Low-energy restoration of Fermi-liquid behavior for two-channel Kondo scattering

Abstract

The origin of zero-bias anomalies ͑ZBA's͒ in pure metal nanoconstrictions is investigated. It is shown that the ZBA's in titanium nanoconstrictions can be completely understood in terms of electron-assisted tunneling systems. The behavior of such a system is expected to depend on two distinct energy scales, a Kondo energy below which the electrons behave in a non-Fermi-liquid manner, and a splitting energy below which the Fermi-liquid behavior is restored. Titanium nanoconstrictions have been found to exhibit zero-bias anomalies that show both the non-Fermi-liquid behavior and the low-energy restoration of the Fermi liquid.

The 2-Channel Kondo Model

“…The qualitative features of these anomalies (such as their behavior in a magnetic field, under annealing and upon the addition of static impurities), which are reviewed in detail in the present paper, lead to the proposal [1] that the ZBAs are caused by a special type of defect in the nanoconstrictions, namely two-level systems (TLSs). This proposal has recently received strong support from a number of subsequent, related experiments (briefly reviewed in section VII) by Upadhyay et al on Ti constrictions [19] and by Keijsers et al on metallic-glass constrictions [20,21].…”

“…Note, though, that they do not occur in all Cu samples showing ZBAs. Moreover, recent experiments by Upadhyay et al [19] on Titanium constrictions and by Keijsers et al [20] on constrictions made from metallic glasses showed TLS-induced ZBAs with properties very similar to RB's quenched Cu constrictions, but no conductance transitions at all (see (Ti.6) and (MG.4) in section VII, where these experiments are reviewed). This suggests that conductance transitions are not a generic ingredient of the phenomenology of ZBAs induced by TLSs.…”

“…In recent years, ZBAs have been found in a number of different nanoconstriction studies [19,20,21,54]. It should be appreciated that in each the ZBA could in principle be caused by a different mechanism.…”

“…7 Moreover, this little calculation has furnished us with an expression, namely Eq. (19), for the universal scaling function Γ(v) in terms of the exactly known universal functionΓ(x).…”

“…On the experimental front, an experiment performed by two of us (RB) [1,11], that investigated certain zero-bias anomalies (ZBAs) in the conductance of quenched Copper nanoconstrictions, has emerged as a potential experimental realization of the 2-channel Kondo (2CK) model and the corresponding non-Fermi-liquid physics [2,12,13,14]. Although criticisms of the 2CK interpretation [15,16] and alternative mechanisms for the ZBAs have been offered [17,18], the 2CK scenario has recently received important additional suppport from experimental results on ZBAs in constrictions made from Titanium [19] and from metallic glasses [20,21].…”