Charge density fluctuations in cuprates

30-08-2019

The observation of a short-range charge modulation in cuprates by resonant inelastic X-ray scattering indicates that charge instability is inherent in cuprates and can be a crucial factor that influences their properties. This observation can be likened to seeing the bulk of the iceberg of the charge order phenomenon, while the thoroughly-known charge density waves only represent its tip.

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The phase diagram of the high-Tc cuprate superconductors (HTS) is shaped by the spontaneous emergence of various ordered states, tuned by doping and driven by the many competing degrees of freedom, where not only charge and spin are of relevance, but also lattice and orbitals have an active role in building up the ground state. The identification of all these ordered states is a crucial step toward the understanding of high-temperature superconductivity, one of the grand challenges in solid state physics.

In strongly correlated systems, the tendency of the valence electrons to segregate into periodically modulated structures can lead to the formation of a peculiar charge order. Theoretically predicted already in the 90s [1,2], the experimental evidence of a new charge state was only produced recently, thanks to the major developments of synchrotron-based X-ray scattering [3,4]. Although observed in several families of cuprates [3,5,6], it is still unclear to what extent the charge order influences the unusual properties of these systems, since it has been consistently observed - in the shape of incommensurate Charge Density Waves (CDW) - only in underdoped samples (with doping p = 0.08 – 0.16 holes/Cu) and at relatively low temperatures (below 170-200 K). This apparent confinement in a relatively small region of the phase diagram has brought part of the community to view charge order as a mere epiphenomenon of the pseudogap opening. This approach has been recently questioned by the observation of long-range CDW in overdoped single layer Bi2201 [7], well outside the pseudogap regime. In this context, the higher sensitivity of the resonant inelastic X-ray scattering (RIXS) instrumentation available at ID32 has been exploited to determine more accurately the temperature dependence of CDW at the Cu L3 absorption edge, in the same (Y,Nd)BCO family where its first observation was made [3].

The intensity has been determined by integrating the quasi-elastic region of the Cu L3 RIXS spectra measured at different q// values along the (H,0) direction.

Figure 1. The intensity has been determined by integrating the quasi-elastic region of the Cu L3 RIXS spectra measured at different q// values along the (H,0) direction. A clear peak is present in the whole temperature range under investigation, in samples from the underdoped up to the slightly overdoped region.

The results have been surprising. Underneath the relatively sharp CDW peak studied by many authors in recent years, a broad and almost temperature-independent signal emerges thanks to the higher signal/noise ratio now available at ID32 (Figure 1). This broad peak is a sort of precursor of the quasi-2D CDW signal, sharing with the latter one the value of the incommensurate wave vector qc. However, differently to CDW, it is still present both above the pseudogap temperature, up to 270 K (maximum temperature compatible with the preservation of the sample chemical integrity under the X-ray beam) and in overdoped samples (p > 0.16 holes/Cu). The broad peak evolves slowly with the temperature: below 150 K, it is superimposed to the quasi 2D CDW peak; below Tc, it is not sensitive to the presence of the superconducting order (Figure 2).

Temperature dependence of the parameters (intensity, FWHM and volume) of the narrow peak (NP) and of the broad peak (BP).

Figure 2. Temperature dependence of the parameters (intensity, FWHM and volume) of the narrow peak (NP) and of the broad peak (BP). The NP has all the characteristics of the well-known incommensurate CDW. The BP parameters have a much weaker T-dependence. The total volume of the charge order is dominated by the broad peak at any temperature.

The broad peak was assigned to dynamic charge density fluctuations. An explanation of this name follows: “Fluctuations”, since they have characteristics very close to those of CDW, but an ultra-short correlation length, of the same order as the wave modulation period. “Dynamics”, since the energy of these fluctuations was estimated from high resolution RIXS spectra to be finite, around 10-15 meV at the optimal doping (p = 0.16 holes/Cu). These experimental results look compatible with the picture provided 23 years ago by Castellani et al. [2] of an inherent charge instability in HTS cuprates. Charge density fluctuations can be thus regarded as pervasively present at all T for superconducting cuprates (Figure 3), and might therefore have a crucial role in determining the peculiar properties of these compounds both in the normal and in the superconducting state.

CDF dominate the phase diagram, coexisting both with the quasi-critical 2D-CDW and with superconductivity.

Figure 3. CDF dominate the phase diagram, coexisting both with the quasi-critical 2D-CDW and with superconductivity. The suggested scenario is of a continuous crossover from the pure 2D dynamical CDF at high T and broad doping range, to a quasi-critical CDW, still 2D, below TQC and for 0.08<p<0.17, to the static 3D CDW usually hindered by superconductivity.

 

Principal publication and authors
Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-Tc superconductor, R. Arpaia (a,b), S. Caprara (c,d), R. Fumagalli (a), G. De Vecchi (a), Y.Y. Peng (a), E. Andersson (b), D. Betto (e), G.M. De Luca (f,g), N.B. Brookes (e), F. Lombardi (b), M. Salluzzo (g), L. Braicovich (a,e), C. Di Castro (c,d), M. Grilli (c,d), G. Ghiringhelli (a,h), Science 365, 906-910 (2019); doi: 10.1126/science.aav1315.
(a) Politecnico di Milano (Italy)
(b) Chalmers University of Technology, Göteborg (Sweden)
(c) Università di Roma La Sapienza (Italy)
(d) CNR-ISC, Roma (Italy)
(e) ESRF
(f) Università di Napoli Federico II (Italy)
(g) CNR-SPIN, Napoli (Italy)
(h) CNR-SPIN, Milano (Italy)

 

References
[1] V. J. Emery, S.A. Kivelson, Physica C 209, 597 (1993).
[2] C. Castellani et al., Phys. Rev. Lett. 75, 4650 (1995).
[3] G. Ghiringhelli et al., Science 337, 821 (2012).
[4] J. Chang et al., Nat. Phys. 8, 871 (2012).
[5] R. Comin et al., Science 343, 390 (2014).  
[6] W. Tabis et al., Nat. Commun. 5, 5875 (2014).
[7] Y.Y. Peng et al., Nat. Mater. 17, 697 (2018).

 

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