  This paper presents a comprehensive theoretical study of the magnetic-tunable
near-field radiative heat transfer (NFRHT) between two twisted graphene
gratings. As a result of the quantum Hall regime of magneto-optical graphene
and the grating effect, three types of graphene surface plasmon polaritons
(SPPs) modes are observed in the system: near-zero modes, high-frequency
hyperbolic modes, and elliptic modes. The elliptic SPPs modes, which are caused
by the combined effect of magnetic field and grating, are observed in the
graphene grating system for the first time. In addition, the near-zero modes
can be greatly enhanced by the combined effect grating and magnetic field,
rendering graphene devices promising for thermal communication at ultra-low
frequency. In particular, the near-zero modes result in a unique enhancement
region of heat transfer, no matter for any twisted angle between gratings. The
combined effect of grating and magnetic field is investigated simultaneously.
By changing the strength of magnetic field, the positions and intensities of
the modes can be modulated, and hence the NFRHT can be tuned accordingly, no
matter for parallel or twisted graphene gratings. The magnetic field endows the
grating action (graphene filling factors and twisted angles) with a higher
modulation ability to modulate the NFRHT compared with zero-field. Moreover,
the modulation ability of twist can be tuned by the magnetic field at different
twisted angles. In sum, the combined effect of magnetic field and grating
provides a tunable way to realize the energy modulation or multi-frequency
thermal communications related to graphene devices.
