The Full Mottness

Abstract

Though most fermionic Mott insulators order at low temperatures, ordering is ancillary to their insulating behaviour. Our emphasis here is on disentangling ordering from the intrinsic strongly correlated physics of a doped half-filled band. To this end, we focus on the 2D Hubbard model. Because the charge gap arises from on-site correlations, we implement a non-perturbative approach which incorporates local physics. Crucial to this method is a self-consistent two-site dynamical cluster expansion which builds in the nearest-neighbour energy scale, $J$. At half-filling, we find that the spectral function possesses a gap of order $U$ and is devoid of any coherent quasi-particle peaks. In the doped case, we find that the Fermi surface exceeds the Luttinger volume. Additionally in the underdoped regime, we find that a pseudogap opens in the single particle density of states.The pseudogap closes above optimal doping and hence our proposal is not inconsistent with that of Loram. In analogy with the Mott gap and antiferromagnetism, we propose that ordering may also accompany the formation of a pseudogap. We suggest a current pattern within a 1-band model that preserves translational but breaks time-reversal symmetry along the canonical x and y axes but not along $x=\pm y$ that is consistent with the experimental observations. Finally, we show that the Hall coefficient in a doped Mott insulator must change sign at a doping level $x<1/3$. The sign change is tied to a termination of strong correlation physics in the doped Mott state.

37 pages, 21 .eps files and 5 appendices. Revised version to appear in PRB

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Cited by in corpus (27)

• Quantum Cluster Theories
• Spatially modulated "Mottness" in La2-xBaxCuO4
• Pseudogap opening and formation of Fermi arcs as an orbital-selective Mott transition in momentum space
• Novel magnetic order in pseudogap state of high Tc copper oxides superconductors
• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions
• Correlation Strength, Gaps and Particle-Hole Asymmetry in High-Tc Cuprates: a Dynamical Mean Field Study of the Three-Band Copper-Oxide Model
• The in-plane electrodynamics of the superconductivity in Bi2Sr2CaCu2O8+d: energy scales and spectral weight distribution
• Mode-Coupling Model of Mott Gap Collapse in the Cuprates: Natural Phase Boundary for Quantum Critical Points
• Negative Hall coefficients of heavily overdoped La2-xSrxCuO4
• Strong Correlations Produce the Curie-Weiss Phase of Na${}_x$CoO${}_2$
• Doped Mott insulators are insulators: hole localization in the cuprates
• Superconductivity-Induced Transfer of In-Plane Spectral Weight in Bi2Sr2CaCu2O8: Resolving a Controversy
• Infrared Signature of the Superconducting State in Pr(2-x)Ce(x)CuO(4)
• Insulators and metals with topological order and discrete symmetry breaking
• Mottness Collapse and T-linear Resistivity in Cuprate Superconductors
• DC Hall coefficient of the strongly correlated Hubbard model
• Breakdown of Strong-Coupling Perturbation Theory in Doped Mott Insulators
• Finite temperature properties of the triangular lattice t-J model, applications to Na${}_x$CoO${}_2$
• Loop current order and d-wave superconductivity: some observable consequences
• Critical charge instability on verge of the Mott transition and the origin of quantum protection in high-$T_c$ cuprates
• Numerical approaches for calculating the low-field dc Hall coefficient of the doped Hubbard model
• Temperature dependence of the spectral weight in p- and n-type cuprates: a study of normal state partial gaps and electronic kinetic energy
• Generic gauge fields in the Hubbard model: emergence of pairing interaction
• The Hall Number, Optical Sum Rule and Carrier Density for the $t$-$t^{\prime }$-$J$ model
• Nature of Split Hubbard Bands at Low Densities
• Intra-unit-cell Magnetic Order in Stoichiometric La${}_2$CuO${}_4$