized is marked using dashed lines.

Figure 7

(a) Schematics of the system under consideration, consisting of two disks of equal radius $R=15\mathrm{nm}$ separated by $a=4R$. Disk $1$ begins at temperature $T_1=400\mathrm{K}$ and has Fermi level $E_{F1}$, while disk $2$ begins at $T_2=300\mathrm{K}$ and has Fermi level $E_{F2}$. The environment is vacuum at temperature $300\mathrm{K}$. (b) Power absorbed by disk $2$ at time $t=0\mathrm{s}$ for different conductivity models and Fermi-level combinations. (c) Temporal evolution of the temperatures of the two disks for $E_{F1}=0.28\mathrm{eV}$ and $E_{F2}={10}^{-3}\mathrm{eV}$. (d) Same as (c), but for Fermi levels $E_{F1}=E_{F2}=0.28\mathrm{eV}$.

Figure 8

Thermalization of two graphene nanodisks of radius $R=15\mathrm{nm}$, center-to-center separation $a=4R$, and equal Fermi levels $E_F$, as shown in the upper schematics, placed in vacuum at $300\mathrm{K}$. The colored curves represent the dynamics for different values of $E_F$, as depicted in the legend.

Figure 9

Thermalization of two graphene nanodisks of radius $R=15\mathrm{nm}$, center-to-center separation $a=4R$, and Fermi level $E_F=0.28\mathrm{eV}$, as shown in the upper schematics, for different values of the electron mobility $\mu$, as indicated by the legend. The environment is vacuum at $300\mathrm{K}$.