Luttinger theorem

An alternative way to clarify the nature of this state is to test its stability with respect to a metal-insulator transition. This has received a lot of theoretical attention recently. The JT singlet ground state makes these compounds free from the tendency towards a magnetic instability observed in so many Mott insulators. In fact, their ground state does not break any symmetry and Capone et al. explained [43] that it then has a zero entropy, which makes a direct connection with a metal impossible (it would violate the Luttinger theorem). These authors predict that the only way to go from the insulator to the metal would be through an exotic superconducting phase or a first-order transition. 

Here Martin and Allen (1979) have shown that for an even count of f and d electrons, and with no other electrons in the conduction band, the appUcation of the Luttinger theorem (Luttinger 1960) leads to being in the gap of an intermediate-valent system. For an odd electron count the Fermi level lies in one of the density of states peaks resulting in intermediate-valent and heavy-fermion behavior (Martin 1982). This theory has been greatly stimulated by the establishment of an insulating behavior of SmBg at low temperatures, which has taken 12 years of research (Nickerson et al. 1971) and 3 conferences on intermediate valence (1977, 1981, 1982). 

A d-f hybridization model according to Brandow (1986) always yields a hybridization gap in the f quasiparticle density of states. The Fermi level can be in the gap or pseudo gap when the Luttinger theorem permits, as e.g. in SmBs, high-pressure SmS or YbBi2, or it can be in a quasiparticle band as in metallic intermediate-valent systems as YbCuAl, CePda or in heavy fermions like UPta, CeAla, CeCug, etc. Quite recently the same theoretical approach has been taken by Czycholl and Schweitzer (1992) and transport and magnetic properties of heavy fermions with a hybridization gap have been calculated in agreement with experiment. 

An important property of the Fermi surface is that the volume (in /c-space) that it encloses is not altered by the interaction between the electrons, unless long-range antiferromagnetic order is set up. This was first shown by Luttinger (1960). We shall make use of this theorem in Chapter 4, Section 3 in discussing metal-insulator transitions due to correlation. 

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