The Commensurate Phases of BCCD Revisited: Domain Walls, Condensates, and Quantum Effects

Abstract

A new analysis of previously published experimental findings on ferroelectric (fe) BCCD (betaine calcium chloride dihydrate) is presented. The commensurately (c) modulated phases, which exist in the temperature interval 46 K ≤ T ≤ 115 K at ambient pressure (sixfold, fivefold, fourfold modulated structures), display a highly anharmonic soliton regime. The domain walls separating the fe microdomains are not static but discrete, spatially localized, stable topological objects, breaking ergodicity, formed by twodimensional Bose-Einstein condensates of nonlinear, time-periodic vibrational excitations in molecular monolayers at low frequencies (≈20 cm−1), derived from the lowest optical (librational) mode of the crystal. These 2d-condensates are stacked coherently along the modulation c-axis, following the soliton wave and forming a 3-dimensional system with extreme anisotropy along c. This remarkable system is the first example, which displays strong quantum pressure effects due to quantum fluctuations, e.g. giving rise to the observed steps and other anomalies in thermal dilatation of BCCD. This interaction between adjacent layers of condensates follows near 46 K quantitatively the predictions of the Gross-Pitaevskii equation. A simple expression for the free energy of the system of domain walls is derived from this equation, which describes quantitatively all thermodynamic properties of the domain wall system with their density as a complex scalar order paramenter in an inverted phase diagram in the c phases of BCCD. Arguments are given for the breaking of gauge symmetry by the domain walls, the existence of a proper temperature scale of this system, especially with a pseudo-zeropoint of temperature, and the existence of a quantum phase transition between 46 K and 160 K, depending on external pressure.