The ω3 scaling of the vibrational density of states in quasi-2D nanoconfined solids

Yuanxi Yu; Chenxing Yang; Matteo Baggioli; Anthony E Phillips; Alessio Zaccone; Lei Zhang; Ryoichi Kajimoto; Mitsutaka Nakamura; Dehong Yu; Liang Hong

doi:10.1038/s41467-022-31349-6

The ω³ scaling of the vibrational density of states in quasi-2D nanoconfined solids

Nat Commun. 2022 Jun 25;13(1):3649. doi: 10.1038/s41467-022-31349-6.

Authors

Yuanxi Yu^#^{1

2}, Chenxing Yang^#^{1

2}, Matteo Baggioli^{3

4}, Anthony E Phillips⁵, Alessio Zaccone^{6

7}, Lei Zhang^{2

8}, Ryoichi Kajimoto⁹, Mitsutaka Nakamura⁹, Dehong Yu¹⁰, Liang Hong^{11

12

13

14

15

16}

Affiliations

¹ School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China.
² Institute of Natural Sciences, Shanghai Jiao Tong University, 200240, Shanghai, China.
³ Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China. b.matteo@sjtu.edu.cn.
⁴ Shanghai Research Center for Quantum Sciences, 201315, Shanghai, China. b.matteo@sjtu.edu.cn.
⁵ School of Physics and Astronomy, Queen Mary University of London, London, UK.
⁶ Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133, Milan, Italy.
⁷ Cavendish Laboratory, University of Cambridge, CB3 0HE, Cambridge, UK.
⁸ School of Materials Science and Engineering, Shanghai Jiao Tong University, 200240, Shanghai, China.
⁹ J-PARC Center, Japan Atomic Energy Agency (JAEA), Tokai, Ibaraki, 319-1195, Japan.
¹⁰ Australian Nuclear Science and Technology Organisation, Lucas Heights, NSW, 2234, Australia.
¹¹ School of Physics and Astronomy, Shanghai Jiao Tong University, 200240, Shanghai, China. hongl3liang@sjtu.edu.cn.
¹² Institute of Natural Sciences, Shanghai Jiao Tong University, 200240, Shanghai, China. hongl3liang@sjtu.edu.cn.
¹³ Shanghai National Center for Applied Mathematics (SJTU Center), Shanghai Jiao Tong University, 200240, Shanghai, China. hongl3liang@sjtu.edu.cn.
¹⁴ Shanghai Artificial Intelligence Laboratory, 200232, Shanghai, China. hongl3liang@sjtu.edu.cn.
¹⁵ School of Medicine, Shanghai Jiao Tong University, 200240, Shanghai, China. hongl3liang@sjtu.edu.cn.
¹⁶ Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University, 200240, Shanghai, China. hongl3liang@sjtu.edu.cn.

^# Contributed equally.

Abstract

The vibrational properties of crystalline bulk materials are well described by Debye theory, which successfully predicts the quadratic ω² low-frequency scaling of the vibrational density of states. However, the analogous framework for nanoconfined materials with fewer degrees of freedom has been far less well explored. Using inelastic neutron scattering, we characterize the vibrational density of states of amorphous ice confined inside graphene oxide membranes and we observe a crossover from the Debye ω² scaling to an anomalous ω³ behaviour upon reducing the confinement size L. Additionally, using molecular dynamics simulations, we confirm the experimental findings and prove that such a scaling appears in both crystalline and amorphous solids under slab-confinement. We theoretically demonstrate that this low-frequency ω³ law results from the geometric constraints on the momentum phase space induced by confinement along one spatial direction. Finally, we predict that the Debye scaling reappears at a characteristic frequency ω_× = vL/2π, with v the speed of sound of the material, and we confirm this quantitative estimate with simulations.