## 1 Introduction  
Terahertz (THz) waves, which lie between microwaves and infrared waves with frequencies ranging from 0.1 to 10 THz, hold significant application value in fields such as medicine, security detection, and communication. Advancements in THz technology [1] have opened up new possibilities for the creation of innovative THz devices, with THz metamaterial absorbers emerging as a particularly crucial device category. Efficiently absorbing THz waves is a key ability of THz metamaterial absorbers, playing a crucial role in utilizing THz waves for various applications. In the realm of infrared detection, the utilization of these devices can lead to the development of highly sensitive THz sensors. By manipulating the structures of materials, one can effectively achieve the shielding and concealment of THz waves in the realm of electromagnetic invisibility [2]. When it comes to sensor technology [3], THz metamaterial absorbers find application in the precise handling and transmission of THz waves. Hence, the progress in the realm of THz metamaterial absorbers [4] brings about significant implications, paving the way for enhanced applications across diverse domains. Since [PERSON] et al. [5] proposed metamaterial absorbers based on electromagnetic resonators in 2008, research has rapidly progressed, leading to various absorber designs, including single-band [6], multi-band [7, 8], and wide-band [9] absorbers. Although these absorbers have achieved some success in electromagnetic wave control, the metal-dielectric-metal sandwich structure is still used, which makes the shape and size of the absorber relatively fixed. Given the inherent rigidity of this configuration, it restricts the absorber's ability to adapt its absorption performance dynamically to specific needs. The inflexibility of this configuration hinders the absorber from adapting its performance in real-time to cater to distinct needs, consequently restricting the effective utilization of metamaterial absorbers in situations demanding immediate performance modifications. Proposals have been made for absorbers that can be adjusted and tuned over a wideband range, utilizing materials such as graphene [10], semiconductors [11], liquid crystals [12; 13], and phase-change materials [14]. Interestingly, the utilization of VO2 in broadband absorbers for adaptable absorption without significant frequency shifts is notable, owing to its electrical conductivity modulation techniques via thermal [15; 16], electrical [17; 18], or photoexcitation [19; 20] methods. For example, [PERSON] et al. [21] introduced a novel design, a wideband absorber utilizing VO2, that demonstrates a remarkable capacity to modulate terahertz band absorption levels, ranging from 5% to a full 100%, yielding a significant relative bandwidth of 71% for absorption rates exceeding 90%. A configuration utilizing liquid crystal [22] materials and employing metal disc and metal elliptical disc structures was conceptualized by researchers. In 2017, there was a notable accomplishment in achieving optimal absorption [23] across three distinct frequency ranges. Through the manipulation of the voltage applied to the liquid crystal material, it becomes feasible to adjust the peak frequency of absorption [24], leading to the potential for dynamic optimization of absorption capabilities. Broadband absorbers in the terahertz range are widely used in many fields. They can be used for antenna design and electromagnetic compatibility analysis in wireless communication systems, as well as in terahertz wave imaging systems and sensors, such as medical imaging, security checks, food quality testing, and other fields. Broadband absorbers in the terahertz range are also of great significance for studying the absorption and transmission characteristics of materials and can be used in the fields of materials science and optics.