The Ginzburg - Landau equation for superconductors of polar symmetry

The superconductivity of metals whose symmetry group includes a polar axis is considered. A modified Ginzburg - Landau free-energy functional is derived, and it is shown that due to the absence of space parity the free-energy density involves an additional term of the form where is the order parameter, , c is the unit vector along the polar axis, , and is a real function of the electronic structure parameters. The consequences of the term on the problem of the critical current in a thin single-crystalline film are studied, and an anomalous effect of the magnetic field on the value of the current is predicted: namely, if the film is produced in such a way that its plane is perpendicular to the vector c, then the magnitude of the critical current should depend on the sign of the mixed product , i.e., the critical current should be different for two opposite directions.