Anomalous local atomic correlations in ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$

We have performed extended x-ray-absorption fine-structure (EXAFS) measurements to study the local atomic structure of the ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ (Hg-1201) system across the superconducting transition temperature ${(T}_c).\mathrm{}$ The Debye-Waller factors of atomic pairs obtained by Cu K-edge EXAFS are compared with diffraction data to calculate atomic correlations. The atomic correlations for Cu-O bonds show anomalous temperature dependences across the $T_c,$ highlighting the important role of electron-lattice interactions to derive the superconducting characteristics of the system.