Elastic properties of few unit cell thick superconducting crystals of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$

TL;DR

This study measures the elastic properties of few-unit-cell thick superconducting Bi$_2$Sr$_2$CaCu$_2$O$_{8+\

Contribution

It provides the first detailed measurement of Young's modulus and pre-stress in ultrathin Bi-2212 crystals using AFM deformation techniques.

Findings

Young's modulus ranges from 22 GPa to 30 GPa for 5-18 UC flakes.

Pre-stress varies from 5 MPa to 46 MPa across samples.

Results are verified with buckling technique.

Abstract

We present systematic measurements of the mechanical properties of few unit cell (UC) thick exfoliated crystals of a high-T$_c$ cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. We determine the elastic properties of these crystals by deformation using an atomic force microscope (AFM) at room temperature. With the spatial measurements of local compliance and their detailed modeling, we independently determine the Young's modulus of rigidity and the pre-stress. The Young's modulus of rigidity is found to be in the range of 22 GPa to 30 GPa for flakes with thickness from 5 UC to 18 UC. The pre-stress spreads over the range of 5 MPa - 46 MPa, indicating a run-to-run variation during the exfoliation process. The determination of Young's modulus of rigidity for thin flakes is further verified from recently reported buckling technique.