The construction of versatile terahertz metamaterial having tunable dual-band electromagnetically induced transparency based on two falling asymmetric T-shaped graphene resonators

•A graphene-based versatile terahertz metamaterial consisting of two asymmetric T-shaped resonators is demonstrated to produce dual-band transparency effect.•Electric field and surface current distributions of these two transparent peaks are discussed to reveal their formation mechanisms.•Dynamic modulation of transparency peaks by controlling the Fermi energy levels of graphene is investigated.•Group delay and sensing performance of the terahertz device are explored, which possess excellent delay effect and sensing performance.