Single Level and Multi-Level Kondo Effect in Granular Aluminum Films

We investigated granular aluminum thin films, having an enhanced critical temperature up to three times more than bulk Al. Two types of samples are obtained by sample preparation on 77K cooled substrates or on room temperature substrates, where lower deposition temperature results in higher Tc and smaller grain size. Upon decreasing the coupling between the grains Tc is first rising, up to a maximum value. Reducing the coupling further, Tc decreases until it vanishes at very low coupling. The degree of coupling is controlled by evaporating clean Al in controlled partial O₂ pressure¹.

Upon cooling the resistivity first decreases, reaches a broad minimum, then increases and finally decreases again at low temperatures toward the superconducting state¹. We discuss these results within the theory of Florens^2,3, predicting that in a regime where the discrete level width exceeds the level separation, a multi-level Kondo effect is expected for quantum dots (QD), showing a non-monotonous temperature dependence of the conductance. This interpretation is in line with the presence of magnetic moments in these films⁴.

Regarding the observed Tc enhancement, Choi⁵ have studied the Josephson effect through a QD connected to two superconducting leads. They showed that if T_K>Δ the pair correlation function Δ_d on the dot is larger than in the leads, Δ_d>Δ. The enhancement ratio Δ_d/Δ is about 3-5 which is of the same order as the T_c enhancement in our granular films. The gap was obtained directly by THz measurements using a Mach-Zehnder interferometer.

References

[1] N. Bachar et al., Phys. Rev. B87, 214512 (2013).

[2] S. Florens et al., Phys. Rev. B68, 245311 (2003).

[3] Moshe, A., Bachar, N., Lerer, S. et al. J Supercond Nov Magn (2018) 31: 733.
[4] N. Bachar et al., Phys. Rev. B91, 041123 (2015).
[5] M. Choi et al., Phys. Rev. B70, 020502 (2004).