Temperature Dependence of the Vacancy Formation Energy in Solid $^4$He

TL;DR

This study investigates how temperature influences vacancy formation energy in solid helium-4, revealing vacancy delocalization and condensate formation at low temperatures through Monte Carlo simulations.

Contribution

It provides the first detailed analysis of temperature-dependent vacancy formation energy and vacancy interactions in solid $^4$He using path integral Monte Carlo methods.

Findings

Vacancies delocalize below a certain temperature.

A finite condensate fraction appears at low temperatures.

Vacancy formation energy shows a two-step temperature dependence.

Abstract

We studied the thermal effects on the behavior of incommensurate solid $^4$He at low temperatures using the path integral Monte Carlo method. Below a certain temperature, depending on the density and the structure of the crystal, the vacancies delocalize and a finite condensate fraction appears. We calculated the vacancy formation energy as a function of the temperature and observed a behavior compatible with a two-step structure, with a gap of few K appearing at the onset temperature of off-diagonal long-range order. Estimation of the energy cost of creating two vacancies seems to indicate an effective attractive interaction among the vacancies but the large error inherent to its numerical estimation precludes a definitive statement.