© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

arXiv:1109.3755 · Physical Review B

Density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multilayer configurations: Exact treatment of exchange interactions

Mehrtash Babadi, Eugene Demler

Published Dec 16, 2011• 35 citations

Abstract

We study the in-plane and out-of-plane density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multilayer configurations. We locate the soft modes by evaluating linear response functions within the conserving time-dependent Hartree-Fock (TDHF) approximation. The short-range exchange effects are taken into account by solving the Bethe-Salpeter integral equation numerically. An instability phase diagram is calculated for both single-layer and multilayer systems and the unstable wave vector is indicated. In all cases, the in-plane density wave instability is found to precede the out-of-plane instability. The unstable wave vector is found to be approximately twice the Fermi wave vector of one of the subbands at a time and can change discontinuously as a function of density and dipolar interaction strength. In multilayer configurations, we find a large enhancement of density-wave instability driven by dilute quasiparticles in the first excited subband. Finally, we provide a simple qualitative description of the phase diagrams using an RPA-like approach. Compared to previous works done within the RPA approximation, we find that inclusion of exchange interactions stabilize the normal liquid phase further and increase the critical dipolar interaction strength corresponding to the onset of density-wave instability by over a factor of two.

DOI: 10.1103/physrevb.84.235124

Related papers

Density wave instabilities of tilted fermionic dipoles in a multilayer geometry

Jens K. Block, Nikolaj Thomas Zinner, Georg M. Bruun

We consider the density wave instability of fermionic dipoles aligned by an external field and moving in equidistant layers at zero temperature. Using a conserving Hartree–Fock approximation, we show that correlations between dipoles in different layers significantly decrease the critical coupling strength for the formation of density waves when the distance between the layers is comparable to the inter-particle distance within each layer. This effect, which is strongest when the dipoles are oriented perpendicular to the planes, causes the density waves in neighboring layers to be in-phase for all orientations of the dipoles. We, furthermore, demonstrate that the effects of the interlayer interaction can be understood from a classical model. Finally, we show that the interlayer correlations are important for experimentally relevant dipolar molecules, including the chemically stable 23 Na 40 K and 40 K 133 Cs, where the density wave regime is within experimental reach.

arXiv:1204.1822•New Journal of Physics•Oct 3, 2012•28 citations

Density Instabilities in a Two-Dimensional Dipolar Fermi Gas

Meera M. Parish, Francesca Maria Marchetti

We study the density instabilities of a two-dimensional gas of dipolar fermions with aligned dipole moments. The random phase approximation (RPA) for the density-density response function is never accurate for the dipolar gas, and so we incorporate correlations beyond RPA via an improved version of the Singwi-Tosi-Land-Sjölander scheme. In addition to density-wave instabilities, our formalism captures the collapse instability that is expected from Hartree-Fock calculations but is absent from RPA. Crucially, we find that when the dipoles are perpendicular to the layer, the system spontaneously breaks rotational symmetry and forms a stripe phase, in defiance of conventional wisdom.

arXiv:1109.2464•Physical Review Letters•Apr 5, 2012•63 citations

Density-wave instability and collective modes in a bilayer system of antiparallel dipoles

E. Akaturk, Saeed H. Abedinpour, B. Tanatar

We consider a bilayer of dipolar particles in which the polarization of dipoles is perpendicular to the planes, in the antiparallel configuration. Using accurate static structure factor data from hypernetted-chain (HNC) and Fermi HNC calculations, respectively for an isolated layer of dipolar bosons and dipolar fermions, we construct effective screened intralayer interactions. Adopting the random-phase approximation for interlayer interactions, we investigate the instability of these homogeneous bilayer systems towards the formation of density waves by studying the poles of the density–density response function. We have also studied the collective modes of these systems and find that the dispersion of their antisymmetric collective mode signals the emergence of the density wave instability as well.

Journal of Physics Communications•Dec 7, 2017•9 citations

Dipolar fermions in a multilayer geometry

Michele Callegari, Meera M. Parish, Francesca Maria Marchetti

We investigate the behavior of identical dipolar fermions with aligned dipole moments in two-dimensional multilayers at zero temperature. We consider density instabilities that are driven by the attractive part of the dipolar interaction and, for the case of bilayers, we elucidate the properties of the stripe phase recently predicted to exist in this interaction regime. When the number of layers is increased, we find that this ``attractive'' stripe phase exists for an increasingly larger range of dipole angles, and if the interlayer distance is sufficiently small, the stripe phase eventually spans the full range of angles, including the situation where the dipole moments are aligned perpendicular to the planes. However, in this regime, we expect the behavior to be strongly modified by the binding of dipoles between layers. In the limit of an infinite number of layers, we derive an analytic expression for the mean-field interlayer effects in the density-density response function and, using this result, we find that the stripe phase is replaced by a collapse of the dipolar system.

arXiv:1601.06988•Physical review. B./Physical review. B•Feb 21, 2017•4 citations

Density-wave instability in a two-dimensional dipolar Fermi gas

Yasuhiro Yamaguchi, Takaaki Sogo, Toru Ito +1 more

We consider a uniform dipolar Fermi gas in two dimensions (2D) where the dipole moments of fermions are aligned by an orientable external field. We obtain the ground state of the gas in the Hartree-Fock approximation and investigate random-phase-approximation stability against density fluctuations of finite momentum. It is shown that the density-wave instability takes place in a broad region where the system is stable against collapse. We also find that the critical temperature can be a significant fraction of Fermi temperature for a realistic system of polar molecules.

arXiv:1003.2029•Physical Review A•Jul 29, 2010•81 citations

Liquid crystal phases of ultracold dipolar fermions on a lattice

Chungwei Lin, Erhai Zhao, W. Vincent Liu

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 $x\text{\ensuremath{-}}y$ plane) with dipoles pointing to the $z$ direction. We determine the phase diagram using two complementary methods, the Hartree-Fock mean-field theory and the linear-response analysis of compressibility. Both give consistent results. In addition to the staggered $(\ensuremath{\pi},\ensuremath{\pi})$ 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 fourfold $({C}_{4})$ 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.

arXiv:0909.5267•Physical Review B•Jan 13, 2010•39 citations

We study the in-plane and out-of-plane density ordering instabilities of quasi-two-dimensional fermionic polar molecules in single-layer and multilayer configurations. We locate the soft modes by evaluating linear response functions within the conserving time-dependent Hartree-Fock (TDHF) approximation. The short-range exchange effects are taken into account by solving the Bethe-Salpeter integral equation numerically. An instability phase diagram is calculated for both single-layer and multilayer systems and the unstable wave vector is indicated. In all cases, the in-plane density wave instability is found to precede the out-of-plane instability. The unstable wave vector is found to be approximately twice the Fermi wave vector of one of the subbands at a time and can change discontinuously as a function of density and dipolar interaction strength. In multilayer configurations, we find a large enhancement of density-wave instability driven by dilute quasiparticles in the first excited subband. Finally, we provide a simple qualitative description of the phase diagrams using an RPA-like approach. Compared to previous works done within the RPA approximation, we find that inclusion of exchange interactions stabilize the normal liquid phase further and increase the critical dipolar interaction strength corresponding to the onset of density-wave instability by over a factor of two.

We consider the density wave instability of fermionic dipoles aligned by an external field and moving in equidistant layers at zero temperature. Using a conserving Hartree–Fock approximation, we show that correlations between dipoles in different layers significantly decrease the critical coupling strength for the formation of density waves when the distance between the layers is comparable to the inter-particle distance within each layer. This effect, which is strongest when the dipoles are oriented perpendicular to the planes, causes the density waves in neighboring layers to be in-phase for all orientations of the dipoles. We, furthermore, demonstrate that the effects of the interlayer interaction can be understood from a classical model. Finally, we show that the interlayer correlations are important for experimentally relevant dipolar molecules, including the chemically stable 23 Na 40 K and 40 K 133 Cs, where the density wave regime is within experimental reach.

We study the density instabilities of a two-dimensional gas of dipolar fermions with aligned dipole moments. The random phase approximation (RPA) for the density-density response function is never accurate for the dipolar gas, and so we incorporate correlations beyond RPA via an improved version of the Singwi-Tosi-Land-Sjölander scheme. In addition to density-wave instabilities, our formalism captures the collapse instability that is expected from Hartree-Fock calculations but is absent from RPA. Crucially, we find that when the dipoles are perpendicular to the layer, the system spontaneously breaks rotational symmetry and forms a stripe phase, in defiance of conventional wisdom.

We consider a bilayer of dipolar particles in which the polarization of dipoles is perpendicular to the planes, in the antiparallel configuration. Using accurate static structure factor data from hypernetted-chain (HNC) and Fermi HNC calculations, respectively for an isolated layer of dipolar bosons and dipolar fermions, we construct effective screened intralayer interactions. Adopting the random-phase approximation for interlayer interactions, we investigate the instability of these homogeneous bilayer systems towards the formation of density waves by studying the poles of the density–density response function. We have also studied the collective modes of these systems and find that the dispersion of their antisymmetric collective mode signals the emergence of the density wave instability as well.

We investigate the behavior of identical dipolar fermions with aligned dipole moments in two-dimensional multilayers at zero temperature. We consider density instabilities that are driven by the attractive part of the dipolar interaction and, for the case of bilayers, we elucidate the properties of the stripe phase recently predicted to exist in this interaction regime. When the number of layers is increased, we find that this ``attractive'' stripe phase exists for an increasingly larger range of dipole angles, and if the interlayer distance is sufficiently small, the stripe phase eventually spans the full range of angles, including the situation where the dipole moments are aligned perpendicular to the planes. However, in this regime, we expect the behavior to be strongly modified by the binding of dipoles between layers. In the limit of an infinite number of layers, we derive an analytic expression for the mean-field interlayer effects in the density-density response function and, using this result, we find that the stripe phase is replaced by a collapse of the dipolar system.

We consider a uniform dipolar Fermi gas in two dimensions (2D) where the dipole moments of fermions are aligned by an orientable external field. We obtain the ground state of the gas in the Hartree-Fock approximation and investigate random-phase-approximation stability against density fluctuations of finite momentum. It is shown that the density-wave instability takes place in a broad region where the system is stable against collapse. We also find that the critical temperature can be a significant fraction of Fermi temperature for a realistic system of polar molecules.

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 $x\text{\ensuremath{-}}y$ plane) with dipoles pointing to the

z

direction. We determine the phase diagram using two complementary methods, the Hartree-Fock mean-field theory and the linear-response analysis of compressibility. Both give consistent results. In addition to the staggered $(\ensuremath{\pi},\ensuremath{\pi})$ 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 fourfold

({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.