Electrons in Metals

Abstract

Identical constituent molecules in a crystal are attractively correlated in the lattice structure. In a binary system below a critical temperature T _c, such correlations can be expressed as J _ij σ _i σ _j , where J _ij is undetermined by the first principle. On the other hand, in Chap. 9, we discussed that such correlations in a whole crystal can be represented by a soliton potential arising from the structure deformed by a collective mode of σ _k . The pseudospin σ _i or its Fourier transform σ _k can be regarded as a classical field, consisting of Fermion particles if quantized. In metallic crystals, electrons are quantum mechanically correlated as described by Pauli’s principle; such electron correlations are related with their spin directions, which are notably similar to σ _i σ _j for classical molecular correlations. In this context, we may expect a similar relation between binary and electron systems, leading to analogous phase transitions.