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

Peayush Choubey,Ting-Kuo Lee,Wei-Lin Tu,P J Hirschfeld

doi:10.1088/1367-2630/19/1/013028

Abstract

We study the incommensurate charge ordered states in the 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.

Highlights

Recent interest in cuprates has been spurred by the observation of charge order, in the underdoped regime of its phase diagram, through a variety of experimental tools like STM12, NMR1, x-ray diffraction[4], and resonant x-ray scattering[28]
We find that in the nodal pair density waves (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
APCDW and nPDW states were found in the doping range of 0.09-0.17 which is below the optimal hole doping of 0.27

Summary

Introduction

Recent interest in cuprates has been spurred by the observation of charge order, in the underdoped regime of its phase diagram, through a variety of experimental tools like STM12, NMR1, x-ray diffraction[4], and resonant x-ray scattering[28]. In contrast to the stripe phase observed, e.g. in LBCO15, charge order in other cuprates does not generally accompany any magnetic order. These are short range, uni-directional and incommesurate charge modulations with wavevectors [0, Q] or [Q, 0] where Q is around 0.3 in reciprocal lattice units. Understanding the momentum - energy dependence of local intra-unit cell density form factors as a function of doping can give clues to the origin and interplay of charge order with other symmetry broken phases of cuprates. The energy dependence of the form factors, along with the observations of pair density waves (PDW), put constraints on theories of charge order in cuprates

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Discussion

Conclusion