Session Y1: New Insights Into the Mott Transition

Renewed Understanding on Doped Mott Insulators

Mott transitions and nearby underdoped metals in two dimensions remain a major challenge in condensed matter physics, because of large spatial and quantum fluctuations, with its relevance to cuprate superconductors. Recent theoretical and computational developments have renewed its understanding with a unified picture for the unconventional metals. We overview historical backgrounds followed by a recent coherent picture obtained by path-integral renormalization group, many-variable variational Monte Carlo methods, and cluster-type dynamical mean-field theory [1]. Coexisting zeros and poles of the single-particle Green's function hold a key for Mott physics. Non-Fermi-liquid caused by topological transitions of Fermi surface including Lifshitz transitions naturally emerges. The energy-momentum dependent spectra reproduce the arc/pocket and pseudogap formation. We propose that the pseudogap in the cuprates is d-wave-like only below the Fermi level while it retains s-wave-like full gap above the Fermi energy even in the nodal point. In addition, the spectral asymmetry, back-bending and waterfall dispersions as well as the low-energy kink emerge within the same framework in agreement with the underdoped cuprates, excluding the scenarios by preformed pairs and d-density-waves, but supporting the proximity to the Mott insulator. We also propose that an extension of the exciton concept to doped Mott insulators by using cofermions accounts for the above unconventionality and superconductivity [2].\\[4pt] [1] S. Sakai et al., Phys. Rev. Lett. 102, 056404 (2009); Phys. Rev. B 82, 134505 (2010)\\[0pt] [2] Y. Yamaji and M. Imada, arXiv:1009.1197.   

Quantum criticality in the Hubbard model

In large scale dynamical cluster quantum Monte Carlo simulations of the two-dimensional (2D) Hubbard model with only nearest neighbor hopping, we find a quantum critical point (QCP) at finite doping separating a Fermi liquid region at low filling from a non-Fermi liquid pseudogap region near half-filling. Marginal Fermi liquid behavior is seen in the thermodynamics and single-particle properties for a wide range of doping and temperatures above the QCP. The QCP is due to the second-order terminus of a line of first order phase separation transitions that is driven to zero temperature as the next near-neighbor hopping t' vanishes. The superconducting dome surrounds the QCP. The proximity the QCP and the dome is due to an algebraic divergence, replacing the BCS log divergence, of the bare pairing polarization. This behavior is captured with a simple variation of the quantum critical BCS formalism.   

Cluster Dynamical Mean Field Methods and the Momentum-selective Mott transition

Innovations in methodology and computational power have enabled cluster dynamical mean field calculations of the Hubbard model with interaction strengths and band structures representative of high temperature copper oxide superconductors, for clusters large enough that the thermodyamic limit behavior may be determined. We present the methods and show how extrapolations to the thermodynamic limit work in practice. We show that the Hubbard model with next-nearest neighbor hopping at intermediate interaction strength captures much of the exotic behavior characteristic of the high temperature superconductors. An important feature of the results is a pseudogap for hole doping but not for electron doping. The pseudogap regime is characterized by a gap for momenta near Brillouin zone face and gapless behavior near the zone diagonal. for dopings outside of the pseudogap regime we find scattering rates which vary around the fermi surface in a way consistent with recent transport measurements. Using the maximum entropy method we calculate spectra, self-energies, and response functions for Raman spectroscopy and optical conductivities, finding results also in good agreement with experiment.   

Finite doping signatures of the Mott transition in the two-dimensional Hubbard model

The evolution from the conventional metal at high doping to the Mott insulator at zero doping remains a central problem in physics of copper-oxide superconductors. Here we solve the cellular dynamical mean-field equations [1,2] for the two-dimensional Hubbard model on a plaquette with continuous-time quantum Monte Carlo [3,4]. The normal-state phase diagram as a function of temperature T, interaction strength U, and filling n reveals that, upon increasing n towards the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point [5,6]. There is a maximum in scattering rate associated with this transition. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T=0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a very low temperature transition between two types of normal state metals at finite doping. The influence of Mott physics extends well beyond half-filling. \\[4pt] [1] G. Kotliar et al., Rev. Mod. Phys. 78, 865 (2006).\\[0pt] [2] T. Maier et al., Rev. Mod. Phys. 77, 1027 (2005).\\[0pt] [3] P. Werner and A.J. Millis, Phys. Rev. B 74, 155107 (2006).\\[0pt] [4] K. Haule, Phys. Rev. B 75, 155113 (2007).\\[0pt] [5] G. Sordi, K. Haule, and A.-M.S. Tremblay, Phys. Rev. Lett. 104, 226402 (2010).\\[0pt] [6] G. Sordi, K. Haule, and A.-M.S. Tremblay, unpublished (2010).   

Computational Studies of Realistic Multiband Models of the Copper Oxides

High temperature superconductivity was achieved by introducing holes in a parent compound consisting of copper oxide layers separated by spacer layers. It is possible to dope some of the parent compounds with electrons, and their physical properties are bearing some similarities but also significant differences from the hole doped counterparts. Here, we use a modern first principles method, to study the electron doped cuprates and elucidate the deep physical reasons why their behavior is so different than the hole doped materials. We find that electron doped compounds are Slater insulators, e.g. a material where the insulating behavior is the result of the presence of magnetic long range order. This is in sharp contrast with the hole doped materials, where the parent compound is a Mott charge transfer insulator, namely a material which is insulating due to the strong electronic correlations but not due to the magnetic order. In particular, we point out that both hole and electron doped compounds are located close to the charge-transfer insulator to metal transition, and we discuss the consequences for optical and specific heat measurements done for the normal state, and additional consequences for the magnetic and superconducting orders of electron and hole doped copper oxides.\\[4pt] Work done in collaboration with Kristjan Haule and Gabriel Kotliar, Rutgers University.