Small Fermi Surface Pockets in Underdoped High Temperature Superconductors: Observation of Shubnikov–de Haas Oscillations in ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$

We report the observation of Shubnikov–de Haas oscillations in the underdoped cuprate superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_4{\mathrm{O}}_8$ (Y124). For fields aligned along the $c$ axis, the frequency of the oscillations is $660\pm 30\mathrm{T}$, which corresponds to $\sim 2.4\%$ of the total area of the first Brillouin zone. The effective mass of the quasiparticles on this orbit is measured to be $2.7\pm 0.3$ times the free electron mass. Both the frequency and mass are comparable to those recently observed for ortho-II ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.5}$ (Y123-II). We show that although small Fermi surface pockets may be expected from band-structure calculations in Y123-II, no such pockets are predicted for Y124. Our results therefore imply that these small pockets are a generic feature of the copper oxide plane in underdoped cuprates.

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Figure 1

Longitudinal and Hall data (${\rho }_{xx}$, ${\rho }_{yy}$ and ${\rho }_{xy}$) for two Y124 samples. The insets show the contact configuration for each sample.

Figure 2

The oscillatory component of the magnetoresistance [$\Delta \rho /\rho (H)$] for both samples at various temperatures. For No. 1, $\rho ={\rho }_{xx}(H)$ while for No. 2, $\rho$ is a mixture of ${\rho }_{yy}(H)$ and ${\rho }_{xy}^H(H)$. In each case, a linear background has been subtracted and the data offset for clarity. The solid lines are fits to Eq. (1) giving $m^{*}=2.7\pm 0.3m_e$.

Figure 3

SdH signal amplitude versus temperature for sample No. 2. The solid line is a fit to the standard expression for the temperature damping factor, $R_T$, yielding an effective mass of $2.5\pm 0.3m_e$. The faint dashed lines give the approximate range of masses consistent with the present data. Inset: Fast Fourier transform of $\rho (1/B,T)$.

Figure 4

(a) Band-structure of Y124 along symmetry directions in the basal plane. The color scale reflects the band character: $C=\mathrm{CuO}$ chain character (including apical oxygen) $P={\mathrm{CuO}}_2$ plane character. (b) Brillouin zone of the Ammm space group of Y124, showing the symmetry points labeled in a). (c) Fermi surface of Y124 viewed along the $c$ axis. The shaded region is the first Brillouin zone. (d) As for (c) but with $E_F$ shifted down by 100 meV.