# Ultrathin and Electrically Tunable Metamaterial with Nearly Perfect Absorption in Mid-Infrared
## 1 Introduction  
Metamaterial absorbers are two-dimensional electromagnetic structures absorbing light at the resonance, which have attracted huge attention over the years [1; 2; 3]. Many functional absorbers integrated with various metamaterial structures have been reported [4; 5; 6], holding potential in a broad range of applications, such as sensors [7], spectroscopy [8], and thermal emitters [9; 10]. In particular, a metamaterial perfect absorber (MPA) based on a metal-insulator-metal (MIM) structure has been a hotspot for researchers due to its near unity absorptivity. By optimizing the periodic subwavelength arrays topping the device, with the bottom layer as effective reflector, near unity absorption can be achieved at its resonance. Although different types of perfect absorbers with various metamaterial structures have been widely investigated and analyzed [11; 12; 13; 14; 15], the realization of MPA structures typically requires heavy computation and repetitive trial and error experiments to achieve the critical damping condition (i.e., Q\({}_{\rm r}\) = Q\({}_{\rm a}\), where Q\({}_{\rm r}\) and Q\({}_{\rm a}\) are quality factors related to radiative loss and intrinsic loss, respectively), because a large amount of geometrical and material parameters are involved and entangled. It is therefore anticipated that the independent tuning of Q\({}_{\rm r}\) and Q\({}_{\rm a}\) by individual parameters can facilitate the easy design. What's more, absorbers in extreme forms, like ultrathin and compact absorbers, are desirable for scaling down the device size and/or minimizing parasitic effects, such as thermal leak conductance and large heat capacity for bolometric detector arrays [16; 17; 18; 19; 20].  
With its unique electronic and optical features, graphene has drawn tremendous attention in recent years [21; 22]. Graphene, with a single atomic layer thickness of only 0.33 nm, is by now thethinnest two-dimensional material and exhibits the remarkable property of changing its conductivity through electrical modulation [23]. Graphene has been reported to be applicable for modulators over a large wavelength region, ranging from near-infrared to far-infrared frequencies [24; 25; 26; 27]. As a result, graphene integrated into metamaterials provides tremendous freedom in tailoring their optical properties. The reported works, however, typically utilized complicated device structures, such as ion-gel gating, to realize electrical modulation [28] and sophisticated interplay between graphene and background absorption remains elusive. It is therefore desirable to design more compact metamaterials with built-in tunability.  
In this article, we demonstrate an ultrathin and electrically tunable graphene MIM metamaterial perfect absorber working at the mid-infrared region, with a total thickness of \(\sim\)270 nm (thickness \(<\lambda_{0}/15\)). The MIM tri-layer structure forms an agile platform to engineer the infrared optical properties of the structure. The bottom metal layer of the MIM structure provides two-fold functions: a mirror to form resonant cavity and an effective gate to adjust the Fermi level in the graphene layer, and hence the absorption. This tunable absorption provides a compact, flexible, and post-fabrication fine adjustment freedom to the hybrid metamaterials.