Session D3: Invited Session: Stripe Order and Fermi-Surface Reconstruction in Cuprate Superconductors

Fermi-surface reconstruction by stripe order in cuprate superconductors

The origin of pairing in a superconductor resides in the underlying normal state. In the cuprate high-temperature superconductor YBCO, application of a magnetic field to suppress superconductivity reveals a ground state that appears to break the translational symmetry of the lattice, pointing to some density-wave order [1,2,3]. In another cuprate, Eu-LSCO, the onset of stripe order - a modulation of spin and charge densities - at low temperature is well established [4]. By a comparative study of thermoelectric transport in the cuprates YBCO and Eu-LSCO, we show that the two materials exhibit a very similar process of Fermi-surface reconstruction as a function of temperature and doping [5,6]. This strongly suggests that Fermi-surface reconstruction is caused by stripe order in both cases, compelling evidence that stripe order is a generic tendency of hole-doped cuprates.\\[4pt] Work done in collaboration with J. Chang, N. Doiron-Leyraud, E. Hassinger, R. Daou, D. LeBoeuf, M. Rondeau, B. J. Ramshaw, R. Liang, D. A. Bonn, W. N. Hardy, S. Pyon, T. Takayama, H. Takagi, I. Sheikin, L. Malone, C. Proust, K. Behnia and L. Taillefer.\\[4pt] [1] N. Doiron-Leyraud \textit{et al.}, Nature \textbf{447}, 565 (2007).\\[0pt] [2] D. LeBoeuf \textit{et al.}, Nature \textbf{450}, 533 (2007).\\[0pt] [3] D. LeBoeuf \textit{et al.}, Phys. Rev. B \textbf{83}, 054506 (2011).\\[0pt] [4] J. Fink \textit{et al}., Phys. Rev. B \textbf{83}, 092503 (2011).\\[0pt] [5] J. Chang \textit{et al.}, Phys. Rev. Lett. \textbf{104}, 057005 (2010).\\[0pt] [6] F. Lalibert\'e \textit{et al.}, Nat. Commun. \textbf{2}, 432 (2011).   

Competition between charge and superconducting orders in underdoped YBCO

We report nuclear magnetic resonance measurements (NMR) showing that high magnetic fields induce a static, unidirectional, modulation of the charge density in the CuO$_{2}$ planes of underdoped YBa$_{2}$Cu$_{3}$O$_{y}$ [T. Wu et al., Nature 477, 191 (2011)]. The appearance of the charge order coincides with the Fermi surface reconstruction inferred from quantum oscillation and other transport measurements. This charge order appears to be most probably the same 4$a$-periodic stripe modulation as in La-214 cuprates. That it develops only when superconductivity fades away (no charge order is observed under strong fields parallel to the planes) and near the same 1/8 hole doping as in La-214 suggests that charge order, although visibly pinned by CuO chains in YBa$_{2}$Cu$_{3}$O$_{y}$, is an intrinsic propensity of the superconducting planes of high-Tc copper oxides. Since field induced stripe order is also compatible with neutron scattering data in La-214 and with STM data in Bi-2212, charge order could be a generic competitor of high Tc superconductivity. \\[4pt] Work performed with T. Wu, H. Mayaffre, S. Kr\"{a}mer, M. Horvatic, C. Berthier (LNCMI Grenoble), W.N. Hardy, R. Liang, D.A. Bonn (University of British Columbia, Vancouver)   

The electronic state of underdoped YBCO at high magnetic fields and low temperatures: evidence from quantum oscillatory phenomena

Quantum oscillations in bulk and transport properties have been observed in underdoped YBa$_2$Cu$_3$O$_{\rm{6+x}}$ via a range of techniques and by independent researchers in applied magnetic fields above 20T and temperatures below 10K. The consensus is that the oscillations are periodic in the reciprocal of the magnetic field and consist of a number of components with frequencies (fundamental or otherwise) of below 2kT, nearly an order of magnitude lower than that observed in the overdoped state of Tl$_2$Ba$_2$CuO$_{\rm {6+x}}$. Moreover, the temperature dependence of the amplitude of the strongest oscillatory components that can be measured accurately follows closely that expected for elementary excitations of fermionic character. I will discuss a model of the Fermi surface that can potentially account for each of the periodic components observed, and that appears to be consistent with a number of other known properties in the high-field low-temperature state.   

Evidence for competing orders in underdoped YBa$_{2}$Cu$_{3}$O$_{y}$

25 years after the discovery of high temperature cuprate superconductors, the observation of quantum oscillations has deeply changed the theoretical landscape relevant to these materials. The measurements of quantum oscillations on both sides of the phase diagram of cuprates confirm the existence of a Fermi surface with sharply defined excitations on the overdoped side and also show that the Fermi surface has suffered a drastic modification on the other side. The small Fermi pockets inferred from quantum oscillations in the underdoped regime combined with the negative Hall and Seebeck coefficients pointing to electrons as dominant charge carriers, greatly strengthen the case that the Fermi surface of underdoped YBa$_{2}$Cu$_{3}$O$_{y}$ undergoes a reconstruction because the translational symmetry of its lattice is broken at low temperature. Many studies, such those of the Hall and Seebeck effects, point to a reconstruction of the Fermi surface due to stripe order. More recently, NMR measurements discover a static, unidirectional, modulation of the charge density in the CuO$_{2}$ planes that has the 4a-periodic stripe modulation. In this talk, I will show the impact of this charge order on some transport properties, in particular $c$-axis transport. A crossover to a coherent regime of metallic behavior of the $c$-axis resistivity at low temperature coincides with the emergence of the charge order. I will also address the topical question of competition between the charge order and superconductivity in high fields.