Session V2: Fermi Surface Reconstruction and Competing Orders in High Tc Cuprates

Broken rotational and translational symmetries in the pseudogap phase of cuprates

A large in-plane anisotropy of the Nernst coefficient in YBCO is found to set in precisely at the pseudogap temperature $T^\star$ throughout the doping phase diagram [1]. This implies that the pseudogap phase is an electronic state that breaks the four-fold rotational symmetry of the copper-oxide planes. At a somewhat lower temperature, of order $T^\star$/2, the positive Hall and Seebeck coefficients of YBCO start dropping, and they reach large negative values at $T = 0$, in the normal state accessed by applying high magnetic fields [2,3]. We interpret this in terms of an electron pocket forming in the Fermi surface of YBCO as a result of a Fermi-surface reconstruction caused by some order which breaks the translational symmetry of the lattice. Because very similar transport anomalies are observed in Eu-LSCO [4], where they coincide with the onset of stripe order, we infer that some form of stripe order is also at play in YBCO, and argue that the pseudogap phase is a precursor region of stripe (or spin-density-wave) fluctuations [5]. \\[4pt] [1] R. Daou {\it et al.}, Nature {\bf 463}, 519 (2010). \\[0pt] [2] J. Chang {\it et al.}, Physical Review Letters {\bf 104}, 057005 (2010). \\[0pt] [3] D. LeBoeuf, arXiv:1009.2078. \\[0pt] [4] O. Cyr-Choini\`ere {\it et al.}, Nature {\bf 458}, 743 (2009). \\[0pt] [5] L. Taillefer, Annual Review of Condensed Matter Physics {\bf 1}, 51 (2010); arXiv:1003.2972.   

Quantum oscillation measurements and their reconciliation with ARPES results in underdoped cuprates

A current conundrum relating to the normal state electronic structure of the underdoped cuprates is the apparent dichotomy between photoemission and quantum oscillations measurements. New quantum oscillation measurements performed over an extended regime on underdoped YBCO are presented that bring results of these two techniques into closer agreement. Further, from the latest quantum oscillation results, we are able to distinguish between various scenarios involving single or multiple carrier types $-$ we show that the experimental findings are only consistent with one of these possibilities. *Work performed in collaboration with N. Harrison, M. Altarawneh, P. A. Goddard, R. Liang, W. N. Hardy, D. A. Bonn, and G. G. Lonzarich   

Magnetic phase diagram and magnetic dynamics of YBa$_{2}$Cu$_{3}$O$_{6+x}$: Implications for the mechanism of high-T$_{c}$ superconductivity

We will present a comprehensive study of the magnetic phase diagram of the high-temperature superconductor YBa$_{2}$Cu$_{3}$O$_{6+x}$. Using elastic neutron scattering, we show that the phase diagram includes incommensurate spin density wave and electronic liquid-crystal states, in addition to the well-known antiferromagnetic, d-wave superconducting, and paramagnetic phases [1]. Using a combination of inelastic neutron scattering and resonant inelastic x-ray scattering, we have also arrived at a comprehensive picture of the magnetic excitation spectrum in all of these phases [2]. The dispersion relations and spectral weights of all compounds, including the slightly overdoped superconductor YBa$_{2}$Cu$_{3}$O$_{7}$, are closely similar to those of magnons in undoped, antiferromagnetically ordered YBa$_{2}$Cu$_{3}$O$_{6}$. The results are in excellent agreement with the spin excitations obtained by exact diagonalization of the t-J Hamiltonian on finite-sized clusters. A numerical solution of the Eliashberg equations based on the experimental spin excitation spectrum of YBa$_{2}$Cu$_{3}$O$_{7}$ reproduces its superconducting transition temperature T$_{c}$ within a factor of two, strongly supporting magnetic Cooper pairing models for the cuprates. Neutron scattering data of the buckling phonon in YBa$_{2}$Cu$_{3}$O$_{7}$ suggest that coupling to this phonon does not substantially enhance d-wave pairing [3]. \\[4pt] [1] D. Haug, V. Hinkov, Y. Sidis, P. Bourges, N. B. Christensen, A. Ivanov, T. Keller, C. T. Lin, B. Keimer, New J. Phys. \textbf{12}, 105006 (2010). \\[0pt] [2] M. Le Tacon, G. Ghiringhelli, J. Chaloupka, M. Moretti Sala, V. Hinkov, M. W. Haverkort, M. Minola, M. Bakr, K. J. Zhou, S. Blanco-Canosa, C. Monney, Y. T. Song, G. L. Sun, C. T. Lin, G. M. De Luca, M. Salluzzo, G. Khaliullin, T. Schmitt, L. Braicovich, B. Keimer, to be published. \\[0pt] [3] M. Raichle \textit{et al}., to be published.   

The spin density wave quantum phase transition in two dimensional metals

The mean-field theory for the onset of spin density wave order in a metal describes a quantum phase transition which reconstructs the ``large'' Fermi surface to small Fermi pockets. Fluctuations near this transition are described by a quantum field theory of fermions near the reconstruction points, and the bosonic order parameter. This field theory is shown to be strongly-coupled in two spatial dimensions. We find an instability near the quantum critical point to $d$-wave pairing: this is a ``log-squared'' instability, stronger than the familiar logarithmic BCS instability. A similar instability is also found towards a modulated bond order. We also discuss an alternative route for the onset of spin density wave order, via intermediate non-Fermi liquid phases which have small Fermi pockets but without long-range spin density wave order.\\ ~\\ M. A. Metlitski and S. Sachdev, Physical Review B {\bf 82}, 075128 (2010)\\ S. Sachdev, M. A. Metlitski, Y. Qi, and C. Xu, Physical Review B {\bf 80}, 155129 (2009)   

Quantum Oscillations and High Magnetic Field Heat Capacity in Underdoped YBCO

This abstract not available.