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3D long-range charge order in a uniaxially-strained cuprate superconductor


A combination of uniaxial compression and inelastic X-ray scattering revealed a new electronic state competing with superconductivity in the cuprates, and its associated phonon anomalies. These results open fresh perspectives for studying competing orders in quantum materials.

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A by-product of strong electronic interactions in the cuprates is the variety of almost degenerate electronic orders competing within their phase diagrams. These encompass superconducting, antiferromagnetic and charge density wave (CDW) orders that can be tuned using external parameters. In turn, the response of these phases to the tuning parameter can provide precious insights regarding the microscopic mechanism yielding their formation.

In this work, uniaxial strain has been used to tune the balance between superconductivity and CDW in YBa2Cu3O6.67, while monitoring its collective lattice response by means of inelastic X-ray scattering (IXS). A large uniaxial compression along the a-axis was found to induce a new three-dimensional (3D) long-range ordered CDW. Temperature-dependent measurements showed that the 3D charge order is in very strong competition with superconductivity. Moreover, the very strong softening of an optical phonon as the 3D order sets in, suggests a phonon-freezing formation mechanism.

The experiments were carried out at beamline ID28 where temperature-dependent high-resolution IXS measurements under uniaxial strain were performed for the first time on YBa2Cu3O6.67 needles using a dedicated piezoelectric-based apparatus [1]. By thinning the central parts of the needles by plasma focused-ion-beam, uniaxial compression as large as 1% could be achieved (Figure 1).

Sketch of the piezoelectric-based strain apparatus and photo of the sample.

Figure 1. Sketch of the piezoelectric-based strain apparatus and photo of the sample thinned by plasma focused-ion-beam (FIB).

The main result is summarised in Figure 2, which shows the momentum dependence of the elastic peak intensity. A broad profile centred around Q2D (L = 6.5) is already present in unstrained conditions and arises from the previously reported quasi-two-dimensional (2D) short-range ordered CDW [2]. Under uniaxial strain, a sharp 3D-CDW peak appears at Q3D (L = 7) on top of the broad profile and rapidly increases in amplitude and correlation length as the compression is increased. The 3D-CDW appears above the superconducting transition temperature Tc of the unstrained sample and is rapidly and completely suppressed –unlike the 2D-CDW– in the superconducting state. Earlier studies have shown that 3D long-range ordered uniaxial CDW emerges when superconductivity is strongly suppressed under magnetic fields larger than ~15 T [3]. Our results show that the long-range 3D CDW order can be accessed without a magnetic field and at temperatures above the superconducting transition temperature Tc by using a-axis uniaxial pressure.

Strain  and temperature dependence  of the elastic peak intensity along the (0 0.315 L) direction

Figure 2. Strain (a) and temperature dependence (b) of the elastic peak intensity along the (0 0.315 L) direction.

Further insights into the origin of the 3D CDW are given by the phononic part of the IXS spectra shown in Figure 3. A very strong softening of an optical phonon is observed at the 3D-CDW ordering wavevector Q3D under uniaxial compression, while the spectra are essentially unchanged away from Q3D. The temperature dependence of this strong softening suggests that the transition to the ordered state is driven by the complete phonon softening and therefore indicates that it is a thermodynamic ground state competing with high temperature superconductivity.

Phonon spectra along the (0 K 7) direction recorded below Tc under unstrained and -1% strained conditions.

Figure 3. Phonon spectra along the (0 K 7) direction recorded below Tc under unstrained (a) and -1% strained (b) conditions. The red lines represent the calculated structure factor of the phonons. The solid blue and grey lines correspond to the least square fit of the data. The red arrows indicate the soft optical mode and the grey arrows the acoustical phonon.

The data collected highlight the potential offered by uniaxial strain to investigate the relationship between superconductivity and charge ordering in the cuprates in great detail and in the absence of magnetic fields. More generally, the current results illustrate the powerful combination of uniaxial strain application and X-ray spectroscopic techniques for the study of competing orders in a broad class of correlated materials and offer a promising prospect for future experiments.


Principal publication and authors
Uniaxial pressure control of competing orders in a high temperature superconductor, H.-H. Kim (a), S.M. Souliou (b), M.E. Barber (c), E. Lefrancois (a), M. Minola (a), M. Tortora (a), R. Heid (d), N. Nandi (c), R.A. Borzi (c,e), G. Garbarino (b), A. Bosak (b), J. Porras (a), T. Loew (a), M. König (c), P.M. Moll (c), A.P. Mackenzie (c), B. Keimer (a), C.W. Hicks (c), M. Le Tacon (d), Science  362, 1040-1044 (2018); doi: 10.1126/science.aat4708.
(a) Max Planck Institute for Solid State Research, Stuttgart (Germany)
(b) ESRF
(c) Max Planck Institute for Chemical Physics of Solids, Dresden (Germany)
(d) Institute for Solid State Physics, Karlsruhe Institute of Technology, Karlsruhe (Germany)
(e) Instituto de Física de Líquidos y Sistemas Biológicos, La Plata (Argentina)


[1] C.W. Hicks et al., Review of Scientific Instruments 85, 065003 (2014).
[2] G. Ghiringhelli et al., Science 337, 821-825 (2012).
[3] S. Gerber et al., Science 350, 949-952 (2015); H. Jang et al., PNAS, 14645-14650 (2016); J. Chang et al., Nat.Comm. 7, 11494 (2016).