Thomas-Fermi von Weizsäcker theory for a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas

Abstract

We systematically develop a density functional description for the equilibrium properties of a two-dimensional, harmonically trapped, spin-polarized dipolar Fermi gas based on the Thomas-Fermi von Weizsäcker approximation. We pay particular attention to the construction of the two-dimensional kinetic energy functional, where corrections beyond the local density approximation must be motivated with care. We also present an intuitive derivation of the interaction energy functional associated with the dipolar interactions, and provide physical insight into why it can be represented as a local functional. Finally, a simple, and highly efficient self-consistent numerical procedure is developed to determine the equilibrium density of the system for a range of dipole interaction strengths.

6 figures. Accepted for publication in Phys. Rev. A. In production

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• A nonlocal kinetic energy functional for an inhomogeneous two-dimensional Fermi gas
• First-principles quantum corrections for carrier correlations in double-layer two-dimensional heterostructures
• Kohn-Sham theory of rotating dipolar Fermi gas in two dimensions
• Physical dipoles and second order perturbation theory for dipolar fermions in two dimensions
• Collective excitations of a harmonically trapped, two-dimensional, spin-polarized dipolar Fermi gas in the hydrodynamic regime
• Kohn-Sham approach to Fermi gas superfluidity: the bilayer of fermionic polar molecules
• A manifestly Hermitian semiclassical expansion for the one-particle density matrix of a two-dimensional Fermi gas
• Orbital-free approach for large-scale electrostatic simulations of quantum nanoelectronics devices
• Testing the nonlocal kinetic energy functional of an inhomogeneous, two-dimensional degenerate Fermi gas within the average density approximation
• Phase Transitions of Repulsive Two-Component Fermi Gases in Two Dimensions
• Ordered phases in a bilayer system of dipolar fermions