Exact pairing correlations for one-dimensionally trapped fermions with stochastic mean-field wave functions

The canonical thermodynamic properties of a one-dimensional system of interacting spin-1/2 fermions with an attractive zero-range pseudopotential are investigated within an exact approach. The density operator is evaluated as the statistical average of dyadics formed from a stochastic mean-field propagation of independent Slater determinants. For a harmonically trapped Fermi gas and for fermions confined in a 1D-like torus, we observe the transition to a quasi-BCS state with Cooper-like momentum correlations and an algebraic long-range order. For a few trapped fermions in a rotating torus, a dominant superfluid component with quantized circulation can be isolated.     

BCS theory for trapped ultracold fermions

We develop an extension of the well-known BCS-theory to systems with trapped fermionic atoms. The theory fully includes the quantized energy levels in the trap. The key ingredient is to model the attractive interaction between two atoms by a pseudo-potential which leads to a well defined scattering problem and consequently to a BCS-theory free of divergences. We present numerical results for the BCS critical temperature and the temperature dependence of the gap. They are used as a test of existing semi-classical approximations. Received 18 December 1998     

Thermodynamics of trapped fermions in gravitational field

Trapped non-interacting Fermi gas in an external gravitational field in Newtonian approximation is considered. Analytical equations for the internal energy, the number of particles are computed. The analytical expression for the specific heat of trapped Fermi gas in non-homogeneous gravitational field is found.     

Qualitative analysis of trapped Dirac fermions in graphene

We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.     

Effective field theory for dilute fermions with pairing

Effective field theory (EFT) methods for a uniform system of fermions with short-range, natural interactions are extended to include pairing correlations, as part of a program to develop a systematic Kohn-Sham density functional theory (DFT) for medium and heavy nuclei. An effective action formalism for local composite operators leads to a free-energy functional that includes pairing by applying an inversion method order by order in the EFT expansion. A consistent renormalization scheme is demonstrated for the uniform system through next-to-leading order, which includes induced-interaction corrections to pairing.     

Inter-layer pairing of two-dimensional electrons

We point out the possibility that the high transition temperatures of the recently discovered oxide superconductors are dominantly caused by the inter-layer Cooper pairing of two-dimensional electrons that are coupled through the exchange of three-dimensional phonons.     

Shell structure and pairing for interacting fermions in a trap

The shell structures for weakly interacting fermions in harmonic oscillator traps at zero temperature undergo several transitions depending on the number of particles in the trap and their interaction strength. Calculations of the one and two-particle spectra give the pairing gaps, and the many particle state is constructed by the seniority scheme. For sufficiently few particles, N less than or similar to 10(4), the pairing field exceeds the mean-field splitting of single particle levels at the Fermi surface and the greater number of almost degenerate states due to the SU(3) symmetry in the harmonic oscillator shell lead to supergaps. Deformation and rotation are also discussed.     

Wilson fermions in a two-dimensional model

Wilson's action for fermions on a lattice is compared to the continuum action in a model obtained from the chiral Gross-Neveu model by performing a chiral transformation. The local definition of the axial current leads to two anomalies unrelated by the constraint of Lorentz invariance. In the large-N limit, the mass counterterm of the action is determined; this term is unnecessary in the Osterwalder-Seiler regularization. An expansion in the fermion propagator and in the axial current coupling may be formulated and summed to all orders for large N.     

Bond order solid of two-dimensional dipolar fermions

The recent experimental realization of dipolar Fermi gases near or below quantum degeneracy provides an opportunity to engineer Hubbard-like models with long-range interactions. Motivated by these experiments, we chart out the theoretical phase diagram of interacting dipolar fermions on the square lattice at zero temperature and half filling. We show that, in addition to p-wave superfluid and charge density wave order, two new and exotic types of bond order emerge generically in dipolar fermion systems. These phases feature homogeneous density but periodic modulations of the kinetic hopping energy between nearest or next-nearest neighbors. Similar, but manifestly different, phases of two-dimensional correlated electrons have previously only been hypothesized and termed "density waves of nonzero angular momentum." Our results suggest that these phases can be constructed flexibly with dipolar fermions, using currently available experimental techniques.     

Path integral bosonization of massive two-dimensional fermions

The bosonization of the Pauli-Villars regularized functional integral for massive fermions is discussed. Thereby the role of the mass dependence in the functional jacobian for finite chiral rotations of the fermionic integration variables is clarified.     

Magnetism, spin-orbit coupling, and superconducting pairing in UGe2

A consistent picture on the mean-field level of the magnetic properties and electronic structure of the superconducting itinerant ferromagnet UGe2 requires inclusion of correlation effects beyond the local density approximation (LDA). The " LDA+U" approach reproduces both the magnitude of the observed moment and the magnetocrystalline anisotropy. The largest Fermi surface sheet is composed primarily of spin majority states with orbital projection m(l) = 0, suggesting a much simpler picture of the pairing than is possible for general strong spin-orbit coupled materials. The quasi-two-dimensional geometry of the Fermi surface supports the likelihood of magnetically mediated p-wave triplet pairing.     

The mass effects on two-dimensional relativistic fermions

We investigate chemical potential, internal energy and specific heat of ideal relativistic fermions in two spatial dimensions taking into account the finite mass effect and the finite carrier concentration. The results show that the heavy mass and low carrier concentration fermions trend to be non-relativistic. The light mass and high carrier concentration lead more relativistic behavior. For massless fermions, the total kinetic energy equals to a constant for a given density (n), which is a function of n^3/2. Meanwhile, the specific heat for massless fermions keeps the linear increasing behavior with temperature with constant slope rather than the slope of zero, which is deduced from the non-relativistic case.     

Suppression of superfluidity upon overflow of trapped fermions: quantal and Thomas-Fermi studies

Two issues are treated in this work. (i) The generic fact that, if a fermionic superfluid in the BCS regime overflows from a narrow container into a much wider one, pairing is much suppressed at the overflow point. Physical examples where this feature may play an important role are discussed. (ii) A Thomas-Fermi approach to inhomogeneous superfluid Fermi systems is presented and shown to work well in cases where the local density approximation breaks down.     

Dynamics of Dirac and Weyl fermions on a two-dimensional surface

The determinants of Dirac and Weyl fermions coupled to the extrinsic geometry of a two-dimensional surface embedded in a 3D euclidean space are calculated exactly. The effective action produced by chiral fermions contains a Wess-Zumino term with the structure of the Hopf topological invariant of a map S³→S².