Thermal Tuning of High-$T_{c}$ Superconducting Bi$_{2}$Sr $_{2}$CaCu$_{2}$ O$_{8+\delta }$ Terahertz Metamaterial

Abstract

We introduce a class of low-loss subwavelength resonators and report the first demonstration of a high-temperature ( $T_{c}$) superconducting Bi ${2}$Sr${2}$ CaCu${2}$O ${8+\delta }$ (BSCCO) terahertz (THz) metamaterial. The numerical simulations and analytical calculations are performed to study the electromagnetic response of the subwavelength BSCCO split-ring resonators (SRRs) to the incident photons with energies below the superconducting gap energy. A transition of resonance strength is observed as a dip in resonance frequency for temperatures below BSCCO $T_{c}$. To interpret the transmission spectra, resonance switching, and frequency tuning of SRRs, we calculate the temperature dependent complex permittivity and surface impedance of a 200 nm thick unpatterned slightly underdoped BSCCO thin film. We compare the resonance tunability of SRRs made of the extremely disorder superconductor (BSCCO) with metamaterials made of a weakly disorder superconductor YBa2Cu3O7 (YBCO) and show that the resonance quality and frequency tuning are comparable for these two metamaterials. Our results may be useful for THz emitters and detectors developments, for instance, by integration of SRRs with BSCCO THz emitters and microstrip antennas, the device functionalities such as polarization, emission pattern directivity, and output power could be controlled and improved.