Quantum hexatic order in two-dimensional dipolar and charged fluids

Abstract

Recent advances in cold atom experimentation suggest that studies of quantum two-dimensional melting of dipolar molecules, with dipoles aligned perpendicular to ordering plane, may be on the horizon. An intriguing aspect of this problem is that two-dimensional \emph{classical} aligned dipoles (already studied in great detail in soft matter experiments on magnetic colloids) are known to melt via a two-stage process, with an intermediate hexatic phase separating the usual crystal and isotropic fluid phases. We estimate here the effect of quantum fluctuations on this hexatic phase, for both dipolar systems and charged Wigner crystals. Our approximate phase diagrams rely on a pair of Lindemann criteria, suitably adapted to deal with effects of thermal fluctuations in two dimensions. As part of our analysis, we determine the phonon spectra of quantum particles on a triangular lattice interacting with repulsive $1/r^3$ and $1/r$ potentials. A large softening of the transverse and longitudinal phonon frequencies, due to both lattice effects and quantum fluctuations, plays a significant role in our analysis. The hexatic phase is predicted to survive down to very low temperatures.

10 pages, 7 figures. Version 2 includes minor revisions and a few new references

References in corpus (8)

• A High Phase-Space-Density Gas of Polar Molecules
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
• Quantum phase transition in a two-dimensional system of dipoles
• Ultracold Fermionic Feshbach Molecules of ${}^{23}$Na${}^{40}$K
• Bragg spectroscopy of a strongly interacting Fermi gas
• Quantum melting of a crystal of dipolar bosons
• Structure and melting behavior of classical bilayer crystals of dipoles

Cited by in corpus (21)

• Long-range interacting quantum systems
• Observation of Wigner crystal of electrons in a monolayer semiconductor
• Dual gauge field theory of quantum liquid crystals in two dimensions
• Dual gauge field theory of quantum liquid crystals in three dimensions
• Evidence of a two-stage melting of Wigner solids in two dimensions
• Two-dimensional Bose gas of tilted dipoles: roton instability and condensate depletion
• Freezing of soft-core bosons at zero temperature: A variational theory
• Classification of nematic order in 2+1D: Dislocation melting and $O(2)/Z_N$ lattice gauge theory
• Liquid crystal phases of two-dimensional dipolar gases and Berezinskii-Kosterlitz-Thouless melting
• Properties of the density-wave phase of a two-dimensional dipolar Fermi gas
• Quantum and thermal melting of stripe forming systems with competing long ranged interactions
• The Role of Quantum Fluctuations in the Hexatic Phase of Cold Polar Molecules
• Buckling transitions and clock order of two-dimensional Coulomb crystals
• Quantum melting of two-component Rydberg crystals
• Twistronics and moiré superlattice physics in 2D transition metal dichalcogenides
• Melting of electronic and excitonic crystals in 2D semiconductor moiré patterns: a perspective from the Lindemann criterion
• Stability of Wigner crystals and Mott insulators in twisted moiré structures
• Classical crystal formation of dipoles in two dimensions
• Supersolid phase in two-dimensional soft-core bosons at finite temperature
• Exciton crystal melting and destruction by disorder in bilayer quantum hall system with total filling factor one
• Exciton interacting with the phonons of an electronic Wigner crystal