Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate

Abstract

Traditionally, x-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, spectroscopic imaging scanning tunneling microscopy (STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize; thus, a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond-length variations obtained from topographic imaging with picometer precision. Application of this technique to the high-T_{c} cuprate superconductor Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} reveals a high-fidelity local lattice distortion of the BiO lattice as large as 2%. In addition, analysis of local breaking of rotational symmetry associated with the bond lengths reveals modulations around four-unit-cell periodicity in both B_{1} and E representations in the C_{4v} group of the lattice, which coincides with the unidirectional d-symmetry CDW (dCDW) previously identified within the CuO_{2} planes, thus providing direct evidence of electron-lattice coupling in the pseudogap state and a link between the x-ray scattering and STM measurements. Overall, our results suggest that the periodic lattice displacements in E representations correspond to a locally frozen version of the soft phonons identified by the x-ray scattering measurements, and a fluctuation of the bond length is reflected by the fluctuation of the dCDW formation near the quantum critical point.