Study of the Shubnikov-de Haas effect. Determination of the fermi surfaces in graphite

  • Soule D
  • McClure J
  • Smith L
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Abstract

Measurements of the oscillatory magnetoresistance of a high-quality
graphite single crystal were made for all angles theta between the
magnetic field and the c axis, for magnetic fields up to 24 kG, and
for temperatures from 1.22 to 4.22°K. The results were analyzed by
a least-squares fitting to a generalized Landau formula. Oscillations
due to electrons were observed for all orientations (including H
perp c, where the amplitude dropped by a factor 105), proving that
the electron Fermi surfaces are closed. Although oscillations due
to holes were not observed beyond theta =84°, indirect arguments
show that the hole Fermi surfaces are also closed. Both electron
and hole surfaces are elongated along the c axis and have anisotropy
ratios of 12.1±1.4 and about 17, respectively. The electron surface
is approximately ellipsoidal, whereas the hole surface is similar
except for extended ends giving it a diamond-like shape. The results
are consistent with a moderate degree of trigonal asymmetry about
the c axis. Comparison between the electron density found from the
volume of the electron Fermi surfaces and that determined previously
from the nonoscillatory galvanomagnetic data confirms the theoretical
prediction that there are four electron Fermi surfaces in the Brillouin
zone. More indirect arguments show that there are two hole surfaces.
Consideration of the size and location of these surfaces along the
six zone edges parallel to the c axis leads to a new determination
of Delta =-0.12 eV for the band parameter which represents the difference
of potential between the two types of atomic sites in the graphite
lattice. Analysis of the temperature and magnetic field dependence
of the oscillatory amplitude yields effective mass values in the
basal plane of (0.039±0.001)m0 for electrons and (0.057±0.002)m0
for holes. These masses show an orientation dependence that is consistent
with the derived Fermi surface anisotropies. The large amplitude
and asymmetric shape of the oscillations in the magnetoconductivity,
measured for H||c at 1.26 and 4.22°K, are accurately described by
the theory of Adams and Holstein. However, there is an unexplained
monotonic variation with magnetic field in the total magnetoconductivity.
The effective change in temperature due to collision broadening Delta
T is about 5 times greater than that estimated from the conductivity
relaxation time. This discrepancy in Delta T is qualitatively explained
and is related directly to the fact, established from the data of
Berlincourt and Steele, that the Delta T found from magnetoresistance
oscillations is greater than that found from susceptibility oscillations
on the same sample.

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Authors

  • D. E. Soule

  • J. W. McClure

  • L. B. Smith

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