Near-Field Energy Transfer between Graphene and Magneto-Optic Media

We consider the near-field radiative energy transfer between two separated parallel plates: graphene supported by a substrate and a magneto-optic medium. We first study the scenario in which the two plates have the same temperature. An electric current through the graphene gives rise to nonequilibrium fluctuations and induces energy transfer. Both the magnitude and direction of the energy flux can be controlled by the electric current and an in-plane magnetic field in the magneto-optic medium. This is due to the interplay between the nonreciprocal photon occupation number in the graphene and nonreciprocal surface modes in the magneto-optic plate. Furthermore, we report that a tunable thermoelectric current can be generated in the graphene in the presence of a temperature difference between the two plates.

Figure 1

(a) Schematic plot of the near-field energy transfer between graphene (1) supported by a substrate (s) and a magneto-optic medium plate (2) with air gap $d$. In the presence of an electric current with drift velocity $v_d$ through the graphene, a net energy flux is transferred even when there is no temperature difference between the two plates. Its magnitude and direction can be modulated by the electric current and the magnetic field $B$ applied to the magneto-optic medium. (b) Energy flux $H$ versus $d$ at different $v_d$ with $B=0$ and $T=300\mathrm{K}$. (c) Energy transmission function $\mathcal{Z}$ (in units of meV) at $v_d=0.3v_F$, $d=20\mathrm{nm}$, and $q_y=0$ against $q_x$ and $\hslash \omega$. The black and magenta dashed lines are the dispersions of graphene plasmons and the surface modes of InSb at $B=0$ in the absence of damping, respectively. (d) Spectrum $h(\omega )$ at $v_d=0.3v_F$ and $d=20\mathrm{nm}$.

Figure 2

(a) Dispersion of the surface modes of InSb in the Voigt configuration at $B=4\mathrm{T}$. (b) Energy flux $H$ versus separation $d$ at $B=4$ and $B=-4\mathrm{T}$ with $v_d=0.3v_F$ and $T=300\mathrm{K}$. (c) Energy transmission function $\mathcal{Z}$ (in units of meV) at $B=4\mathrm{T}$, $d=50\mathrm{nm}$, and $q_y=0$ against $q_x$ and $\hslash \omega$. The black dashed lines are dispersions of the graphene plasmons. The energies $\hslash \omega$ indicated by the arrows are the same as the corresponding energies indicated in (a). (d) Spectrum $h(\omega )$ at $B=4\mathrm{T}$ and $d=50\mathrm{nm}$.

Figure 3

(a) Energy flux $H$ versus magnetic field $B$ at different drift velocities $v_d$ with $d=50\mathrm{nm}$ and $T=300\mathrm{K}$. (b) Energy transmission function $\mathcal{Z}$ at $q_y=0$, $B=18\mathrm{T}$, $v_d=0.3v_F$, and $d=50\mathrm{nm}$ against $q_x$ and $\hslash \omega$. (c) Spectrum $h(\omega )$ at $B=18\mathrm{T}$ and $v_d=0.3v_F$.

Figure 4

Heat flux $H$ versus magnetic field $B$ at $T_1=300\mathrm{K}$, $T_2=330\mathrm{K}$, and $d=50\mathrm{nm}$ (solid line). The contributions to the heat flux from positive $q_x$ (dash-dotted line) and negative $q_x$ (dashed line) are plotted separately. The negative heat flux indicates that the heat flows from the InSb plate to the graphene.