Ground states of stealthy hyperuniform potentials. II. Stacked-slider phases

TL;DR

This paper explores the properties of stacked-slider phases in stealthy hyperuniform potentials, revealing their structure, stability, and unique physical characteristics through numerical and analytical methods.

Contribution

It introduces analytical models for stacked-slider phases in multiple dimensions and analyzes their configuration space and physical properties, expanding understanding of these metastable states.

Findings

Stacked-slider phases are nonperiodic, statistically anisotropic with long-range orientational order.

The feasible configuration space of stacked-slider phases is smaller than that of crystal structures.

Exact pair correlation and structure factor expressions are derived for 2D stacked-slider phases.

Abstract

Stealthy potentials, a family of long-range isotropic pair potentials, produce infinitely degenerate disordered ground states at high densities and crystalline ground states at low densities in d-dimensional Euclidean space R^d. In the previous paper in this series, we numerically studied the entropically favored ground states in the canonical ensemble in the zero-temperature limit across the first three Euclidean space dimensions. In this paper, we investigate using both numerical and theoretical techniques metastable stacked-slider phases, which are part of the ground-state manifold of stealthy potentials at densities in which crystal ground states are favored entropically. Our numerical results enable us to devise analytical models of this phase in two, three, and higher dimensions. Utilizing this model, we estimated the size of the feasible region in configuration space of the stacked-slider phase, finding it to be smaller than that of crystal structures in the infinite-system-size limit, which is consistent with our recent previous work. In two dimensions, we also determine exact expressions for the pair correlation function and structure factor of the analytical model of stacked-slider phases and analyze the connectedness of the ground-state manifold of stealthy potentials in this density regime. We demonstrate that stacked-slider phases are distinguishable states of matter; they are nonperiodic, statistically anisotropic structures that possess long-range orientational order but have zero shear modulus. We outline some possible future avenues of research to elucidate our understanding of this unusual phase of matter.