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

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.

Extended analytical BCS theory of superconductivity in thin films

“…Furthermore, and importantly, the above confinement model has been quantitatively checked and verified in great detail for phonons in ice (both crystalline and amorphous) under nanometric confinement, by means of detailed atomistic simulations and experiments in Ref. [18] (see in particular the section "Failure of the hard-wall boundary conditions" in the Supplementary Information of [18] ).…”

“…In this work, following the ideas from Refs. [15][16][17][18], we consider a system confined in the z-direction, as shown in Fig. 1, and unconfined in the x and y directions; the following discussion is hence directly relevant to the study of the physics of thin films.…”

Suppressed terahertz dynamics of water confined in nanometer gaps

“…To understand the underlying physics behind this phenomenon, we refer to recent studies which predict that confinement may lead to suppression of VDOS at low-energy limit, thereby leading to a low dielectric permittivity (22)(23)(24)60). As the frequency range of our interest (0.1 to 1.5 THz) may be considered sufficiently low in terms of equivalent energy (0.4 to 6 meV), we used this theory (60) to formulate a model to qualitatively explain the reduced dielectric permittivity of nanoconfined water.…”

“…The behaviors of water molecules confined in nanoscale structures underlie various processes in our everyday life such as solvation of ions and biomolecules (1-7), molecular transport through nanopores (8,9), formation of electric double layer on electrodes (10,11), and chemical reactions (12,13). On this stance, understanding the properties of nanoconfined water is of paramount importance in all fields of natural science and has attracted many theoretical and experimental studies (14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28). Thus far, most studies have agreed on the rule of thumb that the nanoconfinement effect comes from the unique response of interfacial water, which forms an ordered state parallel to face of the interface up to 1-nm thickness (approximately four layers of water molecules), leading to a suppressed reorientation of molecular dipole moment under external field bias and consequently a decreased permittivity (29)(30)(31)(32).…”

Near-Field Localization of the Boson Peak on Tantalum Films for Superconducting Quantum Devices

“…44−51 From the linear response theory for disordered materials, the absorption coefficient is proportional to the vibrational density of states [vDOS: g(ν)], and the boson peak is usually characterized by g(ν)/ν 2 , 28,32 except in the case of quasi-two-dimensional materials where it is characterized by g(ν)/ν 3 due to confinement effects (Figure S2). 52 Recently, the boson peak has been observed and characterized using the normalized absorption coefficients α(ν)/ν 2 from THz timedomain spectroscopic measurements on amorphous or glasslike materials. 35−38 As Ta 2 O 5 has well-documented amorphous phases, the spectroscopic signature at 0.5 THz in region B fits with our understanding of the universal nature of the boson peak.…”