The Jahn–Teller effect: An introduction and current review

The Jahn–Teller effect (JTE) is defined and the historical background of the Jahn–Teller theorem is briefly discussed. The E⊗β system, an electronic doublet coupled to a single mode of vibration, is introduced as an elementary example and is used to illustrate features characteristic of Jahn–Teller systems. The spin resonance of Cu++ in various materials is considered and the particular case of Cu++ in a cubic crystal field is used to introduce the E⊗ε Jahn–Teller system. The linear and quadratic E⊗ε systems are discussed, and the linear case is used to illustrate the appearance of the Berry phase in a quantum system. The role of the Jahn–Teller effect in high-temperature superconductivity is also discussed. In particular, the JTE-based superconductivity theories of Englman et al. [Physica C 169, 314–324 (1990)] and Weber et al. [Physica C 162/164, 307–312 (1989)] are briefly reviewed. The possible roles of the Jahn–Teller effect in C60 (buckminsterfullerene) and superconducting K3C60 are also considered.