Kondo resonance

Furthermore, it was shown the unpaired spin S = 1/2, which is delocalized over the two Pc rings, still remained in the Jt-orbitals after absorption on Au(lll). Consequently, STS measurements also provided direct observation ofthe S = 1/2 radical on the TbPc2 molecules on Au(lll) whereby the indicative Kondo-peak could be switched off by tunnelling current pulses [215]. Indeed the tunnelling conductance (dl/dV) was analysed from STS experiments of TbPc2 on Au(lll) near the Fermi level showed a zero-bias peak (ZBP) in the spectra, which could be assigned as a Kondo resonance. Clear Kondo features for the molecules with 9 = 45° were observed when the tip was positioned over one ofthe lobes of TbPc2. 

Mesoscopic physics has defined many of the issues (Landauer limit transport [10, 11], Coulomb blockade regime [12], Kondo resonance regime [13-15]...) that will occur later in this chapter describing molecular transport junctions. These concepts are relevant, but must be reinterpreted to understand the molecular case. 

Liang W, Shores MP, Bockrath M, Long JR, Park H (2002) Kondo resonance in a singlemolecule transistor. Nature 417(6890) 725-729... 

The CeAlj compound shows a VltW value of 1.2JK /Ce atom, but the C /T ratio increases up to 2 JK"VCe atom at 0.5 K, which signals the transition to the coherent coupling of the Kondo resonances in a Kondo lattice (Bredl et al. 1984). Under an applied field the C nlT maximum value is reduced to 1.7 J K /Ce atom for H = 4 T and lightly shifted to lower temperatures (see also Bredl et al. 1984). The effect of pressure on /ltCO) is similar to that in CeCug, reducing its value to 0.55 JK VCe atom under 8.2 kbar, but it is significant that the C /T maximum disappears under only 0.4 kbar of pressure. 

Cubic (space group I43d) Ce3Au3Sb4 exhibits semiconducting resistivity down to at least 0.15 K. The Ce atoms are fully in the ionic 4f state. Inelastic neutron scattering sees three CEF levels appropriate for Ce in tetragonal symmetry (the local symmetry of the Ce site). A huge peak in susceptibility and specific heat arormd 3 K has been attributed to a Kondo resonance within the narrow band gap (Kasaya et al. 1991, 1994). 

However, in the case of a dilute alloy with unstable-moment inpurities (e.g., Ce " ) many-body effects lead to the existence of narrow Kondo resonance states above the Fermi level as discussed in detail in sect. 4. This leads to a strongly energy-dependent scattering rate for conduction electrons E E) = 1/t( ) that is directly proportional to the density of many-body resonance states (see fig. 46). The energy scale for the t E) dependence is now the Kondo temperature which can be comparable with T. Therefore, in this case one should expect that MAQO and dHvA amplitudes may deviate from the LK formula. Experimentally this effect has been quite elusive. One of the rare cases where it was actually observed is the dilute alloy Laj Ce Bg (x = 0.10), see Thalmeier et al. (1987). Figure 41 shows the T-dependence of MAQO amplitudes for a very small extremal area with F = 6.5T or... 

From Coleman 1984.) Inset shows the temperature variation of the normalized Kondo resonance weight Sn (T) = SnXT)/Sn/0). This is a universal function of T/T , independent of model parameters in the Kondo regime. (From Cox 1985.)... 

It is suggestive that the narrow Kondo resonance states of individual 4f impurities will form heavy quasiparticle bands in a periodic lattice of 4f ions. A satisfactory microscopic theory of heavy-band formation has yet to be developed. The Hamiltonian of eq. (107) can be generalized to the lattice by introducing a Bose field h,- at every lattice site. However, in this model it is no longer practicable to restrict to physical states with = 1 at every site. The most successful approach so far consists in a mean-field approximation for the Bose field (Coleman 1985, 1987, Newns and Read 1987) that is valid for large N and r < It can be applied both for the impurity and the lattice model. It starts from the observation that in the limit with QJN= fixed, the rescaled... 

The first equation shows that the center of the quasiparticle bands lies at an energy above the original conduction band Fermi level. This should be compared with the position Tg = aT of the Kondo resonance in the impurity model. The second equation simply results from the charge constraint QflN = g, which is now enforced only on the average in contrast to the impurity model. The occupation f(0) is obtained by setting equal to the actual value of 1 IN. The quasiparticle bands are the result of a hybridization with an effective strength K Here r iT) is the average fraction of sites without f occupation,... 

Fig. 1. PES spectra at various temperatures showing the appearance of the low temperature Kondo resonance in CeCu2Si2. The inset shows 4f-spectral density p f E) of the impurity Anderson model calculated within NCA...

For the non-symmetrical Anderson model with C/ + 2ef 0, one has in the Coqblin Schrieffer and Kondo Hamiltonians in addition to the exchange a potential scattering term. The Kondo resonance is no longer at the Fermi energy ep = 0 but is shifted. This shift leads to a smaller resistivity p(T), the maximum of which, however, is still at T = 0. The potential scattering has a dramatic effect on the thermoelectric power, which vanishes in the symmetric case C/ + 2ef = 0, but has a huge peak near 7k for C/ 4- 2ef 0. 

Fig. 1. Schematic 4f-elcctron density of states for a Ce ion in a simple metal. The energy co is measured relative to the Fermi level. The two broad peaks are due to 4f 4f° and 4f - 4f transitions. The peak dose to m = 0 is the Kondo resonance.

The large f-electron density of states ATf(0) is due to the Kondo resonance which exists in both VF and HF systems. Figure 1 shows a schematic plot of the 4f-electron density of states of a Ce ion at temperatures T< 7]c with the energy co measured relative to the Fermi level. One has at energy 6f < 0 a broad peak due to the transition of a conduction electron to the empty 4f level (f ->f°) and a similar broad peak... 

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