The Search for Quantum Liquid Crystals

Abstract

We report our progress in the search fro quantum liquid crystals. By “quantum liquid crystals,” we mean quantum liquids which exhibit macroscopic orientational order but no (or incomoplete) spatial order. Such a system is necessarily composed of light molecules, so that even at very low temperatures the zero-point motion of the molecules keeps the system in the liquid state. The molecules must be sufficiently anisotropic and theinteractions sufficiently orientation-dependent to bring about macroscopic orientational order under appropriate conditions. Our goal is to occur.

The most natural candidate is ortho-hydrogen. Despite the light mass of the molecules, the strong intermolecular attraction forces the system at low temperature into a crystal in free space. To prevent this from happening, we introduce an external field which makes it energetically advantageous to keep the molecules well apart, by means of an adsorbing substrate such as a graphite surface. At zero temperature and varying areal densities, at least the following two-dimensional phases are possible: lattice gas, liquid and Debye-solid phases incommensurate with the surface symmetry of graphite each with or without orientational order, and superlattices (structures which are commensurate with graphite) with overlayer(s). The factors that determine whether among this rich variety of phases one or more liquid crystalline phases would standout as the most stable now include the orientation-dependent molecule-substrate interaction, putting the theoretical problem at the crossroads of surface physics, low temperature physics, quantum many body problem. and phase transitions.

We employ for the variational wavefunction a highly correlated Feenberg (Jastrow) function:

φ(r, ω,) contains a laterally periodic function, r(ρi, Ωi) expanded in the reciprocal lattice space as

permitting descriptions of all two-dimensional structures, including the liquid phases—in the limit G → 0. We separate I from ρ and has a simplifying approximation. In the evaluation of the energy expectation value <H>, the full Hamiltonian used includes a periodic hydrogen-substrate potential and a realistic hydrogen-hydrogen potential. One- and two-particle correlation functions, P ⁽¹⁾(r, ω) and P ⁽²⁾ (r _l, ω₁, r₂, ω₂), are obtained from coupled integral equations, and then entered into the expression for <H>. P(¹ (r, ω) carries information on the macroscopic order of the system (while P ⁽²⁾ describes short-range correlations). If several solutions for PI' exist, <H> must be evaluated for each. From comparison we then determine which phase is stable in the statistical sense.