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arXiv:1207.3212 · Physical Review B

Possible charge instabilities in two-dimensional doped Mott insulators

Matías Bejas, A. Greco, Hiroyuki Yamase

Published Dec 17, 2012• 62 citations
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Abstract

Motivated by the growing evidence of the importance of charge fluctuations in the pseudogap phase in high-temperature cuprate superconductors, we apply a large-$N$ expansion formulated in a path integral representation of the two-dimensional $t$-$J$ model on a square lattice. We study all possible charge instabilities of the paramagnetic state in leading order of the $1/N$ expansion. While the $d$-wave charge density wave (flux phase) becomes the leading instability for various choices of model parameters, we find that a $d$-wave Pomeranchuk (electronic nematic phase) instability occurs as a next leading one. In particular, the nematic state has a strong tendency to become inhomogeneous. In the presence of a large second nearest-neighbor hopping integral, the flux phase is suppressed and the electronic nematic instability becomes leading in a high doping region. Besides these two major instabilities, bond-order phases occur as weaker instabilities close to half-filling. Phase separation is also detected in a finite temperature region near half-filling.

DOI
10.1103/physrevb.86.224509

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Motivated by the growing evidence of the importance of charge fluctuations in the pseudogap phase in high-temperature cuprate superconductors, we apply a large-NNN expansion formulated in a path integral representation of the two-dimensional ttt-JJJ model on a square lattice. We study all possible charge instabilities of the paramagnetic state in leading order of the 1/N1/N1/N expansion. While the ddd-wave charge density wave (flux phase) becomes the leading instability for various choices of model parameters, we find that a ddd-wave Pomeranchuk (electronic nematic phase) instability occurs as a next leading one. In particular, the nematic state has a strong tendency to become inhomogeneous. In the presence of a large second nearest-neighbor hopping integral, the flux phase is suppressed and the electronic nematic instability becomes leading in a high doping region. Besides these two major instabilities, bond-order phases occur as weaker instabilities close to half-filling. Phase separation is also detected in a finite temperature region near half-filling.
We study possible charge instabilities in doped Mott insulators by employing the two-dimensional t - J model with a positive value of the next nearest-neighbor hopping integral on a square lattice, which is applicable to electron-doped cuprates. Although the d -wave charge density wave (flux phase) and d -wave Pomeranchuk instability (nematic order) are dominant instabilities for a negative that corresponds to hole-doped cuprates, we find that those instabilities are strongly suppressed and become relevant only rather close to half filling. Instead, various types of bond orders with modulation vectors close to are dominant in a moderate doping region. Phase separation is also enhanced, but it can be suppressed substantially by the nearest-neighbor Coulomb repulsion without affecting the aforementioned charge instabilities.
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Unravelling competing orders emergent in doped Mott insulators and their interplay with unconventional superconductivity is one of the major challenges in condensed matter physics. To explore the possible superconducting state in a doped Mott insulator, we study the square-lattice t-J model with both the nearest-neighbor and next-nearest-neighbor electron hoppings and spin interactions. By using the state-of-the-art density matrix renormalization group calculation with imposing charge U(1) and spin SU(2) symmetries on the six-leg cylinders, we establish a quantum phase diagram including three phases: a stripe charge density wave phase, a superconducting phase without static charge order, and a superconducting phase coexistent with a weak charge stripe order. Crucially, we demonstrate that the superconducting phase has a power-law pairing correlation that decays much slower than the charge density and spin correlations, which is a quasi-1D descendant of the uniform d-wave superconductor in two dimensions. These findings reveal that enhanced charge and spin fluctuations with optimal doping is able to produce robust d-wave superconductivity in doped Mott insulators, providing a foundation for connecting theories of superconductivity to models of strongly correlated systems.
Altermagnetic pseudogap from tU\frac{t}{U}Ut​ expansion
Order parameter analysis of the t/U series reveals a uniform altermagnet endemic to the doped Mott insulator, driven by kinetic interactions, occupying a position between the antiferromagnet and hole-doped d-wave superconductor that is normally reserved for the pseudogap. The metastable boundary of the altermagnet punctures and divides the superconductor into underdoped and overdoped regions, reminiscent of the T∗T^\astT∗ crossover or transition in the cuprates. Similarly, the TpairT_{pair}Tpair​ boundary of the superconductor divides the altermagnet, leading to a low temperature phase susceptible to Cooper fluctuations. The altermagnet is unstable to inhomegeneous spin and charge order of sites, bonds, and currents. Its leading instability is to the πππ-flux state, suggesting the possible emergence of spin-charge liquids and quantum ordered states from a physically realistic microscopic model.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/81/81/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/51/51/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.
We investigate charge fluctuations in the two-dimensional Hubbard model as a function of doping, interaction strength, next-nearest-neighbor hopping, and temperature within the eight-site dynamical cluster approximation. In the regime of intermediate interaction strengths, we find that ddd density wave fluctuations, which had previously been postulated using analytical arguments, are present and strong but cannot be interpreted as the cause of the pseudogap in the model, due to their evolution with doping and interaction strength. For all parameters away from half filling, the charge fluctuations investigated, including ddd density wave fluctuations, are weaker than ddd-wave superconducting fluctuations.