Thesis High-Resolution Photoemission Study of Kondo Insulators ...

1.1. Kondo insulator and Kondo metal 5
the coherence temperature. 1 Hybridization between the narrow f band and a broad
conduction band leads to a narrow indirect gap in the case where (i) one conduction
electron and one f electron exist in the unit cell and (ii) the narrow f band crosses only
one conduction band. While a normal band insulator, which is illustrated in Fig. 1.2
(b), is expected to show an activation-type transport properties in a wide temperature
range, strongly-renormalized band insulator would show such properties only below the
coherence temperature, which is lower than TK/32 . Here, the Coulomb repulsion U reduces
both the effective band width and the gap size, but there is no qualitative change
in the band structure from U = 0: The band structure in Fig. 1.2 (a) is qualitatively
the same as the structure in Fig. 1.2 (b) apart from the difference in the energy scale.
To discuss the Kondo insulator from the viewpoint of a renormalized band insulator,
we should refer to the isostructural and isoelectronic band insulator with the f elements
replaced by elements without f electrons. The number of valence electrons per unit
cell is even for Ce-based Kondo insulators in Table 1.1, satisfying the condition of
the band insulator: As shown in Table 1.1, four Ce-based Kondo insulators have their
semiconducting analogues including Ti (3d 2 4s 2 )orTh(6d 2 7s 2 ) at the Ce (4f 2 6s 2 ) sites.
The existence of such analogues without f electrons supports the idea that the physics
of Kondo insulators is qualitatively the same as the band insulator with U = 0 as far
as the low-temperature properties are concerned. In other words, the Kondo insulators
are expected to be good semiconductors with greatly reduced gaps just as the heavy
Fermion metals are good Fermi liquids.
On the other hand, when one goes to another limit of U →∞, the f-level occupancy
is fixed to unity and the Ce or Yb atom behaves as a local Kondo ion. In
that case, the system is accompanied by a spin gap, which corresponds to local singlettriplet
excitation at the Kondo ion sites. It should be remembered that a single-site
Anderson model reproduces most of thermodynamic and spectroscopic properties of
Ce-based Kondo metals. The single-site model predicts characteristic sharp structures
in the photoemission spectra (Fig. 1.3) and the strong temperature dependence of such
structures. Recent progress in energy resolution has enabled the observation of the
line shape of the Kondo peak (4f 14 → 4f 13 transition for Yb compounds) near EF
since late 1980’s [1.5] and it has been found out that not only the deep photoemission
1 If the local moments form a long-range magnetic order by RKKY interaction, the 4f electrons are
localized even at 0 K and do not contribute the band structure near EF .
2 The magnetic susceptibility of Ce-based Kondo systems shows a maximum around TK/3.