Fermi-surface-induced lattice modulation and charge-density wave in optimally doped ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{7-x}$

We have observed a Fermi-surface (FS) induced lattice modulation in a ${\text{YBa}}_2{\text{Cu}}_3{\text{O}}_{7-x}$ superconductor with a wave vector along CuO chains; i.e., ${\mathbf{q}}_1=\left(0,\delta ,0\right)$. The value of $\delta \sim 0.21$ is twice the Fermi wave vector $\left(2{\mathbf{k}}_F\right)$ along ${\mathbf{b}}^{\ast }$ connecting nearly nested FS “ridges.” The ${\mathbf{q}}_1$ modulation exists only within O-vacancy-ordered islands [characterized by ${\mathbf{q}}_0=\left(\frac{1}{4},0,0\right)$] and persists well above and below $T_c$. Our results are consistent with the presence of a FS-induced charge-density wave.

Figure 1

(Color online) Left: $\mathbf{K}$ scans $\left(\text{T}\sim 7\text{K}\right)$ showing ${\mathbf{q}}_1$ shoulders on both sides of the central ${\mathbf{q}}_0$ satellite peaks (lines are from Gaussian profile as a guide to the eyes). Vertical dashes indicate the shoulders displaced along K by $\pm 0.21$ from their respective ${\mathbf{q}}_0$ satellite. Right: the schematic of near nesting of the “ridges” (purple) with nesting vector along ${\mathbf{b}}^{\ast }$ (white) (Refs. 12, 13).

Figure 2

(Color online) (a) Color map of the measured diffuse scattering around (4, 0, 0) and (5, 0, 0) in H-K plane at $\sim 7\text{K}$. (b) Model calculations of the two-dimensional (2D) scattering pattern. Asymmetric HDS around (4, 0, 0), ${\mathbf{q}}_0$ satellite, and ${\mathbf{q}}_1$ shoulders are all reproduced. The dashed lines indicate the line cuts presented in Fig. 3.

Figure 3

(Color online) Solid lines are the fitting results. $\delta$ and $d$ are determined to be 0.21 and 0.9, respectively. The $\mathbf{K}$ scan in (a) across (4.25, 0, 0) is over estimated by $\sim 13\%$ mainly due to the IFS contribution. The lower side of the $\mathbf{H}$ scan in (b) is pushed up by the tail of strong (3.25, 0, 0) satellite peak.

Figure 4

(Color online) (a) Ortho-IV displacement pattern ($ab$ plane) for the chains (Ref. 21). ${\mathbf{q}}_1$ further modulates amplitude of these displacements sinusoidally. (b) one possible AP domain with no modulations of displacement amplitudes. Small dots (red): Cu; big dots (blue): oxygen; squares: vacancy; dashed line: domain boundary; shaded area: 4X5 supercell.