The Jahn-Teller Effect: A Permanent Presence in the Frontiers of Science

Abstract

In 1937 the Jahn-Teller (JT) effect addressed the instability (potential or actual) of non-linear symmetric molecules with degenerate orbital electronic states. In view of the large variety of JT activity that has taken place since then, we might broaden our perspective to look at works whose subjects fall under the more general heading of "Strong interactions between two dissimilar systems" (where one system is usually bosonic and the other fermionic). In these intervening years we find several highly important works in Physics and Chemistry that come under this heading and were either connected with, or arose from, JT systems, problems and approaches. Apart from high temperature superconductors, we mention Yang-Mills gauge-forces, symmetry breaking (in elementary particles), conical intersections in molecular potential surfaces, surface crossings between them in chemical reactions, entanglements in the quantum theory of measurements and Berry phases. We elaborate on the last two topics. We show first that the slow evolution of a T coupling from the weak to strong regime can model the quantum mechanical three-state measurement situation, when the positions of the nuclei acts as the measuring device. We then employ recently derived integral relations between component moduli and phases in a time dependent wave-function to demonstrate the equivalence between the state-reduction and the phase decoherence interpretations of the measurement process.

Jahn–Teller and spin–orbit coupling effects in transition-metal trifluorides

“…In solids, the static JT effect usually is of primary interest, that is, the distortion of the crystal lattice or of impurity centers from the highest possible symmetry to a lower spatial symmetry. 7,8 In some molecules, the distortion can not be detected either due to random movements of bonds, which do not allow the measurement of nuclear geometry within a given time resolution, or else the distortion is too weak as to be observable. However, the distortion can be observed by freezing the nuclear motion out at low temperatures.…”

“…This case is referred as dynamic Jahn-Teller distortion. [6][7][8] The most common case is the E × e JT effect, where a doubly degenerate mode (e) lifts the degeneracy of a doubly degenerate electronic state (E) in trigonal, tetrahedral or 1 2 CHAPTER 1. INTRODUCTION cubic systems.…”

Electron‐phonon interaction in correlated electronic systems: polarons and the formation of orbital ordering

“…where the plus (minus) sign refers to Holstein (E ⊗ β Jahn-Teller) electron-phonon coupling [3]. H 0j is diagonalized by a Lang-Firsov transformation [4] and has energies…”

“…where the plus (minus) sign refers to Holstein (E ⊗ β Jahn-Teller) electron-phonon coupling [3]. H 0j is diagonalized by a Lang-Firsov transformation [4] and has energies E 0j = ω 0 n j − E p σ (n jθσ ± n jǫσ ) 2 + γ U n jγ↑ n jγ↓ + U O (n jθ↑ + n jθ↓ )(n jǫ↑ + n jǫ↓ ) (1) if there are n j (≥ 0) phonons and n jγσ (= 0, 1) electrons with (pseudo)spin σ (γ) at site j.…”

Collective Modes in the Cooperative Jahn–Teller Model: Path Integral Approach

“…Originally, the Jahn-Teller model was introduced to explain the distortions and the nondegenerate energy levels in molecules, via the strong interaction between the localized electronic states and the vibrations of the nuclei [8,9]. In solids, the cJT effect leads to structural phase transition and magnetic ordering of the spins.…”