Laboratoire National des Champs Magnétiques Pulsés CNRS – INSA

- R xy (�)
0.06 1.5 K
2 K
2.5 K
3 K
3.5 K
4.2 K
0.04
0.02
0.00
30 40 50
B (T)
60
Fig. 2 : Hall resistance as a function of magnetic
field B for YBa2Cu3O6.5, at different temperatures
between 1.5 and 4.2 K [5]
16
Thanks to the synthesis of high quality
single crystals by the group of D. Bonn and
the improvement in the signal/noise ratio
measurement under pulsed magnetic field,
we have reported quantum oscillations of the
Hall resistance of the oxygen-ordered copper
oxide YBa 2Cu 3O 6.5 [6]. With a T c of 57.5 K,
these samples have a hole doping per planar
copper atom of p=0.10, corresponding to the
underdoped region of the phase diagram. Fig.
1 shows the magnetic field dependence of
the Hall resistance at different temperatures
between 1.5 K and 4.2K, where clear
oscillations of the resistance are observed
beyond the superconducting transition. The
oscillation frequency of 530 T implies a
Fermi surface pocket that encloses a k-space
area which represents only 1.9 % of the
Brillouin zone. The low oscillation
frequency reveals a Fermi surface made of
small pockets, in contrast to the large
cylinder characteristic of the overdoped
regime. dHvA oscillations have been
observed at the same doping level [7, 8]. In
addition, quantum oscillations have also
been observed in the stoechiometric compound YBa2Cu4O8 (Tc=80 K corresponding to a doping p=0.14) with a
similar frequency F=660 T [9]. The sharp contrast between the sizes of the FS on opposite sides of the phase
diagram is illustrated in Fig. 3. The main panel displays the Fourier transform of QO of underdoped
YBa 2Cu 3O 6.51 (red) and of overdoped Tl2201 (purple).
Fig. 3 : Fourier transform of the oscillatory part of
the torque for underdoped YBa2Cu3O6.51 (red) and for
overdoped Tl2201 (purple). Insert: Sketch of the FS
area deduced from the frequencies of quantum
oscillations via the Onsager relation.
[10].
The inset shows the area of the
corresponding orbit in the FBZ. It is
worth noting that quantum oscillations
tell us neither the number of pockets,
nor their location in the reciprocal
space. This drastic dissimilarity of FS
topology simply reflects the difference
in carrier density on opposite sides of
the phase diagram. While the large
cylinder in the overdoped side
corresponds to a carrier density of 1 +
p, as predicted by band structure
calculations, the band picture fails in
the underdoped side, where the carrier
number scales more closely with p.
One fundamental question for our
understanding of HTSC is what causes
the dramatic change in FS topology
from overdoped to underdoped
regimes? Based on the observation of a
negative Hall effect at low temperature
in underdoped YBCO, the presence of
an electron pocket in the Fermi surface
has been suggested would naturally
arise from a reconstruction of the large
hole FS calculated from band structure