Liquid crystal phases of ultracold dipolar fermions on a lattice

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.Comment: 8 pages, 4 figures; Erratum added in the appendi

Kinks in the dispersion of strongly correlated electrons

The properties of condensed matter are determined by single-particle and collective excitations and their interactions. These quantum-mechanical excitations are characterized by an energy E and a momentum \hbar k which are related through their dispersion E_k. The coupling of two excitations may lead to abrupt changes (kinks) in the slope of the dispersion. Such kinks thus carry important information about interactions in a many-body system. For example, kinks detected at 40-70 meV below the Fermi level in the electronic dispersion of high-temperature superconductors are taken as evidence for phonon or spin-fluctuation based pairing mechanisms. Kinks in the electronic dispersion at binding energies ranging from 30 to 800 meV are also found in various other metals posing questions about their origins. Here we report a novel, purely electronic mechanism yielding kinks in the electron dispersions. It applies to strongly correlated metals whose spectral function shows well separated Hubbard subbands and central peak as, for example, in transition metal-oxides. The position of the kinks and the energy range of validity of Fermi-liquid (FL) theory is determined solely by the FL renormalization factor and the bare, uncorrelated band structure. Angle-resolved photoemission spectroscopy (ARPES) experiments at binding energies outside the FL regime can thus provide new, previously unexpected information about strongly correlated electronic systems.Comment: 8 pages, 5 figure

Meta-nematic, smectic and crystalline phases of dipolar fermions in an optical lattice

It has been suggested that some strongly correlated matter might be understood qualitatively in terms of liquid crystalline phases intervening between the Fermi gas and the Wigner crystal or Mott insulator. We propose a tunable realisation of this soft quantum matter physics in an ultra-cold gas. It uses optical lattices and dipolar interactions to realise a particularly simple model. Our analysis reveals a rich phase diagram featuring a meta-nematic transition where the Fermi liquid changes dimensionality; a smectic phase (stripes); and a crystalline, `checkerboard' phase.Comment: improved figure, added references, text shortened, typos corrected; to appear in Physical Review A (Rapid Communications

Deconfinement and quantum liquid crystalline states of dipolar fermions in optical lattices

We describe a simple model of fermions in quasi-one dimension that features interaction induced deconfinement (a phase transition where the effective dimensionality of the system increases as interactions are turned on) and which can be realised using dipolar fermions in an optical lattice. The model provides a relisation of a "soft quantum matter" phase diagram of strongly-correlated fermions, featuring meta-nematic, smectic and crystalline states, in addition to the normal Fermi liquid. In this paper we review the model and discuss in detail the mechanism behind each of these transitions on the basis of bosonization and detailed analysis of the RPA susceptibility.Comment: Invited paper for CMT32, to appear in the Int. J. Mod. Phys.B, 13 page

Pomeranchuk and topological Fermi surface instabilities from central interactions

We address at the mean field level the emergence of a Pomeranchuk instability in a uniform Fermi liquid with \emph{central} particle-particle interactions. We find that Pomeranchuk instabilities with all symmetries except $l=1$ can take place if the interaction is repulsive and has a finite range $r_{0}$ of the order of the inter-particle distance. We demonstrate this by solving the mean field equations analytically for an explicit model interaction, as well as numerical results for more realistic potentials. We find in addition to the Pomeranchuk instability other, subtler phase transitions in which the Fermi surface changes topology without rotational symmetry-breaking. We argue that such interaction-driven topological transitions may be as generic to such systems as the Pomeranchuk instability.Comment: Published version (added references, typos corrected