Magnetic-Field Dependence of Microwave Absorption and Energy Gap in Superconducting Films

Abstract

We have measured the change in absorption of microwave radiation by superconducting indium, tin, and lead films as a function of magnetic field. Experiments have been conducted on films 145-700 Å thick using 8-mm- and 4-mm-wavelength microwave radiation, primarily with the magnetic field parallel to the plane of the film, but also as a function of angle between the magnetic field and the plane of the film. We observe a second-order phase change in the magnetic field, as is to be expected for films of this thickness according to the theories of Ginzburg and Landau and of Nambu and Tuan. The angular dependence of the critical field found in our measurements is in good agreement with the theory of one of the authors, which predicts an angular dependence given by the formula $\left(\frac{H_{c}sin\theta }{H_{c\perp }}\right)+{\left(\frac{H_{c}cos\theta }{H_{c\mathrm{II}}}\right)}^2=1\mathrm{}$.