Evolution of elastic moduli through a two-dimensional structural transformation

We use an analytical elastic energy landscape describing SnO monolayers to estimate the softening of elastic moduli through a mechanical instability occurring at finite temperature. Although not strictly applicable due to a quantum paraelastic phase in this material [1], this exercise is relevant as it establishes a conceptual procedure to estimate such moduli straight from a two-dimensional elastic energy landscape. As additional support for the existence of a quantum paraelastic phase, we use a qualitative WKB analysis [2] to estimate escape times from an energy well on the landscape. These results continue to establish a case for the usefulness of soft matter concepts in 2D materials and of the potential lurking of quantum effects in soft matter [3].

[1] T. Bishop et al., Phys. Rev. Lett. 122, 015703 (2019)
[2] D. Griffiths, Introduction to Quantum Mechanics, Pearson international edition (Pearson, Prentice-Hall, Englewood Cliffs, NJ, 2005).
[3] A. Pacheco-Sanjuan et al., Phys. Rev. B. 99, 104108 (2019)