Unexpected charge density waves in a family of cuprate superconductors

In layered cuprates, superconductivity sets in with exceptional stability when the CuO₂ planes are doped by the “right” amount of holes, which disrupt the long-range two-dimensional antiferromagnetic order of the parent compounds but preserve the short-range spin correlation. Charge carriers are thus under the effect of very large mutual interactions that can give rise to competing phenomena, eventually manifesting themselves as unusual transport properties, including superconductivity. This scenario includes the formation of charge density waves, or charge order, i.e., spontaneous modulation of the local charge density with a spatial wavelength commensurate or incommensurate to the lattice structure.

Long after having been predicted theoretically [1], charge order (CO) has been observed indirectly by neutron scattering and NMR [3,4], and then directly by X-ray scattering [5,6,7] in several families of cuprates, so that it is now considered ubiquitous in cuprates, although only in a relatively small region of the phase diagram, below the optimal level of doping, p_opt = 0.16 holes/Cu, and below 170-200 K in temperature. In some cases, but not always, charge order competes with superconductivity, so that below the superconducting transition temperature, T_c, it weakens unless superconductivity is perturbed by other factors, e.g. by magnetic fields or by the proximity to other materials. The picture seemed settled, confining the charge-order phenomenon so much within a sub-region of the phase diagram to be considered a consequence of the well-known pseudogap in the electronic structure.

Using resonant inelastic X-ray scattering (RIXS) at the Cu L₃ absorption edge at beamline ID32, a new, totally unexpected form of charge order has been discovered in overdoped Pb-Bi₂Sr₂CuO_6+δ (Bi2201), a compound with a single CuO₂ layer per unit cell. The correlation length obtained from the sharpness of the scattering peak is of the order of 50 unit cells, much larger than in the underdoped samples measured previously (see Figure 1). The wave vector of the charge order (Q_CO ~ 0.14 lattice units) is different from that of the underdoped Bi2201, however, it is in-line with the extrapolation of the trend known at low doping, suggesting that the two regimes are connected by a common microscopic origin. Another surprising property of this charge order is that it is independent of temperature: neither the onset of superconductivity at low T nor the thermal disorder up to almost 300 K modify significantly the intensity and the width of the scattering peak.

Figure 1. The dependence on doping of the charge order properties in single layer Bi2201. a) The incommensurate wave vector QCO, b) the correlation length ζ and c) the intensity of the scattering peak, depend on the doping p differently in the underdoped (p ≤ 0.16) and in the overdoped (p > 0.19) regions of the phase diagram.

The consequences of this discovery are depicted in the phase diagram in Figure 2. A new regime of charge order, outside of the pseudogap region, has to be added, at least for Bi2201, it is labelled CO2. This means that theories requiring a connection between pseudogap and charge order cannot explain CO2. Also its origin from Fermi surface nesting or folding has been ruled out by performing angle-resolved photoemission spectroscopy measurements. A unifying theory is thus proposed, descending from the initial prediction made 25 years ago [1,5]. In this view, charge order is the result of an attractive interaction among charges, insufficient per se to reach criticality, and thus long-range order at low T. However this attraction can emerge at low doping where correlation flattens the electronic bands, manifesting itself as short-range charge order, observed previously, and at high doping of Bi2201, when a particularly large van Hove singularity increases decisively the density of states just below the Fermi level, leading to the medium-range charge order just discovered.

Figure 2. The phase diagram of Bi2201 highlighting the various charge order regions. As all other high Tc superconducting cuprates, the antiferromagnetic (AF) parent compound (p = 0) becomes superconducting (SC) in a domed region peaking around p = 0.16. A pseudo-gap (PG) is observed in the electronic structure of the superconductors above Tc and below T*. Charge order had been observed by STM at low T over a wide range of doping (surface STM-CO), but only in a narrower interval with resonant X-ray scattering (CO1), always inside the PG area. The new RIXS data have unveiled charge order (CO2), almost insensitive to temperature, in the overdoped regime.

Principal publication and authors
Re-entrant charge order in overdoped (Bi,Pb)_2.12Sr_1.88CuO_6+δ outside the pseudogap regime, Y.Y. Peng (a), R. Fumagalli (a), Y. Ding (b), M. Minola (c), S. Caprara (d,e), D. Betto (f), M. Bluscke (c), G.M. De Luca (g,h), K. Kummer (f), E. Lefrançois (c), M. Salluzzo (f), H. Suzuki (c), M. Le Tacon (i), X.J. Zhou (b), N.B. Brookes (f), B. Keimer (c), L. Braicovich (a), M. Grilli (d,e) and G. Ghiringhelli (a,j), Nature Materials (11 June 2018); doi: 10.1038/s41563-018-0108-3.
(a) Politecnico di Milano (Italy)
(b) Institute of Physics, C.A.S. Beijing (China)
(c) Max-Planck-Institut für Festkörperforschung, Stuttgart (Germany)
(d) Università di Roma La Sapienza (Italy)
(e) CNR-ISC, Roma (Italy)
(f) ESRF
(g) Università di Napoli Federico II (Italy)
(h) CNR-SPIN, Napoli (Italy)
(i) Karlsruhe Institute of Technology (Germany)
(j) CNR-SPIN, Milano (Italy)

References
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[2] J.M. Tranquada et al., Nature 375, 561 (1995).
[3] T. Wu et al., Nature 477, 191-194 (2011).
[4] G. Ghiringhelli et al., Science 337, 821 (2012).
[5] J. Chang et al., Nat. Phys. 8, 871 (2012).  
[6] R. Comin et al., Science 343, 390 (2014).  
[7] S. Caprara et al., Phys. Rev. B 95, 224511 (2017).  
[8] Y.Y. Peng et al., Phys. Rev. B 94, 184511 (2016).