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arXiv:cond-mat/0512627

Incommensurate DDW order

Ivailo Dimov, Chetan Nayak

Published Dec 23, 2005• 1 citation
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Abstract

We consider various incommensurate (IC) order parameters for electrons on a square lattice which reduce to $d_{x^2-y^2}$-density wave (DDW) order when the ordering wavevector ${\bf Q}\to (π,π)$. We describe the associated charge and current distributions and their experimental signatures. Such orders can arise at the mean-field level in extended Hubbard models. We compare the phase diagrams of these models with experiments in the underdoped cuprates, where (1) DDW order is a possible explanation of the pseudogap, and (2) there are experimental indications of incommensurability. We find various types of IC DDW and discuss their possible relevance to the physics of the cuprates. Our main finding is that IC DDW order is generally accompanied by superconducting order, but the magnitude of the IC wavevector can be small. A comparison with the analogous AF-ICSDW transition is given.

DOI
10.48550/arxiv.cond-mat/0512627

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We consider various incommensurate (IC) order parameters for electrons on a square lattice which reduce to dx2−y2d_{x^2-y^2}dx2−y2​-density wave (DDW) order when the ordering wavevector Q→(π,π){\bf Q}\to (π,π)Q→(π,π). We describe the associated charge and current distributions and their experimental signatures. Such orders can arise at the mean-field level in extended Hubbard models. We compare the phase diagrams of these models with experiments in the underdoped cuprates, where (1) DDW order is a possible explanation of the pseudogap, and (2) there are experimental indications of incommensurability. We find various types of IC DDW and discuss their possible relevance to the physics of the cuprates. Our main finding is that IC DDW order is generally accompanied by superconducting order, but the magnitude of the IC wavevector can be small. A comparison with the analogous AF-ICSDW transition is given.
dx2−y2d_{x^{2} - y^{2}}dx2−y2​-Density Wave and dx2−y2d_{x^{2} - y^{2}}dx2−y2​-wave Superconducting Gap on the Extended Hubbard Model on a Square Lattice: Approach to Finite Temperature Properties
We investigate the finite temperature properties of the extended Hubbard model with a nearest-neighbor Coulomb repulsion on the square lattice. Solving the self-consistent equations obtained using our mean-field theory [J. Phys. Soc. Jpn. 88, 084706 (2019)] numerically, we obtain three-dimensional phase diagrams of the dx2−y2d_{x^{2} - y^{2}}dx2−y2​-density wave (DDW) and dx2−y2d_{x^{2} - y^{2}}dx2−y2​-wave superconducting (DSC) order parameters according to temperature and hole concentrations. The obtained phase diagrams show three distinctive regions: underdoped, optimal, and overdoped. Within the underdoped region, the ratios of the order parameters at absolute zero temperature to the critical temperatures are in approximate agreement with the experimental results of cuprate high Tc superconductors. The optimal region exhibits a unique reentrant phenomenon regarding the hole concentration. In the overdoped region, the DDW disappears and the DSC becomes normal.
We show in a mean-field calculation that phase diagrams remarkably similar to those recently proposed for the cuprates arise in simple microscopic models of interacting electrons near half-filling. The models are extended Hubbard models with nearest-neighbor interaction and correlated hopping. The underdoped region of the phase diagram features ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ density-wave (DDW) order. In a certain regime of temperature and doping, DDW order coexists with antiferromagnetic order. For larger doping, it coexists with ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity. While phase diagrams of this form are robust, they are not inevitable. For other reasonable values of the coupling constants, drastically different phase diagrams are obtained. We comment on implications for the cuprates.
Motivated by significant discrepancies between experimental observations of electron-doped cuprates and numerical results of the Hubbard and $t\text{\ensuremath{-}}J$ models, we investigate the role of intersite interactions VVV by studying the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$ model on square lattices. Based on large-scale density matrix renormalization group simulations, we identify the ground-state phase diagram across varying intersite interactions VVV and doping concentration $\ensuremath{\delta}$. We find that the phase diagram with finite intersite interactions $2\ensuremath{\lesssim}V/J\ensuremath{\lesssim}3$ offers a more accurate description of electron-doped cuprates than the conventional Hubbard and $t\text{\ensuremath{-}}J$ models. Moreover, we reveal the role of intersite interactions VVV at varying doping levels: at light doping, intersite interactions favor N\'eel antiferromagnetic order, and suppress both superconductivity and charge density wave; around optimal doping, these interactions support a pseudogap-like phase while suppressing superconductivity, and we further perform the slave-boson mean-field analysis to understand the numerical results microscopically; at higher doping, the effects of intersite interactions become insignificant, with our numerical predictions suggesting the emergence of an incommensurate spin density wave phase. Our specific focus around optimal doping with various intersite interactions identifies successive phases including phase separation, uniform ddd-wave SC, and a pseudogap-like phase, and reveals a relative insensitivity of the charge density wave to superconductivity. Our study suggests the $t\text{\ensuremath{-}}J\text{\ensuremath{-}}V$ model as the minimal model to capture the essential physics of electron-doped cuprates.
Recent experiments in the underdoped regime of the hole-doped cuprates have found evidence for an incommensurate charge density-wave state. We present an analysis of the charge ordering instabilities in a metal with antiferromagnetic correlations, where the electronic excitations are coupled to the fractionalized excitations of a quantum fluctuating antiferromagnet on the square lattice. The resulting charge density-wave state emerging out of such a fractionalized Fermi liquid (FL*) has wave vectors of the form $(\ifmmode\pm\else\textpm\fi{}{Q}_{0},0),(0,\ifmmode\pm\else\textpm\fi{}{Q}_{0})$, with a predominantly ddd-form factor, in agreement with experiments on a number of different families of the cuprates. In contrast, as previously shown, the charge density-wave instability of a nearly antiferromagnetic metal with a large Fermi surface, interacting via short-range interactions, has wave vectors of the type $(\ifmmode\pm\else\textpm\fi{}{Q}_{0},\ifmmode\pm\else\textpm\fi{}{Q}_{0})$. Our results show that the observed charge density-wave appears as a low-energy instability of a fractionalized metallic state linked to the proximity to an antiferromagnetic insulator, and the pseudogap regime can be described by such a metal at least over intermediate length and energy scales.
The Hubbard and closely related t-J models are exciting platforms for unconventional superconductivity (SC). Through state-of-the-art density matrix renormalization group calculations using the grand canonical ensemble, we address open issues regarding the ground-state phase diagram of the extended t-J model on a square lattice in the parameter regime relevant to cuprate superconductors. On large 8-leg cylinders, we demonstrate that the pure t-J model with only nearest-neighbor hoppings and superexchange interactions, for a wide range of doping ( δ = 0.1 to 0.2 ), hosts robust d-wave superconductivity possibly coexisting with weak unidirectional pair density wave. Furthermore, a small next nearest neighbor hopping t 2 suppresses pair and charge density waves, resulting in a uniform d-wave SC phase in both electron- and hole-doped cuprate model systems. Our work validates the t-J model as a proper minimum model for the emergence of superconductivity in cuprate superconductors.
It is now well established that superconducting cuprates support a charge-density-wave state in the so-called underdoped region of their phase diagram. We investigate the possibility of charge order in the square-lattice Hubbard model, both alone and in coexistence with ddd-wave superconductivity. The charge order has a period of 4 in one direction, is centered on bonds, and has a ddd form factor. We use the variational cluster approximation, an approach based on a rigorous variational principle that treats short-range correlations exactly, with two clusters of size $2\ifmmode\times\else\texttimes\fi{}6$ that together tile the infinite lattice and provide a nonbiased unit for a period-4 bond-density wave (BDW). We find that the BDW exists in a finite range of hole doping and increases in strength from U=5U=5U=5 to U=8U=8U=8. Its location and intensity depend strongly on the band dispersion. When probed simultaneously with ddd-wave superconductivity, the energy is sometimes lowered by the presence of both phases, depending on the interaction strength. Whenever they coexist, a pair-density wave (a modulation of superconducting pairing with the same period and form factor as the BDW) also exists.