Download The Band Jahn-Teller Effect: A New Perspective on an Old Problem

The Band Jahn-Teller Effect: A New Perspective on an Old Problem
Victor Polinger
Science Div., BCC, 3000 Landerholm Circle SE, Bellevue, 98007-6484 W A, USA
[email protected]
We explore elementary excitations and some related properties of a Jahn-Teller (JT) crystal. In every
elementary cell, due to electron degeneracy, the one-center JT effect results in a dynamic instability
of the ground state. In this work, primary attention is payed to what happens above the temperature
of structural phase transition, T > T0. In this case, most interesting properties are determined by the
corresponding dynamics of JT-coupled electrons in a partly filled valence band, the so-called band
JT effect.
First, in a qualitative way, we demonstrate that the vibronic crossover is a regular phenomenon in
any JT crystal. Using an example of a cubic crystal with linear Eqe coupling, we present the
specifics of elementary excitations in the band JT effect. The consideration is reduced to the
simplest case of weak vibronic coupling to one dispersionless optical phonon band corresponding
to frequency T0 (the Einstein model).
At weak coupling, as the JT coupling is linear with respect to phonon operators b(†(q) and b((q), the
zero-phonon state,
, is admixed to just one-phonon excited states,
,
similar to the one-site (molecular) case. The wave functions do not retain their multiplicative form;
they are not just products of an electron wave function and a phonon wave function. In terms of
probability, with vibronic coupling included, events in the two systems, electron and vibration, are
not independent any more. Instead, due to the JT effect, they are essentially conditional. From this
point of view, the corresponding wave functions describe a traveling entity of the new type, vibronic
in nature, the JT polaron. The extent of the JT hybridization is evaluated by calculating the average
number of phonons in the ground state. It was found that its maximum corresponds to the resonance
part of the energy spectrum where the electron and the phonon branches come close to one another
and intersect. The band JT effect transforms the dispersion curve intersection into the Landau-Zenertype quasi-crossing.
Then we populate the valence band with electrons (holes) and discuss vibronic coupling effects at
a close vicinity of Fermi surface. Most interesting effects occur when x, the number of electrons
(holes) per elementary cell (0 < x < 4) increases to a critical value, x0, bringing the Fermi surface to
the energy position £T0 of JT-induced quasi-crossing of dispersion curves. The one-particle electron
density of states has a pseudo-gap at the frequency region close to the JT quasi-crossing. In the
electron-hole representation, this pseudo-gap manifests itself when x comes close to x0. Also, at x
. x0, the band JT effect introduces nonlinear corrections in temperature dependence of both electron
specific heat and thermal conductivity. The JT induced deviation from the Wiedemann-Franz law
can be interpreted as a non-Fermi-liquid behavior and can serve as a signature of the band JT effect.