The terahertz absorption behaviours of a graphene monolayer placed on top of a onedimensional double-periodic (D-P) quasi-crystal, are studied in the presence of perpendicular magnetostatic bias. It is found that by increasing the D-P generation number, a large band gap of about 3.954 THz < f < 4.61 THz is created in the frequency range. We limit our investigations to this wide band gap frequency range. It is observed that the peak of wideband absorption can be enhanced by increasing the applied magnetic field for a certain circular polarization (CP) state, while it decreases for another state of CP. Interestingly, the absorption remains almost unchanged when the D-P generation number increases. Therefore, it is possible to achieve enhanced absorption with few layers. Moreover, the absorption properties are inspected at various gate voltages for both the hole- and electron-doped graphene. It is indicated that at a fixed magnetic field, the absorption peak is increased by increasing the value of the gate voltage. Therefore, one can tune the absorption by varying either the external magnetic field or the electric bias. These properties can be employed in designing tunable graphene-based quasi-crystal absorbers.
