Incommensurate charge ordered states in the $t-t^{\prime }-J$ model

Abstract

We study the incommensurate charge ordered states in the $t-t^{\prime }-J$ model using the Gutzwiller mean field theory on large systems. In particular, we explore the properties of incommensurate charge modulated states referred to as nodal pair density waves (nPDW) in the literature. nPDW states intertwine site and bond charge order with modulated $d$-wave pair order, and are characterized by a nonzero amplitude of uniform pairing; they also manifest a dominant intra-unit cell $d$-density wave form factor. To compare with a recent scanning tunneling microscopy (STM) study [Hamidian \textit{et al.}, Nat. Phys. 3519 (2015)] of the cuprate superconductor BSCCO-2212, we compute the continuum local density of states (LDOS) at a typical STM tip height using the Wannier function based approach. By Fourier transforming Cu and O sub-lattice LDOS we also obtain bias-dependent intra-unit cell form factors and spatial phase difference. We find that in the nPDW state the behavior of form factors and spatial phase difference as a function of energy agrees remarkably well with the experiment. This is in contrast to commensurate charge modulated states, which we show do not agree with experiment. We propose that the nPDW states are good candidates for the charge density wave phase observed in the superconducting state of underdoped cuprates.

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Cited by in corpus (23)

• Visualizing the Energy-gap Modulations of the Cuprate Pair Density Wave State
• Visualizing the periodic modulation of Cooper pairing in a severely underdoped cuprate
• Charge ordering in superconducting copper oxides
• Atomic-scale Electronic Structure of the Cuprate Pair Density Wave State Coexisting with Superconductivity
• Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors
• Universality of scanning tunneling microscopy in cuprate superconductors
• Evolution of Charge and Pair Density Modulations in Overdoped Bi2Sr2CuO6+delta
• Orbital Symmetries of Charge Density Wave Order in YBa2Cu3O6+x
• Scattering Interference Signature of a Pair Density Wave State in the Cuprate Pseudogap Phase
• Interplay Between $d$-wave Superconductivity and a Bond Density Wave in the one-band Hubbard model
• Electronic Theory for Scanning Tunneling Microscopy Spectra in Infinite-Layer Nickelate Superconductors
• Competing orders in the Hofstadter t-J model
• Surprises in the t-J model: Implications for cuprates
• The phase diagram of the underdoped cuprates at high magnetic field
• Charge, bond, and pair density wave orders in a strongly correlated system
• Out-of-plane bond-order phase, superconductivity, and their competition in the $t$-$J_{\parallel }$-$J_{\perp }$ model: Possible implications for bilayer nickelates
• Field-induced Bose-Einstein condensation and supersolid in the two-dimensional Kondo necklace
• Intertwined Orders and Electronic Structure in Superconducting Vortex Halos
• Quantum Spin Liquid phases in Kitaev Materials
• Pseudogap phase and fractionalization: Predictions for Josephson junction setup
• Proximity-induced charge density wave in a metallic system
• Atomic-Scale Visualization of the Cuprate Pair Density Wave State
• Charge modulation in the background of depleted superconductivity inside vortices