Realizing Persistent Zero Area Compressibility over a Wide Pressure Range in Cu2 GeO4 by Microscopic Orthogonal-Braiding Strategy

Abstract

Zero area compressibility (ZAC) is an extremely rare mechanical response that exhibits an invariant two-dimensional size under hydrostatic pressure. All known ZAC materials are constructed from units in two dimensions as a whole. Here, we propose another strategy to obtain the ZAC by microscopically orthogonal-braiding one-dimensional zero compressibility strips. Accordingly, ZAC is identified in a copper-based compound with a planar [CuO₄ ] unit, Cu₂ GeO₄ , that possesses an area compressibility as low as 1.58(26) TPa^-1 over a wide pressure range from ≈0 GPa to 21.22 GPa. Based on our structural analysis, the subtle counterbalance between the shrinkage of [CuO₄ ] and the expansion effect from the increase in the [CuO₄ ]-[CuO₄ ] dihedral angle attributes to the ZAC response. High-pressure Raman spectroscopy, in combination with first-principles calculations, shows that the electron transfer from in-plane bonding d_x ² _-y ² to out-of-plane nonbonding d_z ² orbitals within copper atoms causes the counterintuitive extension of the [CuO₄ ]-[CuO₄ ] dihedral angle under pressure. Our study provides an understanding on the pressure-induced structural evolution of copper-based oxides at an electronic level and facilitates a new avenue for the exploration of high-dimensional anomalous mechanical materials.

Keywords: Copper-Based Oxides; First-Principles Calculation; High Pressure; Orthogonal-Braiding; Zero Area Compressibility.