Andreev bound states and paramagnetic effect at low temperatures in YBCO thin films

In this work, non-contact studies of a series of thin epitaxial YBa$_2$Cu$_3$O$_{7-x}$ (YBCO) films with different orientations of the $a$ and $b$ axes relative to the film boundaries were carried out. The thicknesses of the films ranged from 2 to 20 nm. From the induction measurements, an anomaly low-temperature increase in the London penetration depth $\lambda$ was observed for several samples below 7–8 K up to 1 K. Within the method of nonlinear near-field microwave microscopy, an increase in the nonlinear microwave response was observed with a decrease in temperature for the samples with the smallest thickness. The experimental results obtained can be related to the presence of Andreev bound states localized near the film boundaries with a certain orientation relative to $a$ and $b$ axes. The presence of these states leads to a paramagnetic effect at low temperatures. The effects of film boundaries and the film thicknesses are discussed.