By Jaewon Choi, Mark H. Fischer and Johan Chang, UZH
Based on article published in Physical Review Letters
The remarkable similarity in the phase diagrams across a large range of correlated quantum materials poses the general question of whether these phase diagrams derive from a primary order, from which all other phases descend via breaking of relevant symmetries. In copper-oxide (or cuprate) superconductors, unidirectional pair-density waves (PDWs) – spatially modulated superconducting states – are the contenders for such a primary order. [See Fig. 1(a)]. However, progress in our understanding has been held back by the difficulty to determine the spatial symmetry of CDW order. As described shown in Fig. 1(b) and 1(c), the observed “four-fold” diffraction pattern is consistent with both bidirectional “checkerboard” and unidirectional “stripe” CDW modulation. This is because stripes generally form mutually 90°-rotated domains in square lattice of CuO2 layers, resulting in virtually indistinguishable CDW patterns.
In our work, we combine a novel uniaxial pressure cell with synchrotron x-ray diffraction at high magnetic fields to unambiguously discern the symmetry of CDW in the prototypical cuprate La1.88Sr0.12CuO4 (LSCO) . We employ uniaxial pressure as an external stimulus that lifts the degeneracy of stripe-ordered domains as illustrated in Fig 1(d) and (c). The key experimental observation, shown in Fig. 1(f) and (g), is that the uniaxial pressure along the in-plane Cu-O bond direction induces a twofold enhancement of the CDW peak along one in-plane direction, whereas it completely suppresses the CDW peak along the other, orthogonal in-plane direction. This anisotropic response is further enhanced to a factor of 5 upon the application of a magnetic field ~10 T, while the CDW correlation length is only marginally improved.
Fig.1: (a) Unidirectional pair-density wave (PDW) intertwined with charge-density wave (CDW). (b) Application of uniaxial pressure disentangles the degeneracy of (b) checkerboard and (c) stripe CDW and provides distinguishable diffraction patterns for (d) checkboard and (e) stripe CDW. Our x-ray diffraction results – (f) twofold enhancement of CDW intensity along H direction and (g) suppression of CDW peak along K direction provide unequivocal evidence of charge stripe order.
Our results provide unequivocal evidence of charge stripe order in LSCO in its purest form. We also demonstrate that the stripe CDW coupled with unconventional superconductivity is an intrinsic electronic property of underdoped cuprates. Although our results do not provide direct evidence, they help distinguish the possible theoretical models describing the PDW state . J. Choi et al., “Unveiling Unequivocal Charge Stripe Order in a Prototypical Cuprate Superconductor”, Phys. Rev. Lett. 128, 207002 (2022).
 D. F. Agterberg et al., “The Physics of Pair-Density Waves: Cuprate Superconductors and Beyond”, Annu. Rev. Condens. Matter Phys. 11, 231-270 (2020).