Electron renormalization of sound interaction with two-level systems in superconducting metglasses

The crossing of temperature dependencies of sound velocity in the normal and the superconducting state of metallic glasses indicates renormalization of the intensity of sound interaction with two-level systems (TLS) caused by their coupling with electrons. In this paper we have analyzed different approaches to a quantitative description of renormalization using the results of low-temperature ultrasonic investigation of ZrTiCuNiBe amorphous alloy. It is shown that the adiabatic renormalization of the coherent tunneling amplitude can explain only part of the whole effect observed in the experiment. There exists another mechanism of renormalization affecting only nearly symmetric TLS.