A characteristic energy scale in glasses

Intrinsically generated structural disorder endows glassy materials with a broad distribution of various microscopic quantities - such as relaxation times and activation energies - without an obvious characteristic scale. At the same time, macroscopic glassy responses - such as Newtonian (linear) viscosity and nonlinear plastic deformation - are widely interpreted in terms of a characteristic energy scale, e.g., an effective temperature-dependent activation energy in Arrhenius relations. Nevertheless, despite its fundamental importance, such a characteristic energy scale has not been robustly identified. Inspired by the accumulated evidence regarding the crucial role played by disorder- and frustration-induced soft quasilocalized excitations in determining the properties and dynamics of glasses, we propose that the bulk average of the glass response to a localized force dipole defines such a characteristic energy scale. We show that this characteristic glassy energy scale features remarkable properties: (i) It increases dramatically in underlying inherent structures of equilibrium supercooled states approaching the glass transition temperature Tg, significantly surpassing the corresponding increase in the macroscopic shear modulus, dismissing the common view that structural variations in supercooled liquids upon vitrification are minute. (ii) Its variation with annealing and system size is very similar in magnitude and form to that of the energy of the softest non-phononic vibrational mode, thus establishing a nontrivial relation between a rare glassy fluctuation and a bulk average response. (iii) It exhibits striking dependence on spatial dimensionality and system size due to the long-ranged fields associated with quasilocalization, which are speculated to be related to peculiarities of the glass transition in two dimensions. In addition, we identify a truly static growing lengthscale associated with the characteristic glassy energy scale and discuss possible connections between the increase of this energy scale and the slowing down of dynamics near the glass transition temperature. Open questions and future directions are discussed.