Pseudogap in the chain states of YBa${}_2$Cu${}_3$O${}_{6.6}$

As established by scanning tunneling microscopy (STM), cleaved surfaces of the high-temperature superconductor YBa${}_2$Cu${}_3$O${}_{7-\delta }$ develop charge-density wave (CDW) modulations in the one-dimensional (1D) CuO chains. At the same time, no signatures of the CDW have been reported in the spectral function of the chain band previously studied by photoemission. We use soft x-ray angle-resolved photoemission spectroscopy to detect a chain-derived surface band that had not been detected in previous work. The $2k_{\mathrm{F}}$ for the new surface band is found to be 0.55 Å${}^{-1}$, which matches the wave vector of the CDW observed in direct space by STM. This reveals the relevance of the Fermi-surface nesting for the formation of CDWs in the CuO chains in YBa${}_2$Cu${}_3$O${}_{7-\delta }$. In agreement with the short-range nature of the CDW order the newly detected surface band exhibits a pseudogap whose energy scale also corresponds to that observed by STM.

Figure 1

Sample aging for YBa${}_2$Cu${}_3$O${}_{6.6}$. (a), (b) FS maps measured directly after cleavage and 28 h later. (c), (d) Corresponding fresh and aged intensity distributions for constant energy cuts at $E=E_{\mathrm{F}}-100$ meV. (e), (f) Energy-momentum intensity distributions along the $\Gamma$-$S$ direction. The white squares are the result of MDC fits. Dark corresponds to high photoemission intensity. Spectra measured at $T=10$ K with 38-meV energy resolution using linearly $s$-polarized light (i.e., no out-of-plane component of the polarization vector).

Figure 2

Excitation energy dependence for the cut passing through the $\Gamma$ point parallel to the $k_y$ axis. The left panel shows the intensity integrated around the Fermi level, $E=E_F$. The right image contains intensity at 200 meV below the Fermi level, demonstrating another set of chain features for $h\nu \lesssim$ 920 eV. Spectra were measured from YBa${}_2$Cu${}_3$O${}_{6.6}$ sample using $p$-polarized light with overall energy resolution of 125 meV.

Figure 3

(a), (b) Momentum intensity distribution at the Fermi level and at 0.1 eV below the FL for YBa${}_2$Cu${}_3$O${}_{6.6}$. The right image reveals another 1D band, which contributes practically no spectral weight at the Fermi level. Spectra measured with $p$-polarized light and energy resolution of 90 meV.

Figure 4

(a) Energy-momentum cut along the Y-$\Gamma$-Y direction demonstrating two types of chain bands in YBa${}_2$Cu${}_3$O${}_{6.6}$. (b) The same as previous, but each MDC in the image has been normalized to 1. The small square symbols denote the peak positions obtained in a four-Lorentzian MDC fit. The inset shows typical fit for the MDC at $E_{\mathrm{B}}=200$ meV. The obtained experimental dispersions are fit to parabolic bands (solid white lines). (c) $k_{\mathrm{F}}$ EDC's for the inner chain band (black line) and outer chain band (gray line). Polarization and resolution are the same as in Fig. 3.

Figure 5

(a), (b) Momentum intensity distribution at the Fermi level and at 0.1 eV below the FL for YBa${}_2$Cu${}_3$O${}_{6.4}$. (c) Energy-momentum cut along the Y-$\Gamma$-Y direction. (d) MDC centered at binding energy of 170 meV and integrated over $\pm$60 meV wide window. In the MDC fit the inner two peaks correspond to the subsurface chains, while the outer two are due to the remnant spectral weight of the heavily disordered surface chains.