Charge order in the pseudogap phase of cuprate superconductors

Abstract

Charge ordering instabilities are studied in a multiorbital model of the cuprate superconductors. A known, key feature of this model is that the large local Coulomb interaction in the Cud x 2 −y 2 orbitals generates local moments with short range antiferromagnetic correlations. The strong simplifying ansatz that these moments are static and ordered allows us to explore a regime not generally accessible to weakcoupling approaches. The antiferromagnetic correlations lead to a pseudogap-like reconstruction of the Fermi surface. We find that the leading charge instability within this pseudogap-like state is to a phase with a spatially modulated transfer of charge between neighboring oxygen p x and p y orbitals accompanied by weak modulations of the charge density on the Cud x 2 −y 2 orbitals. As a prime result of the antiferromagnetic Fermi-surface reconstruction, the wavevectors of the charge modulations are oriented along the crystalline axes with a periodicity that agrees quantitatively with experiments. This suggests a resolution to a discrepancy between experiments, which find axial order, and previous theoretical calculations, which find modulation wavevectors along the Brillouin zone (BZ) diagonal. The axial order is stabilized by hopping processes via the Cu4s orbital, which is commonly not included in model analyses of cuprate superconductors. The main implication of our results is that charge order emerges from the pseudogap state, and is not the primary source of the pseudogap.

Atomic-scale electronic structure of the cuprate d-symmetry form factor density wave state

“…Nevertheless, electron-lattice interactions are not by themselves sufficient to explain the phase diagram of the dFF-DW (refs 11-13) because, for example, they also exist in the overdoped regime where the dFF-DW is absent. Moreover, theoretical models involving k-space instabilities 26,27,29,40 which are consistent with the results herein, emphasize that a density wave with this Q and form factor symmetry cannot emerge from a large Fermi surface; instead, a pre-existing reorganization of k-space due to the pseudogap would be required. Overall, our data support a microscopic picture in which the exotic electronic structure of the pseudogap is parent to the dFF-DW state and not vice versa, where the energy scale and wavevectors of the dFF-DW are intimately linked to those of the pseudogap, and in which the d-symmetry DW competes directly for spectral weight with the d-symmetry superconductor at the k-space 'hot frontier' between superconductivity and the pseudogap.…”

“…Such a state is then described by A(r) = D(r) cos(φ(r) + φ 0 (r)), where A(r) represents whatever is the modulating electronic degree of freedom, φ(r) = Q x · r is the DW spatial phase at location r, φ 0 (r) represents disorder related spatial phase shifts, and D(r) is the magnitude of the d-symmetry form factor 14,21,23 . To distinguish between the various microscopic mechanisms proposed for the Q = (Q, 0); (0, Q) dFF-DW state of cuprates [17][18][19][20][21][22][23][24][25][26][27][28][29] , it is essential to establish its atomic-scale phenomenology, including the momentum space (k-space) eigenstates contributing to its spectral weight, the relationship (if any) between modulations occurring above and below the Fermi energy, whether the modulating states in the DW are associated with a characteristic energy gap, and how the dFF-DW evolves with doping.To visualize such phenomena directly as in Fig. 1c, we use sublattice-phase-resolved imaging of the electronic structure 14 of the CuO 2 plane.…”

“…This is relevant to the high-temperature superconducting cuprates because numerous researchers have recently proposed that the 'pseudogap' regime 1,2 (PG in Fig. 1a) contains an unconventional density wave with a d-symmetry form factor [17][18][19][20][21][22][23][24][25][26][27][28][29] . The basic phenomenology of such a state is that intraunit-cell (IUC) symmetry breaking renders the O x and O y sites within each CuO 2 unit-cell electronically inequivalent, and that this inequivalence is then modulated periodically at wavevector Q parallel to (1,0);(0,1).…”

Doping asymmetry and striping in a three-orbitalCuO2Hubbard model

“…RPA calculations for the three-band Hubbard model have also found nematic phases in certain parameter regimes [31][32][33] . Earlier DMRG calculations for a 3-orbital model of a two-leg CuO 2 ladder showed the expected local asymmetric chargetransfer behavior in which doped holes tend to predominantly go on the 2pσ orbitals while doped electrons go on the Cu 3d x 2 −y 2 orbitals 34,35 .…”

Fluctuating Charge Order: A Universal Phenomenon in Unconventional Superconductivity?

“…Recent experiments in cuprates have revealed ample evidence for incommensurate charge modulations with wavevectors oriented along the crystalline axes, i.e., at 45˝off the SDW vector as well [8,[44][45][46][47][48][49][50][51][52][53][54]. A theoretical investigation examining a multiorbital model of cuprates finds support for such an axial charge order [46] in contrast to previous calculations, which reported wave vectors along the Brillouin zone diagonal.…”