Abstract
Superconducting thin films are widely applied in various fields, including switching devices, because of their phase transition behaviors in relation to temperature changes. Therefore, it is important to quantitatively determine the optical constant of a superconducting material in the thin-film state. We performed a terahertz time-domain spectroscopy, based on a 10 femtoseconds pulse laser, to measure the optical constant of a superconducting GdBa2Cu3O7−x (GdBCO) thin film in the terahertz region. We then estimated the terahertz refractive indices of the 70 nm-thick GdBCO film using a numerical extraction process, even though the film thickness was approximately 1/10,000 times smaller than the terahertz wavelength range of 200 μm to 1 mm. The resulting refractive indices of the GdBCO thin film were consistent with the theoretical results using the two-fluid model. Our work will help to further understand the terahertz optical properties of superconducting thin films with thicknesses under 100 nm, as well as provide a standard platform for characterizing the optical properties of thin films without the need of Kramers–Kronig transformation at the terahertz frequencies.
Highlights
Accepted: 3 June 2021Because of their high conductivity, noble-metal films are most commonly used in various applications, such as metamaterials and sensing devices in the terahertz region [1,2,3,4,5,6,7,8].Recently, many studies have been carried out in order to develop new switching devices combined with phase transition materials modulated via external stimuli, such as temperature and electrical voltage [9,10,11,12]
Many studies have been carried out in order to develop new switching devices combined with phase transition materials modulated via external stimuli, such as temperature and electrical voltage [9,10,11,12]
Superconducting materials are widely applied in the field of switching devices because of their phase transition below the critical temperature Tc [13,14,15,16,17]
Summary
Because of their high conductivity, noble-metal films are most commonly used in various applications, such as metamaterials and sensing devices in the terahertz region [1,2,3,4,5,6,7,8]. Phase retardation of a terahertz-transparent thin film is not sufficient, and the refractive index is difficult to obtain owing to the pulse width resolution of the probe beam [22]. If nd/c > PW, where n is the real part of the refractive index of the material, d is the thickness, c is the speed of light, and PW is the pulse width of the probe beam, we can estimate the complex refractive indices of the material. In the case of a conducting material, it would be relatively easier to estimate its refractive index, even within the form of thin films, but we need one more procedure to accurately estimate complex refractive indices of superconductor thin films, which retain relatively low refractive indices below Tc. In this work, we introduced a method for measuring the complex refractive indices of a target material using terahertz time-domain spectroscopy combined with a numerical extraction process. 70 nm-thick superconducting GdBa2 Cu3 O7−x (GdBCO) thin film with a critical temperature of around 90 K in a broad temperature range of 20–180 K
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