Incommensurate charge ordered states in the t-t′-J model

• Published in: New journal of physics Vol. 19; no. 1; pp. 13028 - 13042
• Main Authors: Choubey, Peayush, Tu, Wei-Lin, Lee, Ting-Kuo, Hirschfeld, P J
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.01.2017; Institute of Physics: Open Access Journals
• Subjects: 74.20.-z; 74.70.Xa; Charge density waves; charge order; Condensed Matter; Cuprates; Form factors; high temperature superconductors; Mean field theory; pair density wave; Phase shift; Physics; Scanning tunneling microscopy; scanning tunneling spectroscopy; Superconductivity; Unit cell
• DOI: 10.1088/1367-2630/19/1/013028
• ISSN: 1367-2630

We study the incommensurate charge ordered states in the t - t ′ - 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 et al 2015 Nat. Phys. 12 150) 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.