Session L3: Invited Session: Fermiology of Electron and Hole Doped Cuprates - A Guide to High Temperature Superconductivity

Quantum oscillations and nodal pockets from Fermi surface reconstruction in the underdoped cuprates

Fermiology in the underdoped high $T_{\rm c}$ cuprates presents us with unique challenges, requiring experimentalists to look deeper into the data than is normally required for clues. Recent measurements of an oscillatory chemical potential affecting the oscillations at high magnetic fields provide a strong indication of a single type of carrier pocket. When considered in conjunction with photoemission and specific heat measurements, a Fermi surface comprised almost entirely of nodal pockets is suggested. The mystery of the Fermi surface is deepened, however, by a near doping-independent Fermi surface cross-sectional area and negative Hall and Seebeck coefficients. We explore ways in which these findings can be reconciled, taking an important hint from the diverging effective mass yielded by quantum oscillations at low dopings. The author wishes to thank Suchitra Sebastian, Moaz Atarawneh, Doug Bonn, Walter Hardy, Ruixing Liang, Charles Mielke and Gilbert Lonzarich who have contributed to this work. The work is supported by the NSF through the NHMFL and by the DOE project ``Science at 100 tesla.''   

Phase competition in trisected superconducting dome

The momentum-resolved nature of angle-resolved photoemission spectroscopy (ARPES) has made it a key probe of emergent phases in the cuprates, such as superconductivity and the pseudogap, which have anisotropic momentum-space structure. ARPES can be used to infer the origin of spectral gaps from their distinct phenomenology---temperature, doping, and momentum dependence, and this principle has been used to argue that the pseudogap is a distinct phase from superconductivity, rather than a precursor [1]. We have studied Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ (Bi-2212) using laser-ARPES, and our data give evidence for three distinct quantum phases comprising the superconducting ground state, accompanied by abrupt changes at p$\sim $0.076 and p$\sim $0.19 in the doping-and-temperature dependence of the gaps near the bond-diagonal (nodal) direction [2]. The latter doping likely marks the quantum critical point of the pseudogap, while the former represents a distinct competing phase at the edge of the superconducting dome. Additionally, we find that the pseudogap advances closer towards the node when superconductivity is weak, just below T$_{c}$ or at low doping, and retreats towards the antinode well below T$_{c}$ and at higher doping. This phase competition picture together with the two critical doping are synthesized into our proposed phase diagram, which also reconciles conflicting phase diagrams commonly used in the field. Our results underscore the importance of quantum critical phenomena to cuprate superconductivity, provide a microscopic picture of phase competition in momentum space, and predict the existence of phase boundaries inside the superconducting dome which are different from simple extrapolations from outside the dome. \\[4pt] [1] I. M. Vishik, W. S. Lee, R.-H. He, M. Hashimoto, Z. Hussain, T. P. Devereaux, and Z.-X. Shen. \textit{New J. Phys. }\textbf{12}, 105008 (2010). \\[0pt] [2] I. M. Vishik, M. Hashimoto, R.-H. He, W. S. Lee, F. Schmitt, D. H. Lu, R.G. Moore, C. Zhang, W. Meevasana, T. Sasagawa, S. Uchida, K. Fujita, S. Ishida, M. Ishikado, Y. Yoshida, H. Eisaki, Z. Hussain, T. P. Devereaux, and Z.-X. Shen, \textit{Submitted} (2011).   

Novel Magnetism in the Pseudogap Phase of the Cuprates

Magnetic correlations might cause the superconductivity in the cuprates and are generally believed to be antiferromagnetic. Following our success in growing sizable crystals of the tetragonal compound HgBa$_2$CuO$_{4+\delta}$ [1], we used polarized neutron diffraction to demonstrate that the unusual magnetic order previously observed in YBa$_2$Cu$_3$O$_{6+\delta}$ [2] is a universal property of the pseudogap phase [3]. Subsequent inelastic neutron scattering experiments revealed several accompanying, weakly-dispersive magnetic excitation branches in HgBa$_2$CuO$_{4+\delta}$ [4]. Unlike antiferromagnetism, the novel magnetic order does not break the lattice translational symmetry. Nevertheless, the excitations mix with conventional antiferromagnetic fluctuations. Our results point toward the need for a multi-band description of the cuprates, and they are consistent with the notion that the phase diagram is controlled by an underlying quantum critical point [5]. The neutron scattering results will be discussed together with new dc resistivity data for the pseudogap phase of HgBa$_2$CuO$_{4+\delta}$ [6].\\[4pt] [1] X. Zhao {\it et al.}, Adv. Mat. {\bf 18}, 3243 (2006).\\[0pt] [2] B. Fauque {\it et al.}, Phys. Rev. Lett. {\bf 96}, 197001 (2006).\\[0pt] [3] Y. Li {\it et al.}, Nature {\bf 455}, 372 (2008).\\[0pt] [4] Y. Li {\it et al.}, Nature {\bf 468}, 283 (2010), and unpublished results.\\[0pt] [5] C. Varma, Nature {\bf 468}, 184 (2010).\\[0pt] [6] N. Barisic {\it et al.}, unpublished results.   

From Spin Liquid to High T$_{c}$ Superconductors

The discovery of high T$_{c}$ superconductors has revived interest in Anderson's resonating valence bond theory (RVB) of a quantum spin liquid, first proposed in 1973. In the past few years, several examples of quantum spin liquids have been discovered experimentally. The organic spin liquid has been studied most thoroughly and shows strong evidence for emergent fermionic spinons. I shall review some of the data and argue that theories based on slave particles and gauge fields have been successful in accounting for these remarkable data. The question remains as to whether a similar formulation of fermionic spinon and bosonic holes can form the basis for a theory of high T$_{c}$ superconductors. I shall show that a recent modification\footnote{T. Senthil and P.A. Lee, Phys. Rev. Lett. \textbf{103}, 076402 (2009).} of the mean field RVB phase diagram can explain a lot of the phenomenology. I shall also attempt to put this theory in the context of recent discoveries concerning symmetry breaking in the pseudogap phase.