Elastic Moduli in Nano-Size Samples of Amorphous Solids: System Size Dependence

This Letter is motivated by some recent experiments on pan-cake shaped nano-samples of metallic glass that indicate a decline in the measured shear modulus upon decreasing the sample radius. Similar measurements on crystalline samples of the same dimensions showed a much more modest change. In this Letter we offer a theory of this phenomenon; we argue that such results are generically expected for any amorphous solid, with the main effect being related to the increased contribution of surfaces with respect to bulk when the samples get smaller. We employ exact relations between the shear modulus and the eigenvalues of the system's Hessian matrix to explore the role of surface modes in affecting the elastic moduli.