www.nature.com/scientificreports OPEN Kondo-like transport and magnetic feld efect of charge carrier fuctuations in granular aluminum Received: 21 May 2018 Accepted: 31 August 2018 oxide thin flms Published: xx xx xxxx C. Barone 1, H. Rotzinger2, C. Mauro1,3, D. Dorer2, J. Münzberg2, A. V. Ustinov2,4 & S. Pagano 1 Granular aluminum oxide is an attractive material for superconducting quantum electronics. However, its low-temperature normal state transport properties are still not fully understood, while they could be related to the unconventional phenomenon of the superconductivity in this material. In order to obtain useful information on this aspect, a detailed study of charge carrier fuctuations has been performed in granular aluminum oxide flms. The results of electric noise measurements indicate the presence of a Kondo-type spin-fip scattering mechanism for the conducting electrons in the normal state, at low temperatures. Moreover, the magnetic feld dependence of the noise amplitude suggests that interface magnetic moments are the main source of fuctuations. The identifcation of the nature of fuctuation processes is a mandatory requirement for the improvement of quality and performance of quantum devices. Quantum computation is one of the most attracting research felds, due to the possibility of implementing com- putational machines much more performant than classical computers1. In the last yeas, great progresses have been achieved both from a theoretical and technological side2, with the realization of proof-of-concept algorithms on quantum processors3,4. Among the most useful materials for quantum electronics, superconductors allow in principle the realization of scalable quantum integrated circuits. In particular, aluminum has already shown its potentials thanks to its low surface dielectric loss tangent5 and to the growth of a controllable oxide barrier between the electrodes of Josephson junctions. For quantum circuits where an enhanced kinetic inductance is of interest, granular alu- minum oxide (AlOx) is, among other materials, an interesting candidate. It ofers a good combination of a low microwave loss superconducting state, as well as a very high normal state sheet resistance6. However, several issues regarding the normal state transport properties of AlOx thin flms deserve to be still understood, while they can have a relation with the unconventional superconducting mechanism in this type of material. More in details, the origin of a metal-to-insulator transition, frequently observed above the superconducting critical temperature in AlOx samples, is still a matter of debate and diferent theoretical interpretations have been proposed. As a frst hypothesis, weak-localization efects, arising from electron interference, were considered responsible for the reduction of the low-temperature normal state conductivity of percolative superconducting aluminum flms7. Later on, the low-temperature normal state resistance behaviour of granular aluminum flms was explained in terms of a Kondo-like transport mechanism8. Recently, a low-temperature Mott transition has been identifed in granular aluminum, as a consequence of a nanosize grains decoupling induced by a progressive reduction of the intergrain tunneling probability9. All these models have a solid physical background and seem to satisfactorily apply to the case of granular metals. Terefore, on the basis of standard electric transport investiga- tions, it is very difcult to disentangle between them. A more sensitive experimental technique is then required. In this respect, electric noise spectroscopy has proved to be a very efective and efcient method for studying the kinetic processes of the charge carriers in several systems. As examples, it has strongly contributed to clarify 1Dipartimento di Fisica “E.R. Caianiello” and CNR-SPIN Salerno, Università di Salerno, I-84084 Fisciano, Salerno, Italy. 2Physikalisches Institut, Karlsruhe Institute of Technology, 76131, Karlsruhe, Germany. 3Dipartimento di Ingegneria, Università del Sannio, I-82100, Benevento, Italy. 4Russian Quantum Center, National University of Science and Technology MISIS, 119049, Moscow, Russia. Correspondence and requests for materials should be addressed to C.B. (email: [email protected]) SCIENTIFIC REPORTS | (2018) 8:13892 | DOI:10.1038/s41598-018-32298-1 1 www.nature.com/scientificreports/ Figure 1. Resistivity versus temperature plots. Te data refer to the large-strip device #1 (a) and to the small- strip device #2 (b). Te red solid lines are the best ftting curves using equation (1) with the Kondo resistivity as the “insulating” term ρI. Te enlargements of the low-temperature region (8–60 K) are shown as insets with a logarithmic temperature scale. unsolved fundamental questions regarding the electronic properties of manganites10,11, iron-based supercon- ductors12,13, carbon nanotube composites14, and perovskite-based solar cells15. Moreover, the study and control of fuctuation mechanisms plays a crucial role to improve the efciency of the future devices for quantum infor- mation processing16. Indeed, it is evident that an improvement of the quality of quantum computing devices is obtained by isolating the quantum bits (qubits) from external decoherence sources. Te identifcation of the origin of charge carriers fuctuations is, therefore, essential for the reduction of these sources of decoherence16. In view of all these considerations, detailed DC electric and magneto-transport measurements, as well as voltage-noise analysis, of granular aluminum thin flms are here reported. Diferent theoretical models have been considered and analyzed, in order to reproduce the experimental fndings. Te results obtained contribute to shed light on the normal state conductivity mechanisms, providing, also, interesting information that could help for a better understanding of the unconventional phenomenon of the superconductivity in granular flms. Results and Discussion DC electrical transport measurements. Te resistivity temperature dependence is shown in Fig. 1 for the large-strip device (device #1 in Fig. 1(a)) and for the small-strip device (device #2 in Fig. 1(b)). An evident increase at low temperatures is observed, in agreement with earlier fndings in similar resistive flms7,8. Moreover, a characteristic minimum is clearly found only for the smaller device, see Fig. 1(b). In general, the ρ vs T behav- iour can be modeled by two additive contributions: a metal-like and a generic “insulating” term as ρρ=+n ()TATTI(), (1) where the metallic resistivity AT n is a power law with n = 1, 2, or 5. In particular: n = 1 indicates the presence of charged-impurity resistivity contributions17,18, n = 2 is characteristic of the standard metallic Fermi-liquid behav- 19 iour, n = 5 reveals resistivity contributions due to lattice vibration . Te “insulating” term ρI can be analyzed in terms of diferent models, as20: (I) Mott variable-range hopping (VRH), (II) Efros-Shklovskii (ES) localization, (III) two-dimensional (2D) weak localization (WL), (IV) three-dimensional (3D) weak localization (WL), (V) fuctuation-induced tunneling (FIT), and (VI) Kondo efect. Te explicit temperature dependencies are reported in Tables 1 and 2. All these models are generally able to reproduce well the data, giving very similar values of statistical parameters (i.e., reduced χ2 and coefcient of determination r2) as shown in Tables 1 and 2, where the coefcients related to the metallic resistivity term are also reported. Te various parameters describing the ρI term are discussed in details in ref.20. As an example, the curve corresponding to the Kondo-resistivity term is shown SCIENTIFIC REPORTS | (2018) 8:13892 | DOI:10.1038/s41598-018-32298-1 2 www.nature.com/scientificreports/ −n 2 −6 2 Model A (μΩcmK ) n ρI(T)-dependence χ × 10 r 02. 5 T VRH 17.2 ± 0.8 0.36 ± 0.08 Bexp 0 2.75 0.987 ()T 05. T ES localization 0.32 ± 0.03 0.9 ± 0.1 Bexp 0 3.34 0.985 ()T −1 2DWL 307 ± 22 0.15 ± 0.04 [G0 + G1ln(T)] 2.62 0.988 p/2 −1 3DWL 2.8 ± 0.4 0.8 ± 0.2 [G0 + G1T ] 6.11 0.928 T FIT 0.080 ± 0.004 1.0 ± 0.1 ρ exp 1 2.13 0.991 0 TT+ 0 T Kondo efect 0.52 ± 0.04 0.92 ± 0.09 ρ ln 0 2.43 0.989 0 T Table 1. Comparison between diferent theoretical models of ρ vs T curves for device #1. −n 2 −6 2 Model A (μΩcmK ) n ρI(T)-dependence χ × 10 r 02. 5 T VRH 6.0 ± 0.2 0.53 ± 0.05 Bexp 0 7.71 0.979 ()T 05. T ES localization 0.39 ± 0.02 0.9 ± 0.1 Bexp 0 7.94 0.974 ()T −1 2DWL 71 ± 7 0.29 ± 0.03 [G0 + G1ln(T)] 6.97 0.981 p/2 −1 3DWL 0.7 ± 0.2 0.9 ± 0.2 [G0 + G1T ] 14.9 0.863 T FIT 0.154 ± 0.004 1.0 ± 0.1 ρ exp 1 6.41 0.983 0 TT+ 0 T Kondo efect 0.50 ± 0.04 0.93 ± 0.09 ρ ln 0 7.04 0.980 0 T Table 2. Comparison between diferent theoretical models of ρ vs T curves for device #2. in Fig. 1 as a red solid line. Te good agreement between theory and data is also shown by the enlargement of the low-temperature region, reported in the insets of Fig. 1 with a logarithmic temperature scale. By analyzing the values of n, however, it is observed that, in the case of VRH and 2DWL, they are very far from the values predicted by the theory for the diferent scattering mechanisms producing the metallic resistivity term. Moreover, the best ftting curves obtained with ES localization give values of T0 parameter several orders of magnitude smaller than those of aluminum compounds, which are usually characterized by a very high energy barrier. Terefore, the only theoretical interpretations, capable to reproduce the experimental resistivity data and rea- sonable from a physical point of view, are: 3DWL, FIT, and Kondo efect. It is important to stress that the standard DC electrical analysis alone is not sufcient to precisely identify the exact physical origin of the transport mecha- nisms at work.