X-ray diffraction unveils pressure effects on a high-temperature superconductor

In superconducting materials, electrons pair up at low temperature to form Cooper pairs. This electronic ordering allows the material to conduct electricity with zero resistance at relatively high temperatures, with potential applications in lossless electricity transmission and medical devices.

The high-temperature superconducting material YBa₂Cu₃O_y is part of a class of layered copper-oxides known as cuprates. Cuprates still have the highest known superconducting critical temperatures (T_c) at ambient pressure – up to ~133 K (-140°C) – eliminating the need for cooling with liquid helium, making them more practical for use in potential devices. 

Applying pressure can dramatically change the properties of superconducting materials, including increasing the T_c. Indeed, the highest superconducting T_c in cuprates can be achieved by applying hydrostatic (i.e., uniform) pressures of up to 30 GPa (300,000 atmospheres), but the exact reason for the corresponding increase in T_c is unclear.

One hypothesis concerns another type of electronic ordering called charge density waves (CDWs), patterns in the material where both electronic charge density and atomic positions vary periodically. These CDWs compete with superconductivity, meaning that as one grows stronger, the other becomes weaker. Applying hydrostatic (homogeneous) pressure suppresses CDWs, which may contribute to the increase in T_c [1].

Interestingly, applying uniaxial pressure (i.e., pressure in one direction only) can have the opposite effect and be used to reduce T_c. Research on the cuprate YBa₂Cu₃O_y has shown that applying uniaxial pressure induced the formation of a long-range CDW [2]. These findings highlight the importance of further studying how pressure affects various quantum materials. 

This work set out to explore how the application of uniaxial pressure affects the properties of the cuprate YBa₂Cu₃O_y. Researchers integrated a uniaxial pressure cell into the hard X-ray diffraction cryostat at the ID15B beamline. This setup, coupled with the Eiger 2 CdTe detector, enabled them to track the evolution of short-range (or 2D) CDWs in the material from ambient pressure to a pressured or strained state, where a long-range (or 3D) CDW emerged (Figure 1).

Click figure to enlarge

Fig. 1: Experimental scheme: Polished needles of the crystal are compressed in situ by voltage-controlled piezoelectric stacks of the pressure cell. Large reciprocal space maps enable careful determination of the applied strain, as well as the intensity of broad 2D CDW and sharp 3D CDW peaks (inset) [3].

The main results of this experiment showed that while the uniaxial pressure initially enhanced the 2D CDW, the subsequent induction of the 3D CDW halted the growth of the 2D CDW (Figure 2). This finding is significant because it shows that multiple factors must be at play to determine the CDW strength, leading to complex CDW behaviour with both 2D and 3D CDWs, which is unique to YBa₂Cu₃O_y.
 

Click figure to enlarge

Fig. 2: Left: Evolution of the integrated intensity of the strain-induced 3D CDW and the short-range 2D CDW for a- and b-axis compressions. Right: Experimental (top) and theoretical (bottom) temperature-strain phase diagrams showing the depressed superconducting T_c and the extent of the 3D CDW state based on the CDW intensity for a-axis compression (ε_xx < 0, corresponding to an increased mass anisotropy of a- and b-CDWs, Δg_s, in the non-linear sigma model [3]). Note that the temperature scale in the theory panel is normalized to the bare superconducting stiffness, which serves as the basic energy scale in the model.

To explain their observations, the researchers developed a model to describe the experimental CDW intensities and their competition with superconductivity, as illustrated in the strain-temperature phase diagrams shown in Figure 2. The non-linear sigma model [4,5] effectively reproduces the behaviour of the strain-induced long-range 3D CDW and its interaction with the short-range 2D CDW. The model also considers how disorder in the material and interaction between layers of the crystal structure affect the growth of CDWs.  

In conclusion, this study demonstrates that strain can be a powerful tool for manipulating the properties of high-temperature superconductors, offering new ways to explore and potentially enhance superconductivity in these materials.

Principal publication and authors
Using strain to uncover the interplay between two- and three-dimensional charge density waves in high-temperature superconducting YBa₂Cu₃O_y, I. Vinograd (a,b), S. M. Souliou (a), A.-A. Haghighirad (a), T. Lacmann (a), Y. Caplan (c), M. Frachet (a), M. Merz (a,d), G. Garbarino (e), Y. Liu (f), S. Nakata (f), K. Ishida (g), H.M.L. Noad (g), M. Minola (f), B. Keimer (f), D. Orgad (c), C.W. Hicks (g,h),  M. Le Tacon (a), Nat. Commun. 15, 3277 (2024); https://doi.org/10.1038/s41467-024-47540-w
(a) Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology (Germany)
(b) 4th Physical Institute - Solids and Nanostructures, University of Göttingen (Germany)
(b) Racah Institute of Physics, The Hebrew University, Jerusalem (Israel)
(d) Karlsruhe Nano Micro Facility (KNMFi), Karlsruhe Institute of Technology (Germany)
(e) ESRF
(f) Max Planck Institute for Solid State Research, Stuttgart (Germany)
(g) Max Planck Institute for Chemical Physics of Solids, Dresden (Germany)
(h) School of Physics and Astronomy, University of Birmingham (UK)

References
[1] O. Cyr-Choinière et al., Phys. Rev. B 98, 064513 (2018).
[2] H.-H. Kim et al., Science 362, 1040 (2018).
[3] I. Vinograd et al., Nat. Commun. 15, 3277 (2024).
[4] Y. Caplan et al., Phys. Rev. B 92, 224504 (2015).
[5] Y. Caplan & D. Orgad, Phys. Rev. Lett. 119, 107002 (2017).