Metamaterials, often called “left-handed materials,” are a novel class of artificial electromagnetic materials with sub-wavelength structures and negative dielectric constants and magnetic permeability [1,2]. These materials exhibit unique properties that are not found in natural substances. The concept of metamaterials was first introduced by Veselago [3] in 1968, and the first practical metamaterials were fabricated in 2000. Since then, metamaterials have emerged as highly promising candidates for a wide range of applications. They offer superior capabilities, such as controlling electromagnetic waves [4,5], detecting light waves [6,7], and enabling wave absorption [[8], [9], [10]], among others. The development of integrated metamaterial-based devices, including absorbers [11,12], planar super lens [13], and holographic plates [14], has been well-established through extensive research. Metamaterial absorbers, which semi are microstructured periodic electromagnetic devices, have garnered significant attention due to their excellent optical properties. Notably, the characteristic spectra of most macromolecules and crystals fall within the terahertz (THz) band, a region of the electromagnetic spectra between the microwave and infrared ranges, spanning from 0.1 THz to 10 THz [[15], [16], [17]]. The “terahertz gap” represents a transitional region in the electromagnetic spectra that has not been widely exploited [18], yet as the relevant studies are carried out, scientists have identified several unique properties of terahertz waves, including coherence, high resolution, non-ionization, and strong penetration [[19], [20], [21], [22]]. These attributes suggest that terahertz technology holds significant potential for advancements in various fields, such as communications [23], imaging [24], biochemical sensing [25,26], and biomolecular spectroscopy [27]. Nevertheless, the low photon energy of terahertz waves limits effective coupling with conventional materials [28]. The integration of terahertz technology with metamaterials allows precise control of electromagnetic waves, making metamaterial-based absorbers excellent in performance and functionality [[29], [30], [31]]. This integration paves the way for innovative devices and establishes terahertz metamaterial absorbers as a key focus of current research.

Metamaterial absorbers typically consist of a multi-layer structure, with a metal or metamaterial top layer, a low refractive index dielectric layer in the middle, and a bottom metal plate. The key to enhancing absorption performance lies in matching the impedance of the absorber with that of free space, thereby minimizing reflection and maximizing absorption [32,33]. Theoretically, to achieve various resonant characteristics, the microstructure of the metamaterial device can be adjusted to realize narrowband [[34], [35], [36]], multi-band [37,38], or wide-band [39,40] absorption, among other functionalities. In recent years, extensive research has been conducted on metamaterial absorbers. Since Landy et al. [41] proposed the first metamaterial-based perfect absorber (MPA), it has been demonstrated that metamaterial absorbers can achieve perfect single-band absorption within the GHz frequency range. Researchers have made significant efforts to enhance the tunability of metamaterial absorbers. Wu et al. [42] introduced a microwave absorber featuring a ZnO coating with adjustable thickness, enabling an ultra-wide tunable frequency range and vibrant structural colors. The absorber's effective absorption frequency can be dynamically tuned to cover 94.3 % of the entire microwave spectra. Similarly, Z. Mahdavikiia et al. [43]. proposed a tunable four-band perfect absorber utilizing metamaterial graphene, achieving three absorption peaks with efficiencies exceeding 96 % in the infrared region. Numerous studies have shown that the development of tunable narrowband absorbers in the terahertz range is still limited, with significant potential for further exploration. As a result, integrating novel tunable active materials into metamaterial absorbers has gained considerable attention for the development of more versatile and efficient tunable terahertz absorbers.

A newly discovered topological quantum material, BDS [44], has garnered significant academic interest in its potential in fabricating tunable absorbers with exceptional sensing capabilities [30,45]. As a three-dimensional analogue of graphene, BDS demonstrates distinctive properties that position it as a promising candidate for a wide range of technological applications [46,47]. The linear dispersion relation of BDS along all three directions, coupled with the preservation of crystal symmetry in its films, enables superior manipulation of optical properties and results in carrier mobility at 5 K that significantly surpasses that of graphene. In an experimental study, Dai et al. [48] utilized Dirac semimetal cadmium arsenide (Cd3As2) thin films to achieve all-optical and ultra-high-speed broadband modulation in the terahertz (THz) spectra, demonstrating an exceptional electron mobility of 7200 cm2/(V·s) for Cd3As2 in this frequency range. Meanwhile, graphene's zero or near-zero bandgap, coupled with its single-atomic-layer thickness, presents significant challenges for precise fabrication and limits its practical application in the terahertz spectra [49,50]. In contrast, BDS maintains metallic properties, which simplify fabrication and enhance stability, while the deposition of a single BDS layer on a dielectric substrate notably improves wave absorption and resistance to dielectric interference [51]; Additionally, BDS exhibits favorable dielectric characteristics above the Fermi energy level and metallic properties below it. Unlike graphene, BDS can be tuned by applying a gate voltage or surface doping with alkaline elements, which allows control over the Fermi energy level and the dielectric constant of BDS [52,53]. Given these properties, BDS is a promising material for optical device design and fabrication, as replacing traditional materials with BDS in absorber design not only reduces costs but also enhances flexibility.

In 2019, Zhang et al. [54]proposed a tunable two-band terahertz absorber comprising a dielectric layer and a Dirac circular layer. By adjusting the Fermi energy of the BDS, the absorption can be tuned from 90 % to 99 %. In 2021, Li et al. [31]designed a BDS-based narrowband absorber with photonic crystal slabs, achieving three absorption peaks over 95 % within 1.0–2.4 THz and a maximum quality factor (FOM) of 4.26. In 2023, Azam Parkam et al. [55] introduced a sensitive tunable absorber based on a discoidal Dirac semimetal. A buffer layer enhances sensitivity (S = 17.74 μm/RIU) and achieves a highest FOM = 20.22. However, current research is primarily focused on simulations and structural optimization, which significantly limits the practical applications of metamaterials. It has been noted by several researchers that the resonance frequency of metamaterials is highly sensitive to changes in the surrounding dielectric environment. Du et al. [56] developed a flexible metamaterial absorber consisting of a rectangular ring-rectangular planar array, which can achieve double resonance peak absorption. The designed absorber has high sensitivity with a maximum sensitivity of 91.67 GHz/RIU at the resonance peak, which can enable the highly sensitive detection of the plant growth regulator forchlorfenuron with a detection limit of 0.01 mg/L. Wang et al. [26]proposed a polyimide-based dual-band flexible metamaterial sensor for refractive index and pesticide detection. The sensor achieved refractive index sensitivities of 0.09 and 0.28 THz/RIU at two resonant frequencies when exposed to chlorpyrifos-methyl acetone solutions. As narrow-band absorbers are widely used for sensing and detection, tunable multi-band absorbers in the terahertz range are still scarce and multi-band absorbers are preferred for more accurate measurements and sensitive applications. Although the terahertz metamaterial absorbers proposed in the above paper are notable for their simple structural design, superior absorption performance and high refractive index sensitivity, they are distinguished by multiband absorption peaks. Consequently, a preliminary investigation has been conducted in this area with the objective of resolving this challenging problem.

This paper proposes a three-layer, four-band perfect absorber based on a BDS-dielectric-metal structure. The top BDS layer is designed with two open ring configurations, using stable gold as the reflector. The absorber achieves over 96 % absorption within 0.1–2.4 THz, exceeding 99 % at 1.44 THz and 1.83 THz, with a sensing sensitivity of 145 GHz/RIU. The physical mechanisms are analyzed using impedance matching theory and electric field distribution at resonance frequencies. The present study investigates the influence of top-layer structural parameters on the absorption spectra, thereby revealing their role in enhancing the absorber's tolerance to manufacturing errors. Dynamic tuning of the absorption peak frequency is achieved by adjusting the Fermi energy level of the BDS through a bias voltage. Compared to previous studies, our narrowband absorber features a simple design, superior controllable absorption performance, and higher refractive index sensitivity. It offers guidance for designing future multiband metamaterial absorbers and has potential applications in biosensing, security detection, and terahertz communications.