Jahn-Teller Center as Quasiparticle of Fractional Statistics

Abstract

The Jahn-Teller (JT) effect [1] describes the interaction between the two components of a degenerate electronic state (E) through a, usually degenerate, pair of nuclear modes (e). An unusual aspect of the E®e-type JT effect is that the Born-Oppenheimer electronic wave functions, which diagonalize the electronic Hamiltonian in the fixed-nuclei approximation, undergo a sign change when the nuclear coordinates traverse a closed path around the conical intersection [2-4]. As it has been shown by Mead and Truhlar [5], the resulting double-valuedness of the electronic wave functions can be removed, but only at the expense of introducing a vector-potential-like term into the effective Hamiltonian for the nuclear motion, which has been termed the molecular Aharonov-Bohm effect [6]. The above-mentioned sign change is a special case of Berry's geometrical phase [7] which holds implications for topics as diverse as the theory of the fractional quantum Hall effect [8], the optical activity of a helical fiber [9], superconductivity [10], and gauge field theories [11]. A more general discussion in the context of molecular physics can be found in the review article by Mead [12]. In the present paper we argue that JT centers can, in some applications, be considered as quasiparticles of fractional statistics. Thus in Sec. 2 a brief re-derivation of the adia&atic analytical solution of the linear E®e-type Hamiltonian is presented and some of its properties are discussed. The arguments in favor of the fractional nature of the statistics of the JT quasiparticles and their relevance for description of the type-II superconductivity are discussed in Sec. 3. Some conclusions concerning high-T c superconductors are presented in Sec. 4.