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L. Hozoi, M. S. Laad, and P. Fulde
Fermiology, the shape and size of the Fermi surface (FS), underpins the low-temperature physical properties of a metal. Recent investigations of the FS of high-temperature superconductors, however, show a most unusual behavior: upon addition of carriers, "Fermi" pockets appear around nodal (hole doping) and antinodal (electron doping) regions of the Brillouin zone in the "pseudogap" state. With progressive doping, these evolve into well-defined Fermi surfaces around optimal doping, with no pseudogap. Correspondingly, various physical responses, including d-wave superconductivity,evolve from highly anomalous up to optimal doping to more conventional beyond. Describing this evolution holds the key to understanding high-temperature superconductivity. Here, we present ab initio quantum chemical results for cuprates, in an attempt to provide a quantitative description of the evolution of the FS with doping, for both hole and electron doped cuprates [1,2]. We adequately describe strong correlation effects involving Cu 3d and O 2p electrons. In particular, the O 2p states giving rise to the Zhang-Rice band are explicitly considered. The mixing with "triplet" 3d(z2) hole states at higher binding energy is also accounted for. Additionally, our scheme incorporates renormalization effects due to nonlocal spin interactions. The resulting quasiparticle dispersion and FS evolution with doping are compared with recent angle-resolved photoemission and quantum oscillation data in high magnetic fields [3,4]. Most interestingly, the FS of the hole doped material evolves from small hole pockets in the deeply underdoped region, via one with both hole- and electron-like sheets at slightly higher hole doping, to a large FS consistent with Luttinger's theorem at still higher doping levels. Our finding of additional electron-like pockets around the corners of the Brillouin zone in the hole doped case offers a route toward a resolution of one of the central controversies surrounding the recent quantum oscillation experiments, where the carrier concentration is x=0.15 for hole doped cuprates with p=0.10 [3]. While this is irreconcilable with theories having only hole pockets, our finding of additional electron-like sheets can reconcile the Shubnikov-deHaas quantum oscillation results with the Luttinger sum rule for doping levels of about 10% [3,4]. Moreover, the Hall constant R(x) is now expected to track the evolution of the renormalized FS with doping. Depending upon the concentrations of hole and electron carriers and their mobilities, R(x) may change sign from hole-like to electron-like with T [5], reconciling the quantum oscillation [3,4] and Hall-effect [5] data. [1] L. Hozoi and M. S. Laad, Phys. Rev. Lett. 99, 256404 (2007). [2] L. Hozoi, M. S. Laad, and P. Fulde, arXiv:0801.3607 (unpublished). [3] N. Doiron-Leyraud, C. Proust, D. LeBoeuf, J. Levallois, J.-B. Bonnemaison, R. Liang, D. A. Bonn, W. N. Hardy, and L. Taillefer, Nature 447, 565 (2007). [4] E. A. Yelland, J. Singleton, C. H. Mielke, N. Harrison, F. F. Balakirev, B. Dabrowski, and J. R. Cooper, Phys. Rev. Lett. 100, 047003 (2008). [5] D. LeBoeuf, N. Doiron-Leyraud, J. Levallois, R. Daou, J.-B. Bonnemaison, N. E. Hussey, L. Balicas, B. J. Ramshaw, R. Liang, D. A. Bonn, W. N. Hardy, S. Adachi, C. Proust, and L. Taillefer, Nature 450, 533 (2007). |
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