Scale invariant structures and marginal stability in jammed amorphous solids

A major issue in condensed matter physics is how the structures of amorphous solids are self-organized, which leads to peculiar properties distinct from crystalline counterparts. Due to their disordered nature which is complex and system dependent, there has been no consensus on the existence of amorphous order, not to mention a quantitative description with a firm theoretical basis. Here we derive a new structure indicator, Ψ, from the mechanical aspect of amorphous solids which is universal for systems with different constituents, structures, interactions, and in both 2D and 3D. We find that the distribution of Ψ has a power-law tail, whose exponent shows critical scaling approaching the jamming transition. Such a power-law distribution indicates marginal stability of amorphous solids, even if the system is away from jamming point. Scale invariant structures are identified, which shows long-range correlations and non-trivial fractal dimensions. We argue that this is related to the global organization of force networks under disordered constraint and a link with the long-range stress correlation is discussed. Our findings reveal critically correlated nature of amorphous structures and promote Ψ as a solid starting point for further theoretical description of amorphous solids.