We propose one possible mechanism for deconfinement based on an SU(2) slave-boson theory. Resorting to an effective field theory approach, we show that introduction of an isospin interaction potential gives rise to a fermion zero mode in an instanton-hedgehog configuration. As a result, meron-type vortices are allowed. We demonstrate how emergence of such vortices results in the doping-independent decreasing ratio of superfluid weight.
Whether it occurs in superconductors, helium-3 or inside a neutron star, fermionic superfluidity requires pairing of fermions, particles with half-integer spin. For an equal mixture of two states of fermions ("spin up" and "spin down"), pairing can be complete and the entire system will become superfluid. When the two populations of fermions are unequal, not every particle can find a partner. Will the system nevertheless stay superfluid? Here we study this intriguing question in an unequal mixture of strongly interacting ultracold fermionic atoms. The superfluid region vs population imbalance …
Fermionic superfluidity requires the formation of pairs. The actual size of these fermion pairs varies by orders of magnitude from the femtometer scale in neutron stars and nuclei to the micrometer range in conventional superconductors. Many properties of the superfluid depend on the pair size relative to the interparticle spacing. This is expressed in BCS-BEC crossover theories, describing the crossover from a Bardeen-Cooper-Schrieffer (BCS) type superfluid of loosely bound and large Cooper pairs to Bose-Einstein condensation (BEC) of tightly bound molecules. Such a crossover superfluid has b…
We examine antiferromagnetic and d-wave superfluid phases of cold fermionic atoms with repulsive interactions in a two-dimensional optical lattice combined with a harmonic trapping potential. For experimentally realistic parameters, the trapping potential leads to the coexistence of magnetic and superfluid ordered phases with the normal phase. We study the intriguing shell structures arising from the competition between the magnetic and superfluid order as a function of the filling fraction. In certain cases antiferromagnetism induce superfluidity by charge redistributions. We furthermore demo…
It is well known that bosons on an optical lattice undergo a second-order superfluid-insulator transition (SIT) when the lattice potential increases. In this paper we study SIT when fermions coexist with the bosons. We find that the critical properties of particle-hole symmetric SIT with dynamical exponent z=1 is modified when fermions are present; it either becomes a fluctuation-driven first order transition or a different second-order transition. On the other hand the more generic particle-hole asymmetric (with z=2) SIT is stable against coupling with fermions. We also discuss pairing intera…
The physical properties of arbitrary half-integer spins $F = N - 1/2$ fermionic cold atoms trapped in a one-dimensional optical lattice are investigated by means of a low-energy approach. Two different superfluid phases are found for $F \ge 3/2$ depending on whether a discrete symmetry is spontaneously broken or not: an unconfined BCS pairing phase and a confined molecular superfluid instability made of $2N$ fermions. We propose an experimental distinction between these phases for a gas trapped in an annular geometry. The confined-unconfined transition is shown to belong to the $Z_N$ generaliz…
Motivated by recent London penetration depth measurement [H. Kim et al. Phys. Rev. Lett. \textbf{114}, 027003 (2015)] and novel composite pairing scenario [O. Erten, R. Flint and P. Coleman, Phys. Rev. Lett. \textbf{114}, 027002 (2015)] on Yb-doped heavy fermion superconductor CeCoIn$_{5}$, we revisit the issue of superfluid response in microscopic heavy fermion lattice model. However, it is found that in literature explicit expression of superfluid response function in heavy fermion superconductor is rare. In this paper, we make a contribution to this issue by investigating superfluid density…
We calculate the effect of order parameter fluctuations on the fermionic single-particle excitations in the superfluid state of neutral fermions interacting with short range attractive forces. We show that in dimensions D \leq 3 the singular effective interaction between the fermions mediated by the gapless Bogoliubov-Anderson mode prohibits the existence of well-defined quasi-particles. We explicitly calculate the single-particle spectral function in the BEC regime in D=3 and show that in this case the quasi-particle residue and the density of states are logarithmically suppressed.
We present real-space dynamical mean-field theory calculations for attractively interacting fermions in three-dimensional lattices with elongated traps. The critical polarization is found to be 0.8, regardless of the trap elongation. Below the critical polarization, we find unconventional superfluid structures where the polarized superfluid and Fulde-Ferrell-Larkin-Ovchinnikov-type states emerge across the entire core region.
We compute the orbital angular momentum $L_z$ of an s-wave paired superfluid in the presence of an axisymmetric multiply quantized vortex. For vortices with winding number $|k| > 1$, we find that in the weak-pairing BCS regime $L_z$ is significantly reduced from its value $\hbar N k/2$ in the Bose-Einstein condensation (BEC) regime, where $N$ is the total number of fermions. This deviation results from the presence of unpaired fermions in the BCS ground state, which arise as a consequence of spectral flow along the vortex sub-gap states. We support our results analytically and numerically by s…
Motivated by recent experimental progress in the field of dipolar-Fermi gases, we investigate the quantum phases of dipolar fermions, on a triangular ladder at half filling. Using density matrix renormalization group method, in presence of onsite repulsion and intersite attractive interaction, we find exotic spin-triplet superfluid phase in addition to the usual spin-density and charge-density waves. We examine the stability of spin-triplet superfluid phase by varying hopping along the rungs of the triangle. Possibility of fermionic supersolidity has also been discussed, by considering three- …
We study a simple model of N-component fermions with contact interactions which describes fermionic atoms with N=2F+1 hyperfine states loaded into a one-dimensional optical lattice. We show by means of analytical and numerical approaches that, for attractive interaction, a quasi-long-range molecular superfluid phase emerges at low density. In such a phase, the pairing instability is strongly suppressed and the leading instability is formed from bound-states made of N fermions. At small density, the molecular superfluid phase is generic and exists for a wide range of attractive contact interact…
We analyze the finite-temperature phase diagram of the boson-fermion-Hubbard model with Feshbach converting interaction, using the coherent-state path-integral method. We show that depending on the position of the bosonic band, this type of interaction, even if weak, can drive the system into the resonant superfluid phase in the strong bosonic interaction limit. It turns out that this phase can exist for an arbitrary number of fermions (i.e., fermionic concentration between 0 and 2) but with the bosonic particle number very close to an integer value. We point out that the standard time-of-flig…
In this chapter the recent theoretical work on phase transition in imbalanced fermion superfluids is reviewed. The imbalanced systems are those in which the two fermionic species candidate to form pairing have different Fermi surfaces or densities. We consider systems subjected to weak interactions. In this scenario two distinct phase transitions are predicted to occur. A thermodynamical phase transition, induced by the temperature (T), and a quantum phase transition as a function of the increasing chemical potentials asymmetry, that takes place at zero temperature. We also briefly discuss som…
Superfluid 3He-B belongs to the important special class of time-reversal invariant topological superfluids. It has Majorana fermions as edge states on the surface of bulk 3He-B. On the rough wall these fermion zero modes have finite density of states at E=0. It is possible that Lancaster experiments with a wire vibrating in 3He-B have already probed Majorana fermions living on the surface of the wire.
The few-fermion atomic gas is an ideal setting to explore inhomogeneous superfluid pairing analogous to the Larkin-Ovchinnikov state. Two up and one down-spin atom is the minimal configuration that displays an inhomogeneous pairing density whereas imbalanced systems containing more fermions present a more complex pairing topology. With more than eight atoms trapped the system approaches the macroscopic superfluid limit. An oblate trap with a central barrier offers a direct experimental probe of pairing inhomogeneity.
We derive the energy of the surface between the normal and superfluid components of a mixed phase of a system composed of two particle species with different densities. The surface energy is obtained by the integration of the free energy density in the interface between the two phases. We show that the mixed phase remains as the favored ground state over the gapless phase in weak coupling. We find that the surface energy effects emerge only at strong coupling.
The experimentally observed loss of superfluidity by introducing fermions to the boson Hubbard system on an optical lattice is explained. We show that the virtual transitions of the bosons to the higher Bloch bands, coupled with the contact boson-fermion interactions of either sign, result in an effective increase of the boson on-site repulsion. If this renormalization of the on-site potential is dominant over the fermion screening of the boson interactions, the Mott insulating lobes of the Bose-Hubbard phase diagram will be enhanced for either sign of the boson-fermion interactions. We discus…
We study the two-dimensional Bose-Fermi mixture on square lattice at finite temperature by using the determinant quantum Monte Carlo method within the weakly interacting regime. Here we consider the attractive Bose-Hubbard model and free spinless fermions. In the absence of bosonfermion interactions, we obtain the boundary of the collapsed state of the attractive bosons. In the presence of boson-fermion interactions, an effective p-wave interaction between fermions will be induced as far as the bosons are in a superfluid state. Moreover, we find the emergence of the composite fermion pairs at …
We analyze the effects of order parameter fluctuations on the ground state of fully gapped charge-neutral fermionic superfluids. The Goldstone mode associated with the spontaneously broken symmetry leads to a problem of coupled singularities in $d \leq 3$ dimensions. We derive a minimal set of one-loop renormalization group equations which fully captures the interplay of the singularities. The flow equations are based on a symmetry conserving truncation of a scale dependent effective action. We compute the low energy behavior of longitudinal, transverse and mixed order parameter correlations, …
We present a comprehensive analysis of quantum fluctuation effects in the superfluid ground state of an attractively interacting Fermi system, employing the attractive Hubbard model as a prototype. The superfluid order parameter, and fluctuations thereof, are implemented by a bosonic Hubbard-Stratonovich field, which splits into two components corresponding to longitudinal and transverse (Goldstone) fluctuations. Physical properties of the system are computed from a set of approximate flow equations obtained by truncating the exact functional renormalization group flow of the coupled fermion-b…
