Phonons and the Isotopically Induced Mott transition - Physics

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Phonons and the Isotopically Induced Mott transition - Physics

5.4 Determination of Holstein parameters

5.4.1 Calculation of vibrational modes

The vibrational frequencies of the ET molecules can be obtained from the analysis of

infrared and Raman spectra but in order to calculate the electron-phonon coupling

each of these frequencies must be associated with a corresponding normal

coordinate. As previously mentioned, much of the experimental work in determining

the vibrational spectra of both H 8 -(ET) 2 Br and D 8 -(ET) 2 Br was carried out by Kozlov

et. al. 20 and later expanded upon by Eldridge et. al. 21 who also considered of

C → C and

12 13

S → S substitutions. To simplify calculations both Kozlov and

32 34

Eldridge assumed planar symmetry (D 2 symmetry) for the molecule in the

subsequent mode calculations which is not strictly true. Experimental observations

by Leung et. al. using X-ray spectroscopy indicate that that there are actually two

conformations that predominate in the crystal – staggered and eclipsed. These

conformations are shown in Fig. 5.1.

suggests that fast cooling not only increases the disorder in the sample, but also

reduces the “effective chemical pressure” (see Fig. 7.2).

Utilizing a Gaussian based, all electron DFT calculation Powell et. al. 6 calculated the

Raman spectra of the neutral ET molecule in both conformations giving results (Fig.

5.2) which are in good agreement with the experimental spectra observed by

Eldridge et. al. 21

(a)

(b)

Figure 5.1

(a) The staggered conformation and (b) the eclipsed conformation for the ET molecule. Note that

the conformational state is primarily dependant upon the configurations of the terminal ethylene

groups. Both states are energetically separated by 3.4 meV. 6

Figure 5.2

The calculated vibrational spectra for both the staggered and eclipsed conformations of the neutral

ET molecule. These show very good agreement with the experimental data obtained by Eldridge et.

al. Taken from Ref. 6

Although the former is favoured as the groundstate Powell et. al. 6 37 suggest that the

‘freezing in’ of both phases may lead to the increased disorder in the crystal and

therefore explain the changes in critical temperature with cooling rate observed by

Taniguchi et. al. 9 However, for partially deuterated samples dρ / dT < 0 (insulating

behaviour), where ρ is the resistivity, just above T c in the fast cooled samples. This

We have performed similar calculations on the eclipsed and staggered conformations

for both the hydrogenated and deuterated molecules along with the 13 C-(ET) 2 Br. The

results for the DFT vibrational calculations are summarized in Appendix B.

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