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Evidence for a small hole pocket in the Fermi surface of underdoped YBCO

The observation of quantum oscillations and negative Hall effect in underdoped YBa2Cu3Oy (YBCO) showed that the Fermi surface is reconstructed at low temperature, and contains at least a small electron pocket, implying a state with broken translational symmetry. More recently, charge-density-wave (CDW) modulations were observed in YBCO first by NMR [1], and then by x-ray diffraction [2]. Fermi-surface reconstruction and CDW modulations are two universal properties of underdoped cuprates, which begs the following question : Is the Fermi surface of YBCO compatible with a reconstruction by the observed CDW order ?

Here, we report quantum oscillations in thermopower and c-axis resistance measurements that reveal an additional, hole-like Fermi pocket in underdoped YBCO. As seen in Fig. 1a, at T = 2 K the quantum oscillations (QO) seen in the thermopower have a main frequency Fa1 = 540 ± 20 T and a beat pattern indicative of other, nearby, frequencies, as seen in the Fourier transform shown in Fig. 1c. This observation is consistent with previous reports. With increasing temperature, the amplitude of these fast oscillations decreases rapidly and above T = 10 K we are left with a slowly undulating normal-state signal. After their discovery in the Seebeck signal, the slow oscillations were also detected in the c-axis resistance, as shown in Fig. 1b. In both the Seebeck and c -axis resistance data, the frequency of these slow oscillations is Fb = 95 ± 10 T for p = 0.11 and Fb = 120 ± 15 T for p = 0.12. This slow oscillation bears all the key signatures of QO from a minuscule, quasi-2D Fermi pocket : it obeys the Lifshitz-Kosevitch temperature-dependence with a light mass of m* = 0.45 ± 0.1 m0, and the field-angle dependence of Fb is close to 1/cos(theta). Therefore, we argue that it comes from a small Fermi surface, distinct from the larger electron-like Fermi pocket responsible for the main frequency Fa1= 540 T. By performing a quantitative analysis of the doping dependence of the Seebeck and Hall coefficients in YBCO, we have shown that the reconstructed Fermi surface of underdoped YBCO (for 0.08 < p < 0.18) contains not only the well-established electron pocket, but also another hole-like surface (of lower mobility).

There is compelling evidence that the Fermi surface of YBCO is reconstructed by the CDW order detected by NMR and x-ray diffraction. Because the CDW modulations are along both the a and b axes, the reconstruction naturally produces a small closed electron pocket along the Brillouin zone diagonal, at the so-called nodal position. Given the wavevectors measured by x-ray diffraction, there will also be small closed hole-like ellipses located between the diamond-shaped nodal electron pockets. An example of the Fermi surface calculated [3] using the measured CDW wavevectors is sketched in Fig. 1d. It contains two distinct closed pockets : a nodal electron pocket of area such that Fe = 500 T and a hole-like ellipse such that Fh = 100 T. In conclusion, a Fermi surface consisting of one electron and two hole pockets of the measured sizes and masses is consistent with a reconstruction by the observed CDW.


[1] T. Wu et al, Nature 477, 191 (2011).

[2] G. Ghiringhelli et al , Science 337, 821 (2012) / J. Chang et al, Nature Physics 8, 871 (2012).

[3] A. Allais et al, Nature Communications5, 5771 (2014).


Reference : Evidence for a small hole pocket in the Fermi surface of underdoped YBa2Cu3Oy

N. Doiron-Leyraud, S. Badoux, S. René de Cotret, S. Lepault, D. LeBoeuf, F. Laliberté, E. Hassinger, B.J. Ramshaw, D.A. Bonn, W.N. Hardy, R. Liang, J.-H. Park, D. Vignolles, B. Vignolle, L. Taillefer and C. Proust.

Nature Communications /full/ncomms7034.html 6, 6034 (2015) 


Figure 1 : (a) Oscillatory part of the Seebeck coefficient S/T in YBCO (p = 0.11) as a function of 1/B, showing the usual fast quantum oscillations at T = 2 K (red), and the new slow oscillations with Fb 100 T at T = 18 K (blue, multiplied by 20). (b) Oscillatory part of the c-axis electrical resistance in YBCO (p = 0.12). (c) Fourier transform of the c-axis resistance data (p = 0.11), showing the new “low” frequency Fb 100 T reported here, and the three main frequencies Fa1 (blue), Fa2 (red), and Fa3 (green) attributed to the electron pocket. (d) Sketch of the reconstructed Fermi surface using the CDW wavevectors (arrows) measured in YBCO, showing a nodal electron pocket (red) and two hole-like (blue and green).