Strong coupling critique of spin fluctuation driven charge order in underdoped cuprates

Charge order has emerged as a generic feature of doped cuprates, leading to important questions about its origin and its relation to superconductivity. Recent experiments on two classes of hole doped cuprates indicate a novel $d$-wave symmetry for the order. These were motivated by earlier spin fluctuation theoretical studies based on an expansion about hot spots in the Brillouin zone that indicated such an order would be competitive with $d$-wave superconductivity. Here, we reexamine this problem by solving strong coupling equations in the full Brillouin zone for experimentally relevant parameters. We find that bond-oriented order, as seen experimentally, is strongly suppressed. We also include coupling to $B_{1g}$ phonons and do not see any qualitative change. Our results argue against an itinerant model for the charge order, implying instead that such order is likely due to Coulombic phase separation of the doped holes.

Figure 1

Fermi surface for the tight binding dispersion considered in this work. The dashed lines show the antiferromagnetic Brillouin zone and the dotted lines the structural one. Solid circles denote the hot spots and solid squares the antinodal points. The wave vectors studied here are indicated by the arrows.

Figure 2

Temperature dependence of the leading eigenvalues for the superconducting $d$-wave state (SC), the diagonal CDW state (CDW-diag), and the bond-oriented CDW state (CDW-x), in an approximation where $G$ is based on a renormalized dispersion taken from ARPES data. The ordering vector for CDW-diag is $(Q_{hs},Q_{hs})$. For CDW-x, two vectors were considered, $(Q_{an},0)$ and $(Q_{hs},0)$.

Figure 3

The momentum dependence of the eigenvectors at the lowest Matsubara frequency ($T=40$ K) corresponding to leading eigenvalues (Fig. 2) for the (a) CDW-diag and (b) CDW-x states. For CDW-x, the ordering vector is $(Q_{an},0)$, though the eigenvector for $(Q_{hs},0)$ is similar. A normalization condition of $T{\sum }_{{\omega }_n,k}{\left|{\mathrm{\Phi }}^Q(k,i{\omega }_n)\right|}^2=1$ is employed.

Figure 4

Temperature dependence of the leading eigenvalues for the superconducting $d$-wave state (SC), the diagonal CDW state (CDW-diag), and the bond-oriented CDW state (CDW-x), obtained using dressed Green's functions.