Revealing bond level origin of stability in disordered solids from marginal stability to ultrastability.

Disordered solids can be prepared with a vast spectrum of stabilities, ranging from marginally stable to ultra-stable. While understanding the structural origin of stability is crucial for predicting mechanical failure, as well as for revealing the nature and manipulating the properties of disordered solids, structural disorder poses a significant obstacle. Here, we propose and identify stabilizing bonds-interactions between particles whose removal would trigger mechanical failure-as a key microscopic feature governing stability. We present compelling evidence that stabilizing bonds dictate marginal stability, demonstrated by their recovery of the weak force distribution predicted by theories and their power to predict failure under load. The evolution from marginal stability to ultra-stability is further captured by the amount, spatial organization, and unstable modes of stabilizing bonds, revealing their role as 'defects' in disordered solids. Our work establishes stabilizing bonds as a fundamental structural entity responsible for unusual properties of disordered solids, paving the way for a generalized description of these materials.