Fermi surface reconstruction in high-$T_{c}$ superconductors

The recent observation of quantum oscillations in underdoped high-$T_{c}$ superconductors (1), combined with their negative Hall coefficient at low temperature (2), reveals that the Fermi surface of hole-doped cuprates includes a small electron pocket. This strongly suggests that the large hole Fermi surface characteristic of the overdoped regime undergoes a reconstruction caused by the onset of some order which breaks translational symmetry. Here we consider the possibility that this order is ``stripe'' order, a form of combined charge / spin modulation observed most clearly in materials like Eu- doped and Nd-doped LSCO. In these materials, the onset of stripe order coincides with major changes in transport properties (3), providing strong evidence that stripe order is indeed the cause of Fermi-surface reconstruction. We identify the critical doping where this reconstruction occurs and show that the temperature dependence of transport coefficients at that doping is typical of metals at a quantum critical point (4). We discuss an interpretation of the pseudogap as a fluctuating precursor of the stripe-ordered phase.\\ \\ This work was performed in collaboration with L. Balicas, D.A. Bonn, J. Chang, O. Cyr-Choini\`{e}re, R. Daou, N. Doiron- Leyraud, W.N. Hardy, N.E. Hussey, F. Lalibert\'{e}, D. LeBoeuf, S.Y. Li, R. Liang, C. Proust, H. Takagi, and J.S. Zhou.\\ \\ (1) N. Doiron-Leyraud \textit{et al}., Nature \textbf{447}, 565 (2007).\\ (2) D. LeBoeuf \textit{et al}., Nature \textbf{450}, 533 (2007).\\ (3) R. Daou \textit{et al}., Nature Physics, in press (DOI 10.1038/nphys1109); http://arXiv.org/abs/0806.2881.\\ (4) R. Daou \textit{et al}., to be published; http://arXiv.org/abs/0810.4280.