Mixed states inA−15-structure superconductors: The ultrasonic anomaly observed in the mixed state ofV3Si

A theoretical model is proposed for explaining the anomaly observed in the ultrasonic and specific-heat measurements in the mixed state of ${\mathrm{V}}_3$Si. The martensitic transformation in the $A-15$ structure compounds causes a drastic change of the electronic structure in the vicinity of the Fermi level, and due to this change the mixed state of the compounds becomes highly anisotropic. The Gibbs free energy, and the lower critical field which depend on the direction of the tetragonal crystal axis relative to an external magnetic field, are calculated by extending the boson theory developed by Umezawa et al. to the case of anisotropic superconductors. The calculation shows that the domains elongated along an applied field in ${\mathrm{V}}_3$Si become unstable when the field strength exceeds a critical value. The relation between this instability and the anomaly mentioned above is discussed.