Graphene has emerged as a promising platform for THz metasurfaces supporting electrically tunable deep-subwavelength plasmonic excitations. Here, we introduce a broadband graphene metasurface based on the Hilbert curve, a continuous, space-filling fractal. We demonstrate enhancement of graphene absorption over a broad frequency band (0.5-60 THz) with an average absorption level exceeding 20%. Owing to the continuous nature of the metasurface patterns, both absorption level and bandwidth can be controlled electrically by varying the graphene charge carrier concentration.Keywords: graphene plasmonics, fractal metasurfaces, broadband absorber 2 Structuring materials [1][2][3][4] at the subwavelength scale has led to the emergence of metamaterials [5][6][7], a paradigm shift in the design of artificial electromagnetic materials [8] resulting in technologically important, as well as exotic, applications, including perfect lenses [9], transformation optics and invisibility cloaks [10], and perfect absorbers [11]. The properties of metamaterials largely arise from resonant dispersion; hence material loss restricts the strength [12] and bandwidth of the metamaterial response [13].In particular, with respect to perfect absorbers, various schemes have been suggested in order to achieve strong absorption in gigahertz [14] [25]. However, such methods often result in complex, bulky configurations, with little tunability. Graphene, a monolayer of carbon atoms, provides an appealing alternative: owing to its band structure, graphene supports plasmonic excitations at the deep sub-wavelength scale [26]. Plasmonic resonators can be realized by structuring graphene at the nanoscale [27][28][29], which can then be employed to construct graphene metasurfaces targeting the THz part of the spectrum [30][31][32][33][34]. At the same time the high sensitivity of the electromagnetic properties of graphene to the charge carrier [35] concentration provides means of electrical control of plasmons [36][37][38]. In 3 addition to tunability, graphene as a plasmonic material allows to strongly confine electromagnetic radiation to much smaller physical volumes compared to typical metals.For example, the plasmon wavelength for graphene is about 50 times smaller than the free-space wavelength, while for noble metals this is an order of magnitude smaller [26,29]. Such strong field confinement allows people to realize very complex graphene structures while retaining a subwavelength footprint. Graphene exhibits broadband nonlinearities and high thermal conductivity, whereas its atomic thickness facilitates device integration.Here, we introduce fractal graphene metasurfaces as tunable, broadband THz absorbers of monoatomic thickness (see Fig. 1(a)). We demonstrate multifold enhancement of absorption over an extremely broad frequency band, where average absorption levels exceed 20% from 0.5 to 60 THz in strongly doped graphene. We show that the absorption band is strongly dependent on the charge carrier concentration enabling dynamic electrosta...