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We report on a novel effect of temperature-dependent modulation in graphene-supported metamaterials. The effect was observed during the theoretical analysis of a model graphene-supported electro-optical modulator having silicon dioxide (SiO _2 ) or hafnium dioxide (HfO _2 ) as a buffer dielectric layer. Comparative analysis of the two materials showed that they provide approximately the same maximum values for transmission and reflection modulation depths. However, in the case of a HfO _2 buffer layer, a lower chemical potential of the graphene is required to achieve the maximum value. Moreover, theoretical calculations revealed that a lower gate voltage (up to 6.4 times) is required to be applied in the case of a HfO _2 layer to achieve the same graphene chemical potential. The graphene layer was found to possesses high absorption (due to the additional resonance excitation) for some values of chemical potential and this effect is extremely temperature dependent. The discovered modulation effect was demonstrated to further increase the transmission modulation depth for the simple model structure up to 2.7 times (from 18.4% to 50.1%), while for the reflection modulation depth, this enhancement was equal to 2.2 times (from 24.4% to 52.8%). The novel modulation effect could easily be adopted and applied over a wide range of metadevices which would serve as a quick booster for the development of related research areas.

In the present paper, we discuss the temperature-dependent epsilon-near-zero (ENZ) effect in graphene arising in the framework of its isotropic model. The effect was theoretically investigated in detail using a simplified model design of the slot line containing a graphene layer in which all other effects are eliminated allowing us to focus solely on the ENZ effect. With the reduction of graphene effective temperature, the ENZ effect in the near-IR wavelength range was found to become pronounced even for structures and metasurfaces for which it has been considered neglectable and has not been previously observed at room temperatures. This temperature-dependent behaviour was interpreted analytically within the approximation in which the real part of the graphene dielectric constant is considered vanishingly small in comparison with the imaginary part (this condition is always satisfied at the ENZ point in graphene). Furthermore, the results presented in the paper may be potentially helpful in the construction of an experiment designed to finally prove or disregard the applicability of the isotropic model of graphene.