Graphene plasmons, possessing a lot of unique optical properties, have been employed to enable a variety of applications in the THz frequency range. Here, we demonstrate bound states in the continuum (BICs), electromagnetically induced transparency (EIT)-like effects, high-performance broadband optical absorption (OA), and narrow-band OA in a square lattice of graphene non-concentric rings (GNCRs). We show that due to inversion symmetry breaking, the symmetry-protected BICs will evolve into quasi-BICs as the eccentricity of GNCRs becomes nonzero, manifested itself as a new resonance dip appearing in the transmission spectrum. The observation can be well described by a coupled-oscillator model, namely, the coupling between a dipole state and a quadrupole state. Besides, as the eccentricity becomes very large, the structure can also support EIT-like effects, in which a transparency window will occur at the frequency of the original transmission dip caused by the dipole state, and the transmission spectrum turns into a typical W-shape. Based on the idea of BICs, we propose a broadband terahertz (THz) perfect OA by using the typical sandwiched structure, namely, with the configuration of the GNCR layer-spacer layer-metal layer. Full wave simulations are performed, which show that the OA of over 90% absorptance can be achieved at frequencies from 0.67 THz to 1.66 THz, and over 99% absorptance can be achieved at frequencies from 1.24 THz to 1.49 THz. In the absorption band, three peaks come from three graphene plasmonic modes, which are two dipole resonances and a quadrupole resonance induced by symmetry breaking. Moreover, the perfect OA performance can be well maintained for oblique incidences of transverse electric polarization, with an incidence angle of up to 30°. Finally, we show that the broadband perfect OA can be switched to narrowband perfect OA, and its operating frequency can be continuously tuned by changing the Fermi level. Our results will promote the development of graphene-based applications in THz and infrared regimes.
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