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Submitted on 1 Jan 1978
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INFLUENCE OF THE ELECTRON-PHONON INTERACTION ON THE dHvA EFFECT
AMPLITUDE IN MERCURY
M. Elliot, T. Ellis, M. Springford
To cite this version:
M. Elliot, T. Ellis, M. Springford. INFLUENCE OF THE ELECTRON-PHONON INTERACTION
ON THE dHvA EFFECT AMPLITUDE IN MERCURY. Journal de Physique Colloques, 1978, 39
(C6), pp.C6-1089-C6-1090. �10.1051/jphyscol:19786482�. �jpa-00217964�
JOURNAL DE PHYSIQUE Colloque C6, supplc?ment au no 8, Tome 39, aotit 1978, page
C6-1089
INFLUENCE O F THE ELECTRON-PHONON INTERACTION ON T H E
dHvAEFFECT AMPLITUDE I N MERCURY
M. Elliot, T. Ellis and M. Springford
SchooZ of MathematicaZ and Physical Sciences, University of Sussex, FaZmer, Brighton, Sussex, U. K.
Rdsum6.- Les rdsultats de mesure d'effet dHvA dans le mercure sont compar6s P la thdorie dVEngelsberg et de Simpson. Les Lcarts P la thsorie de Lifshitz et de Kosevich qu'on attendait, ont Qtd remarqugs.
Abstract.- Measurements of dHvA effect amplitudes in mercury are compared to the theory of Engelsberg and Simpson. The expected departures from the Lifshitz-Kosevich theory are observed.
For a metal such as mercury with its low lying phonon peak (21 K) and strong electron-phonon coupling, one would expect to see appreciable mo- difications of the renormalized electron effective mass, m 3C
,
and lifetime, with changes inmagnetic field and temperature.Indeed such effects have been observed in, for example, cyclotron resonance expe- riments /l/. On the basis of simple arguments one might also expect to see these effects reflected in amplitude measurements of the dHvA effect, but careful measurements by Palin /2/ failed to reveal them. This surprising result has been explained by Engelsberg and Simpson /3/ who showed that the in- fluence of the electron-phonon interaction on the dHvA effect is rather subtle and that, for the experimental conditions employed by Palin, depar- tures from quasiparticle behaviour are expected to be small. We report on some new measurements aimed as observing such departures under experimental con- ditions rather more favourable than those of Palin.In particular we have studied electrons with lower m
' and recogni ed the importance of B rather than
of the dHvA effect, using a curve fitting procedu- re. Amplitudes were determined over the range 1 to 5.5 T and conventional Dingle plots (essentially graphs of log ( A ~ B ~ / ~ ) versus ~-')were constructed.
At low magnetic fields (B 7 2 T) such graphs were linear in accord with the Lifshitz-Kosevich theo- ry 151 and, using the value of m* determined from the temperature dependence of A between 1.2 and 2.1 K which, depending on orientation was close to 0.15 mo, indicated Dingle temperatures in the ran- ge 40
-
100 mK. However, for higher magnetic fields an anomalous behaviour was observed, the measured dHvA amplitudes exceeding the value predicted according to the classical Lifshitz-Kosevich theo- ry. At the highest field of 5.0 T the deviation was 7 %*
2 %.According to Engelsberg and Simpson /3/ the entire influence of the electron-phonon interaction on the dHvA effect is contained in a term for the amplitude of the rth harmonic, .
A r n,n=o m C exp
1 [ - Yiwc 2nr[Wn+i(Wn)]) T as the sensitive variable 141.
in which w is the cyclotron frequency, eB/m and Experiments were performed on spherical
S(@,) is related th the full self-energy evaluated single crystals ('W.5 mm3) of high purity mercury
at the poles, iwn, of the Fermi function, where (99.999 % by wt.) by the low frequency field modu-
w = (2n + 1) II kBT. Thus, (W,) = iC (iwn), and lation technique. Measurements were confined to n
m r
the B-orbit at orientations for which the frequency S(W,) = II k B ~ -
l.
~ 2a2 (w)F W \ (W)was within 5T of its minimum value of 74T, with + (Z'K~,?T] 2 1 - l -~
1 L
.-J discrimination against unwanted higher frequencies
achieved using the frequency selectivity of the The form of these equations is such that the limi- modulation method and temperatures $2 K. dHvA effect ting behaviour of A at low fields and temperatu- amplitudes, Ar, were computed from a digital record res is expressed by,
of the signal which extended over one or two cycles Ar % ~ z / s i n h ~ z (3)
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19786482
in which 2n2rkB~ (l+Xo) /Kwc where
~ ( u , )
= lrkBTAOThe field dependence of Ar would then appear to conform to the classical L-K theory 151, but with the cyclotron effective mass renormalized, m = m(] + Xo). We refer to this as the quasipar- ticle regime. However, as indicated by Mueller and Myron /h/, with increasing B increasingly more terms in equ. (I) become significant, and when (@,/a ) %l, at the highest values of TI which
ph
effectively contribute to equ.(l), then deviations from quasiparticle behaviour are expected. Calcu- lations based on a knowledge of a2(w)~(w) for mer- cury from the tuneling data of McMillan and Ro- well /6/ were made by Mueller and Myron /4/. For the present experimental conditions we have compu- ted and amplitude for AI which, at 5.5 T, exceeds that expected on the basis of the Lifshitz-Kosevich theory by %9 % in very good agreement with our experimental result.
Thus, arising out of the influence of the electron-phonon interaction in the dHvA effect we claim to have observed for the first time departu- res from quaisparticle behaviour as expressed by the alassicalLifshitz-Kosevich theory.
References
/ l / Poulsen, R.G. and Datars, R.W., Solid State
Commun.
8
(1970) 1969./2/ Palin, C.J., Proc. Ray. Soc., Lond.A.329 (1972) 17.
/ 3 / Engelsberg, S. and Simpson, G., Phys. Rev.
(1970) 1657.
/ 4 / Mueller, F.M. and Myron, H.W., Commun. on
Phys.. 1 (19761 99.
/5/ Lifshit-z. I.H. and Kosevich. A.M. Sov. Phvs.
JETP., 2 (1 956) 636.
/6/ McMillan. W. and Rowell. J. Superconductivitv, ed. R.D. Parks (Marcell Dekker, New York) 1969.
