Liquid crystal phases of ultracold dipolar fermions on a lattice

Abstract

Motivated by the search for quantum liquid crystal phases in a gas of ultracold atoms and molecules, we study the density wave and nematic instabilities of dipolar fermions on the two-dimensional square lattice (in the $x-y$ plane) with dipoles pointing to the $z$ direction. We determine the phase diagram using two complimentary methods, the Hatree-Fock mean field theory and the linear response analysis of compressibility. Both give consistent results. In addition to the staggered ($\pi$, $\pi$) density wave, over a finite range of densities and hopping parameters, the ground state of the system first becomes nematic and then smectic, when the dipolar interaction strength is increased. Both phases are characterized by the same broken four-fold (C${}_4$) rotational symmetry. The difference is that the nematic phase has a closed Fermi surface but the smectic does not. The transition from the nematic to the smectic phase is associated with a jump in the nematic order parameter. This jump is closely related to the van Hove singularities. We derive the kinetic equation for collective excitations in the normal isotropic phase and find that the zero sound mode is strongly Landau damped and thus is not a well defined excitation. Experimental implications of our results are discussed.

8 pages, 4 figures; Erratum added in the appendix

References in corpus (17)

• A High Phase-Space-Density Gas of Polar Molecules
• Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential
• Formation of a Nematic Fluid at High Fields in Sr3Ru2O7
• Cold polar molecules in 2D traps: Tailoring interactions with external fields for novel quantum phases
• Instability toward Formation of Quasi-One-Dimensional Fermi Surface in Two-Dimensional t-J Model
• Possible Quasi-One-Dimensional Fermi Surface in La_{2-x}Sr_{x}CuO_4
• Magneto-electrostatic trapping of ground state OH molecules
• Quantum phases of a Two-Dimensional Dipolar Fermi Gas
• Phase space deformation of a trapped dipolar Fermi gas
• Formation of Electronic Nematic Phase in Interacting Systems
• Ferro-Nematic ground state of the dilute dipolar Fermi gas
• Deconfinement in a 2D optical lattice of coupled 1D boson systems
• Fluctuating Stripes in Strongly Correlated Electron Systems and the Nematic-Smectic Quantum Phase Transition
• Meta-nematic, smectic and crystalline phases of dipolar fermions in an optical lattice
• Dipolar bosons in a planar array of one-dimensional tubes
• Effect of magnetic field on spontaneous Fermi surface symmetry breaking
• Fermi Liquid instabilities in two-dimensional lattice models

Cited by in corpus (30)

• A Strongly Dipolar Bose-Einstein Condensate of Dysprosium
• Condensed Matter Theory of Dipolar Quantum Gases
• Quantum degenerate dipolar Fermi gas
• Density wave instability in a 2D dipolar Fermi gas
• Spontaneous inhomogeneous phases in ultracold dipolar Fermi gases
• Dislocation-mediated melting of one-dimensional Rydberg crystals
• Bond order solid of two-dimensional dipolar fermions
• Supersolid Phase of Cold Fermionic Polar Molecules in 2D Optical Lattices
• Density wave patterns for fermionic dipolar molecules on a square optical lattice: Mean-field-theory analysis
• The J-triplet Cooper pairing with magnetic dipolar interactions
• Harmonically trapped dipolar fermions in a two-dimensional square lattice
• Lifshitz transitions and crystallization of fully-polarised dipolar Fermions in an anisotropic 2D lattice
• Unconventional magnetism in imbalanced Fermi systems with magnetic dipolar interactions
• Spin-orbit coupled Fermi liquid theory of ultra-cold magnetic dipolar fermions
• Dipolar fermions in a two-dimensional lattice at non-zero temperature
• Supersolidity of a dipolar Fermi gas in a cubic optical lattice
• Spectroscopy of dipolar fermions in 2D pancakes and 3D lattices
• Density-functional theory for the crystalline phases of a two-dimensional dipolar Fermi gas
• Dynamical properties of a trapped dipolar Fermi gas at finite temperature
• Kohn-Sham theory of rotating dipolar Fermi gas in two dimensions
• Unconventional symmetries of Fermi liquid and Cooper pairing properties with electric and magnetic dipolar fermions
• Momentum distribution and ordering in mixtures of ultracold light and heavy fermionic atoms
• Stripe, checkerboard, and liquid-crystal ordering from anisotropic p-orbital Fermi surfaces in optical lattices
• Phase diagram of two-component dipolar fermions in one-dimensional optical lattices
• Electronic nematic phase transition in the presence of anisotropy
• Pomeranchuk instabilities in multicomponent lattice systems at finite Temperature
• Wigner Crystallization in Two Dimensions: Evolution from Long- to Short-Ranged Forces
• Competing Orders in a Dipolar Bose-Fermi Mixture on a Square Optical Lattice: Mean-Field Perspective
• Triplet Superfluidity on a triangular ladder with dipolar fermions
• Particle-hole bound states of dipolar molecules in optical lattice