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arXiv:0809.4972

Excitation Spectrum and Stability from a Filled Landau Level in Rotating Dipolar Fermi Gases

Szu-Cheng Cheng

Published Sep 29, 2008• 0 citations
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Abstract

We apply the equation-of-motion method to study the collective excitation spectrum from a filled Landau level in rotating dipolar Fermi gases. The predicted excitation spectrum of rotating dipolar Fermi gases can exhibit a roton-minimum character. This roton character is tunable by varying the dipole interaction strength and confining potential. An increase of the dipole interaction strength makes the roton minimum becoming zero, and the system becomes unstable. We also obtain a condition for the dynamical stability of rotating dipolar Fermi gases.

DOI
10.48550/arxiv.0809.4972

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We apply the equation-of-motion method to study the collective excitation spectrum from a filled Landau level in rotating dipolar Fermi gases. The predicted excitation spectrum of rotating dipolar Fermi gases can exhibit a roton-minimum character. This roton character is tunable by varying the dipole interaction strength and confining potential. An increase of the dipole interaction strength makes the roton minimum becoming zero, and the system becomes unstable. We also obtain a condition for the dynamical stability of rotating dipolar Fermi gases.
[[abstract]]The collective-excitation spectrum from a filled Landau level in a rotating dipolar Fermi gas is investigated through the equation of motion method. The predicted excitation spectrum exhibits a roton structure which is affected by the strength of dipolar interactions and trapping potential. The correlation effect on the roton minimum is observed by varying the dipolar interaction strength. An increase of the dipolar interaction strength leads to a deeper roton minimum. The roton minimum can even become zero, where the system exhibits instability, as the dipolar strength approaches a critical value. As the dynamical stability of the system is studied through the roton structure, we find that this zero-value roton minimum is a precursor of the occurrence of a bubble crystal.
We apply the magneto-roton theory of the fractional quantum Hall effect to study the collective excitation spectrum of rotating dipolar Fermi gases. The predicted spectrum has a finite energy gap in the long wavelength limit and a roton minimum at finite wave vector. The roton minimum being deepened from filling factor 1/3 to filling factor 1/5 is a signature of incipient crystallization near filling factor 1/7. We also demonstrate that there are no low-lying single-particle excitations below the roton mode. The fractional-quantum-Hall fluid rotating dipolar fermions behaves as an incompressible superfluid at low temperature.
We point out that the Wigner crystal (WC) state of rotating dipolar fermions in the lowest Landau level is strongly correlated. From intra-Landau-level excitations of the fractional quantum Hall effect (FQHE) liquid, we find that the roton minimum of the excitation spectrum at $\ensuremath{\nu}=1/7$ becomes negative, indicating an absence of the FQHE state, which is supposed to be the ground state of the system. Therefore, we show that the Hartree-Fock theory of the WC does not predict the correct ground-state energy in the lowest Landau level. There exists a strong correlation effect on the Wigner crystallization of rotating dipolar gases.
Using an ansatz wave function for the ground state of rotating two-dimensional dipolar fermions, which occupy only partially the lowest Landau level, we study the correlation energy and elastic properties of the Wigner crystal of rotating dipolar Fermi gases. From a simple Hartree-Fock approach, we show that the correlation energy of a particle crystal is lower and higher than the correlation energy of a hole crystal for filling factors v<1/2 and v>1/2, respectively. Furthermore we find that the shear moduli of these dipolar crystals have a nonmonotonic behavior as a function of the filling factor. We also examine the stability of a Wigner crystal. The Wigner crystal with the sample width being zero is locally stable for 0< v <1/2, while the corresponding hole crystal is locally stable for 1/2< v <1. Due to the WC being unstable around v=1/2, we also conclude that a new liquid state, not a quantum Hall state, can exist at v=1/2.
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.