Dipole-Induced Transition in 3-Dimensions

TL;DR

This paper reports a novel dipole-induced phase transition in three-dimensional amorphous solids under strain, characterized by symmetry breaking, plasticity, and diverging correlation lengths, expanding topological transition concepts beyond two dimensions.

Contribution

It introduces the first known 3D dipole-induced transition in amorphous solids, demonstrating symmetry breaking and critical behavior analogous to 2D topological transitions.

Findings

Identification of an intermediate phase with plasticity between elastic and fluid states.

Observation of diverging correlation lengths and critical scaling at the transition.

Evidence of symmetry breaking and screening effects due to dipole-like quadrupolar fields.

Abstract

The Kosterlitz-Thouless and the Hexatic phase transitions are celebrated examples of dipole (vortex, dislocation) induced transitions in condensed matter physics. For very clear reasons, these important ``topological" transitions are restricted to 2-dimensions. Here we present a genuine dipole-induced transition in the 3-dimensional response of (athermal) amorphous solids to applied strain. Similarly to the existence of a hexatic phase between normal solid and fluid, we identify an intermediate phase between a phase of normal elastic response at high pressure, and fluid matter at zero pressure. The mechanical response in the intermediate phase is accompanied by plasticity that is generically associated with ``non-affine" quadrupolar events seen in the resulting displacement field. Gradients of the quadrupolar fields act as dipole charges that screen elasticity, breaking both translational and Chiral symmetries. We highlight {\em angular} correlations that exhibit diverging correlation lengths at this transition and determine the critical scaling exponents.