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arXiv:1111.7114 · Physical Review A

Fermi liquid of two-dimensional polar molecules

Zhen-Kai Lu, Gora V. Shlyapnikov

Published Feb 13, 2012• 39 citations
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Abstract

We study Fermi-liquid properties of a weakly interacting two-dimensional gas of single-component fermionic polar molecules with dipole moments $d$ oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean-field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as $1/{r}^{3}$ at large distances $r$, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter ${k}_{F}{r}_{*}$, where ${k}_{F}$ is the Fermi momentum and ${r}_{*}=m{d}^{2}/{\ensuremath{\hbar}}^{2}$ is the dipole-dipole length, with $m$ being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in ${k}_{F}{r}_{*}$ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, as it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.

DOI
10.1103/physreva.85.023614

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We study Fermi-liquid properties of a weakly interacting two-dimensional gas of single-component fermionic polar molecules with dipole moments ddd oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean-field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r31/{r}^{3}1/r3 at large distances rrr, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter kFr∗{k}_{F}{r}_{*}kF​r∗​, where kF{k}_{F}kF​ is the Fermi momentum and r∗=md2/\ensuremathℏ2{r}_{*}=m{d}^{2}/{\ensuremath{\hbar}}^{2}r∗​=md2/\ensuremathℏ2 is the dipole-dipole length, with mmm being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in kFr∗{k}_{F}{r}_{*}kF​r∗​ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, as it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.
We study Fermi liquid properties of a weakly interacting 2D gas of single-component fermionic polar molecules with dipole moments ddd oriented perpendicularly to the plane of their translational motion. This geometry allows the minimization of inelastic losses due to chemical reactions for reactive molecules and, at the same time, provides a possibility of a clear description of many-body (beyond mean field) effects. The long-range character of the dipole-dipole repulsive interaction between the molecules, which scales as 1/r31/r^31/r3 at large distances rrr, makes the problem drastically different from the well-known problem of the two-species Fermi gas with repulsive contact interspecies interaction. We solve the low-energy scattering problem and develop a many-body perturbation theory beyond the mean field. The theory relies on the presence of a small parameter kFr∗k_Fr_*kF​r∗​, where kFk_FkF​ is the Fermi momentum, and r∗=md2/ℏ2r_*=md^2/\hbar^2r∗​=md2/ℏ2 is the dipole-dipole length, with mmm being the molecule mass. We obtain thermodynamic quantities as a series of expansion up to the second order in kFr∗k_Fr_*kF​r∗​ and argue that many-body corrections to the ground-state energy can be identified in experiments with ultracold molecules, like it has been recently done for ultracold fermionic atoms. Moreover, we show that only many-body effects provide the existence of zero sound and calculate the sound velocity.
We study zero sound in a weakly interacting two-dimensional (2D) gas of single-component fermionic dipoles (polar molecules or atoms with a large magnetic moment) tilted with respect to the plane of their translational motion. It is shown that the propagation of zero sound is provided by both mean-field and many-body (beyond mean field) effects, and the anisotropy of the sound velocity is the same as the one of the Fermi velocity. The damping of zero sound modes can be much slower than that of quasiparticle excitations of the same energy. One thus has wide possibilities for the observation of zero sound modes in experiments with 2D fermionic dipoles, although the zero sound peak in the structure function is very close to the particle-hole continuum.
We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the ${d}_{{r}^{2}\ensuremath{-}3{z}^{2}}$ type in three dimensions and of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tridiagonal Landau interaction matrices in the dipolar Fermi liquids which renormalize thermodynamic susceptibilities. With large dipolar interaction strength, the Fermi surface collapses along directions perpendicular to the dipole orientation. The dynamic collective zero sound modes exhibit an anisotropic dispersion with the largest sound velocity propagating along the polar directions. Similarly, the longitudinal ppp-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multicomponent dipolar systems.
We study the Fermi liquid properties of a single component Fermi gas with p-wave interactions. In the weak repulsive limit, we obtain exact perturbative expansions for the ground state energy, the chemical potential, and the effective mass of the Landau quasiparticle up to second order in scattering volume a. We also calculated the corresponding Landau functions and Landau parameters and show that they satisfy the general Fermi liquid identities. Using the Landau transport equation, we show that undamped zero sound only appears in the second order in scattering volume, in contrast to the s-wave case.
We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive 1/r31/{r}^{3}1/r3 potential. This model can be realized with ultracold atoms or molecules when their dipole moments are aligned in the confinement direction orthogonal to the plane. We characterize the unpolarized mixture by means of the diffusion Monte Carlo technique. Computing the equation of state, we identify the regime of validity for a mean-field theory based on a low-density expansion and compare our results with the hard-disk model of repulsive fermions. At high density, we address the possibility of itinerant ferromagnetism, namely, whether the ground state can be fully polarized in the fluid phase. Within the fixed-node approximation, we show that the accuracy of Jastrow-Slater trial wave functions, even with the typical two-body backflow correction, is not sufficient to resolve the relevant energy differences. By making use of the iterative-backflow improved trial wave functions, we observe no signature of a fully polarized ground state up to the freezing density.
We consider a weakly interacting two-component Fermi gas of dipolar particles (magnetic atoms or polar molecules) in two-dimensional geometry. The dipole-dipole interaction (together with the short-range interaction at Feshbach resonances) for dipoles perpendicular to the plane of translational motion may provide a superfluid transition. The dipole-dipole scattering amplitude is momentum dependent, which violates the Anderson theorem that claims the independence of the transition temperature on the presence of weak disorder. We have shown that the disorder can strongly increase the critical temperature (up to 10nK10\phantom{\rule{0.16em}{0ex}}\mathrm{nK}10nK at realistic densities). This opens wide possibilities for the studies of the superfluid regime in weakly interacting Fermi gases, which has not been observed so far.