Unconventional ordering phenomena in cuprates

High-temperature superconductivity (HTSC) represents one of the most fascinating yet puzzling phenomena in contemporary condensed matter physics, with a convincing microscopic theory of the pairing mechanism still lacking. Among the various materials exhibiting unconventional superconductivity, the family of copper-oxides -- or cuprates -- has so far dominated the scene, drawing considerable efforts both on the experimental and theoretical side. A particularly relevant question regards the nature of the normal state, which characterizes the CuO₂ planes above the critical temperature. In the normal state of the underdoped cuprates (around 12% hole-doping) there is evidence for various lattice instabilities, which include different phenomena, such as stripes, checkerboard order, and charge-density waves. Using complementary surface and bulk sensitive synchrotron based techniques these phenomena in a family of single-layered cuprates, Bi₂Sr_2-xLa_xCuO₆, or Bi2201, as a function of doping and temperature, have been studied.
Bi-based cuprates are in general characterized by a well-known corrugation of the lattice, also known as supermodulation: in Bi2201 this structural feature, labeled Q₁, has a period of 4 unit cells, and runs along the [110] tetragonal direction (b* axis). We discovered that electron-lattice coupling in these materials triggers a second modulation, but only in a narrow doping range. Figure 1(a) shows the angle-resolved photoemission spectroscopy (ARPES) data measured at the BaDElPh beamline on a 11% doped samples, where a new set of bands (see yellow circles) is found, providing evidence for a new structural feature (henceforth denominated Q₂), running parallel to Q₁, i.e. along b*. Interestingly, these bands show an intriguing temperature evolution, highlighted in Fig. 1(b,c). The temperature-dependent separation between the bands is controlled by the wavevector of the new supermodulation Q₂. The latter can be tracked with both ARPES and low-energy electron diffraction (LEED) [see inset of Fig. 1(e) and linecut in Fig. 1(d)], which consistently reveal its quasi-linear drift from high (Q~1/12) to low (Q~1/8) temperature, starting around 150K [see Fig. 1(e)], while Q₁ stays fixed at Q=0.25.

Figure 1: ARPES/LEED results on Bi2201 UD15K. (a) ARPES momentum-energy map along the nodal direction Γ→ (π,π). (b,c) Zoom-in of (a) showing the temperature evolution of the supermodulated bandstructure. (d) LEED cuts along b* [see also inset of (e)]. (e) Temperature evolution of the Q₁ and Q₂ wavevectors.
 

The ARPES and LEED results characterize the surface structure of Bi2201 samples. The next crucial question is whether the same features are present in the bulk of the material. In order to investigate this phenomenology deeper in the bulk, we resorted to photon-based techniques, which possess a larger probing depth. Hard x-ray diffraction (XRD) and scattering (REXS) maps as a function of temperature have been acquired at hν=17 keV (Mo-K_α emission) and hν~9 keV (Cu-K edge), respectively. These results, shown in Fig. 2(a-d), provide evidence that the new supermodulation Q₂ is also found in the bulk of the material: its fingerprint in XRD/REXS is revealed through the presence of elongated rods [see legend in Fig.2(b)]. They correspond to a charge modulation well-defined in the CuO₂ planes (i.e., along Q_b*) but with poor coherence perpendicular to them (along Q_c). Most interestingly, the extension of Q₂ in the bulk does not show any temperature dependence as can be seen, comparing the REXS maps in Figs. 2(c,d), taken at 6 K and 120 K, respectively.

 

Figure 2:  (a,b) X-ray diffraction map and pictorial legend of visible structural reflections, respectively. (c,d) Resonant scattering maps (Cu-K edge) at low and high temperature, respectively. (e) Supermodulated Fermi surface, with nesting mechanisms (AN/N connectors) highlighted.

Analysis of possible electronic instabilities revealed that nesting channels of the Q₁-modulated Fermi surface could explain the extremal wavevectors observed in ARPES and LEED [see Fig. 2(e)]. In this sense, the interplay between nodal (N) and antinodal (AN) nesting mechanisms, together with reduced-dimensionality at the surface, explain the observed behavior as originating from an incipient surface-enhanced charge-density wave (see original paper for more details). Ultimately, we have discovered another manifestation of strong electron-lattice coupling in cuprates, which is found to be an important mechanism even in a material characterized by a complex structure to start with.