Topological Catastrophe and Isostructural Phase Transition in Calcium

TL;DR

This paper predicts a topological quantum phase transition in face-centered cubic calcium under pressure, characterized by a change in electron charge density topology and associated elastic property softening.

Contribution

It introduces a novel topological order parameter based on Morse theory to describe the phase transition in calcium.

Findings

Charge density topology changes at 80 kbar pressure.

Elastic modulus C' softens near the transition.

Charge density features evolve from bifurcated bonds to non-nuclear maxima.

Abstract

We predict a quantum phase transition in fcc Ca under hydrostatic pressure. Using density functional theory, we find at pressures below 80 kbar, the topology of the electron charge density is characterized by nearest neighbor atoms connected through bifurcated bond paths and deep minima in the octahedral holes. At pressures above 80 kbar, the atoms bond through non-nuclear maxima that form in the octahedral holes. This topological change in the charge density softens the C' elastic modulus of fcc Ca, while C$_{44}$ remains unchanged. We propose an order parameter based on applying Morse theory to the charge density, and we show that near the critical point it follows the expected mean-field scaling law with reduced pressure.