Magnetically tunable multiband near-field radiative heat transfer between two graphene sheets

Near-field radiative heat transfer (NFRHT) is strongly related with many applications such as near-field imaging, thermo-photovoltaics and thermal circuit devices. The active control of NFRHT is of great interest since it provides a degree of tunability by external means. In this work, a magnetically tunable multiband NFRHT is revealed in a system of two suspended graphene sheets at room temperature. It is found that the single-band spectra for $B=0$ split into multiband spectra under an external magnetic field. Dual-band spectra can be realized for a modest magnetic field (e.g., $B=4\mathrm{T}$). One band is determined by intraband transitions in the classical regime, which undergoes a blue shift as the chemical potential increases. Meanwhile, the other band is contributed by inter-Landau-level transitions in the quantum regime, which is robust against the change of chemical potentials. For a strong magnetic field (e.g., $B=15\mathrm{T}$), there is an additional band with the resonant peak appearing at near-zero frequency (microwave regime), stemming from the magnetoplasmon zero modes. The great enhancement of NFRHT at such low frequency has been little reported. This work may pave a way for multiband thermal information transfer based on atomically thin graphene sheets.

Figure 1

Schematic view of near-field radiative heat transfer between two suspended graphene sheets in free space. The upper sheet with higher temperature ($T_1$) radiates electromagnetic waves to the bottom one with lower temperature ($T_2$). (a) The spectrum of radiative heat flux is single band in the absence of an external magnetic field. (b) The spectrum becomes multiband under a sufficient strong magnetic field.

Figure 2

(a) The Fermi-Dirac distribution of graphene for different temperatures. The inset illustrates the band structure of a graphene sheet with chemical potential ${\mu }_c$ below the first LL. The imaginary part of longitudinal conductivity $\mathrm{Im}\left[{\sigma }_L\right]$ for (b) ${\mu }_c=0.04\mathrm{eV}$ and (c) ${\mu }_c=0.08\mathrm{eV}$. The shaded regimes in (b) and (c) indicate the peaks of conductivity contributed by different LL transitions. The scattering rate is set to be a constant with ${\mathrm{\Gamma }}_{nm}=\mathrm{\Gamma }=4\mathrm{meV}$. The external magnetic field $B=4\mathrm{T}$, and the first LL $E_1\sim 0.07\mathrm{eV}$.

Figure 3

(a) Spectral heat flux and (b) transmission coefficients (logarithmic scale) for two parallel graphene sheets under different values of magnetic field. The inset in (a) shows the spectrum near-zero frequency for $B=15\mathrm{T}$. In (b), the white line illustrates the light line $q=\omega /\mathrm{c}$, and the gray lines represent the corresponding dispersions of magnetoplasmon for single graphene sheet. The dashed gray lines stand for the dispersions generated from the intraband transition $E_2\to E_3$. We set the chemical potential for two graphene sheets ${\mu }_{c1}={\mu }_{c2}=0.08\mathrm{eV}$, the scattering rate $\mathrm{\Gamma }=4\mathrm{meV}$, the high temperature $T_1=310\mathrm{K}$, the low temperature $T_2=T_1-10\mathrm{K}$, and the separation distance $d=100$ nm.

Figure 4

Spectral heat flux via chemical potential (${\mu }_{c1}={\mu }_{c2}$) for (a) $B=4\mathrm{T}$. The red dashed curves represent the corresponding spectra for $B=0$, where the resonant peaks have a blue shift as the chemical potential increases. (b) $B=15\mathrm{T}$. The middle spectral band (the orange-shaded regime) changes dramatically with increasing the chemical potential. However, the spectral bands marked by the blue-shaded regimes in (a) and (b) are almost unchanged, showing a robust feature.

Figure 5

Contour plots of spectral heat flux for different scattering rate. (a) $B=4\mathrm{T}$ and (b) $B=15\mathrm{T}$. The black arrows indicate the primary bands, and the gray arrows represent secondary bands contributed from high-order LL transitions. The chemical potential, temperatures, and separation distance are kept the same as those in Fig. 3.

Figure 6

(a) The radiative heat flux as a function of magnetic field, normalized by blackbody limit ($\sim 64.2 \text{W}{\text{m}}^{-2}$). (b) The modulation of radiative heat flux in the presence of magnetic field, defined as $\eta =〈S(B=0)〉/〈S\left(B\right)〉$. The solid and dashed curves represent the scattering rate $\mathrm{\Gamma }=4$ and 8 meV, respectively. The chemical potential and temperatures are kept the same as those in Fig. 3.

Figure 7

Spectral heat flux for graphene sheets placed on top of substrates with permittivity ${\varepsilon }_s$, where the thickness of the substrates is semi-infinite. The magnetic fields are (a) 4 T and (b) 15 T, respectively. Other parameters are kept the same as those in Fig. 3.