A new design of terahertz (THz) metamaterial is proposed for modulating and sensing purposes. The metamaterial consists of two resonators based on periodical arrays of graphene rings with different radii. For each small ring, it is surrounded by four large rings, and vice versa. By varying the Fermi level through electrostatically gating, the transmission of the graphene metamaterial can be controlled dynamically and the maximum modulation depths can reach up to 86% and 73%. Especially, an electromagnetically induced transparency (EIT)-like phenomenon can be generated, which results from the weak hybridization between two nearest neighbor rings performed as bright modes induced by electric dipole. Consequently, frequency sensitivity of 830 GHz per refractive index unit and figure-of-merit of 17 can be realized at the transparency peak. Our work offers an additional opportunity to achieve an EIT-like effect and potential applications in designing active THz modulators and sensors.
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