Session H3: Invited Session: Electronic Properties of the Pseudogap Phase in Cuprates

Extremely Correlated Fermi Liquids

A new framework is reported for calculating the properties of extremely correlated electronic systems with eliminated double occupancy. Based on Schwinger's approach to field theory, it avoids using auxiliary variables, and leads to a low (particle) density expansion with equations that approximately double the complexity of the standard theory for interacting electrons. Concrete results for the one electron spectral function of the $t$-$J$ model in 2-dimensions are presented to lowest non trivial order in density. These already show considerable promise in the context of cuprate superconductors. A distinguishing characteristic of this theory is the low energy long wavelength asymmetry between adding holes and particles. Prospects for the experimental observation of this asymmetry are discussed. \\[4pt] [1] ``Extremely Correlated Fermi Liquids,'' B. S. Shastry, arXiv:1102.2858 (2011), Phys. Rev. Letts. 107, 056403 (2011).\\[0pt] [2] ``Dynamical Particle Hole Asymmetry in Cuprate Superconductors,'' B. S. Shastry, arXiv: 1110.1032 (2011)   

The new extremely correlated electron perspective of the normal state of high temperature superconductors

In this talk, two recent angle resolved photoelectron spectroscopy (ARPES) studies on high temperature superconductors are discussed. These studies show the importance of the ``extreme electron correlation'' a la t-J model. First, we will discuss the normal state single particle spectral function, which has been considered both anomalous and crucial to understand. Here, we report [1] an unprecedented success of applying the new t-J model based ``extremely correlated Fermi liquid theory'' by Shastry, to describe both laser ARPES data and conventional synchrotron ARPES data on Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and synchrotron ARPES data on La$_{1.85}$Sr$_{0.15}$CuO$_4$. It fits all data sets with the same physical parameter values, satisfies the particle sum rule and successfully addresses two widely discussed kink anomalies in the dispersion. Second, new ARPES investigation [2] of the Fermi surface geometry of Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$ from underdoping to overdoping shows that the ``weak correlation'' Luttinger sum rule, based on Fermi surface only, clearly breaks down in the underdoped case. We note that a t-J model based theory by Yang, Rice and Zhang provides an alternative ``extreme correlation'' Luttinger sum rule, based on both Fermi surface and ``Luttinger surface.'' This extreme correlation Luttinger sum rule offers much more natural explanation for the observed ARPES data. These two studies imply that the extreme correlation as embodied in the t-J model is essential for understanding high temperature superconductors over a wide doping range. \\[4pt] [1] Gweon, Shastry, and Gu, Phys. Rev. Lett. 107, 056404 (2011).\\[0pt] [2] Meng, Gweon et al., Phys. Rev. B 84, 060513(R) (2011).   

A Phenomenological Theory of the Anomalous Pseudogap Phase in Underdoped Cuprates

A consistent theoretical description of the many anomalous properties that characterize the pseudogap phase in the underdoped region of the cuprate phase diagram has proved challenging. The continuous progress in spectroscopic and other experiments suggests a phenomenological approach. An ansatz based on analogies to the transition to Mott localization at weak coupling in lower dimensional systems, has been proposed by Yang, Rice and Zhang some years back [1]. This ansatz has had success in describing a wide range of experiments [2]. The motivation underlying this ansatz will be described and some of the comparisons to experiment reviewed. The implications for a more microscopic theory will be discussed together with the relation to microscopic theories that start directly from strongly coupled Hamiltonians. \\[4pt] [1] K-Y. Yang, T. M. Rice {\&} F. C. Zhang, Phys. Rev. B\textbf{73},174501 (2006)\\[0pt] [2] T. M. Rice, K.-Y. Yang {\&} F. C. Zhang, arXiv 1109.0632   

Fermi pockets and the pseudogap in underdoped $Bi_2Sr_2CaCu_2O_8$

The Fermi surface topologies of underdoped samples of the high $T_c$ superconductor $Bi_2Sr_2CaCu_2O_8$ have been measured with angle resolved photoemission. By examining thermally excited states above the Fermi level, we show that the observed Fermi surfaces in the pseudogap phase are actually components of enclosed hole-pockets. The spectral weight of these pockets is vanishingly small at the magnetic zone boundary, creating the illusion of Fermi ``arc''. The area of the pockets as measured in this study is consistent with the doping level, and hence carrier density, of the samples measured. Furthermore, the shape and area of the pockets is well reproduced by phenomenological models of the pseudogap phase as a spin liquid. The demonstration that the pseudogap in the anti-nodal region is a gap symmetric about the chemical potential is a clear indication that singlet pairing takes place in the normal state.   

Nodal-antinodal dichotomy in underdoped cuprates: a cluster-dynamical mean-field theory perspective.

A distinctive feature of the normal state of underdoped cuprates is the strong dichotomy between nodal and antinodal regions. The nodal regions display well-defined quasiparticle excitations. In contrast, single-particle lineshapes are very broad near the antinodes, where a pseudogap opens. Cluster extensions of dynamical mean-field theory provide an understanding of this phenomenon as a momentum-selective Mott transition. This will be reviewed in this talk and confronted to experiments and to other theoretical approaches.