32 research outputs found
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
plane) with dipoles pointing to the 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 (, ) 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)
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 can
take place if the interaction is repulsive and has a finite range 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