A finite-temperature (
T>0) study of a model of a mixture of spin-zero hardcore bosons and spinless fermions, with filling fractions
ρB and
ρF, respectively, on a two-dimensional square lattice with composite hopping
t is presented. The composite hopping swaps the locations of a fermion and a boson that occupy nearest-neighbor sites of the lattice. The superfluid order parameter
ψ, the femion hopping amplitude
ϕ, the chemical potential
μ, the free energy minimum
F~ and entropy
S are calculated in the limit
ρB+ρF=1 within a mean-field approximation, and lead to a phase diagram in the
ρF−T plane. This phase diagram consists of a metallic superfluid phase under a dome-shaped
T(ρF), and insulating normal liquid and insulating normal gas phases outside the dome. These phases are separated by coupled discontinuous transitions as indicated by jumps in
ψ and
ϕ. The maximum critical transition temperature
Tc is observed very close to
ρF=1/2. While
F~(T) is continuous with a derivative discontinuity at
T=Tc(ρF) for
01/2 (zeroth-order transition), where the entropy becomes negative for a range of temperatures below
Tc. The ratio of
Tc to Fermi band width agrees remarkably with the ratio of
Tc/
TF (where
TF is the Fermi temperature) of unconventional superfluids and superconductors like Fermi-Bose mixtures, the high-
Tc cuprates, iron-based and hydride superconductors, that exhibit experimental values of
Tc spread over nine orders of magnitude from
∼200nK to
∼260K.
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 interaction between fermions mediated by quantum critical fluctuations near SIT and show that the fermion pairing and/or superfluid transition temperature peaks near SIT when a single species of fermion is present.
We examine a two-dimensional mixture of single-component fermions and dipolar bosons. We calculate the self-enregies of the fermions in the normal state and the Cooper-pair channel by including first-order vertex correction to derive a modified Eliashberg equation. We predict the appearance of superfluids with various nonstandard pairing symmetries at experimentally feasible transition temperatures within the strong-coupling limit of the Eliashberg equation. Excitations in these superfluids are anyonic and follow non-Abelian statistics.
We examine the effect of boson-fermion interaction in a one-dimensional Bose-Fermi mixture by using the density matrix renormalization group method. We show that the boson superfluidity is enhanced by fermions for a weak boson-fermion coupling at an approximate integer boson filling factor (e.g.,
0.935≤ρb≤1.0), and this enhancement is produced both in a fermion metallic state and in a fermion insulating state. A metal-insulator phase transition of fermions induced by boson-fermion interaction is observed even though there is no fermion-fermion interaction in the parent Hamiltonian. Furthermore, we find that the boson superfluid order and density wave order can coexist in a deep fermion Mott region. All these features could be measured in future experiments and open up the possibility of detecting the new physical effect in the Bose-Fermi mixture.
Pairing between fermions that attract each other, reveal itself to the macroscopic world in the form of superfluidity. Since the discovery of fermionic superfluidity, intense search has been going on to find various unconventional forms of fermion pairing as well as to increase the transition temperature. Here, we show that a two dimensional mixture of single-component fermions and dipolar bosons allows to reach experimentally feasible superfluid transition temperatures for non-standard pairing symmetries. Excitations in these superfluids are anyonic and their statistics depends on the order of their permutations, i.e is non-Abelian. Our results provide for the first time an example of a highly tunable system which exhibits various kind of pairing symmetry and high transition temperature. Additionally, they provide a playground to observe anyonic excitations and their braiding properties.
Confinement of atoms by laser technology has opened up a new field of physics. Following the realization of Bose– Einstein condensation (BEC) of bosonic atoms, fermionic atom systems and even boson–fermion mixture systems were successfully trapped and cooled. Application of a periodic potential, so called optical lattice, could also unveil interesting nature of the atoms. One of the interesting phenomena of the atoms on optical lattice is Mott transition. Although there is a long history of the study on bosons or fermions on lattice, coexistence of bosons and fermions on lattice is a rather new topic to study. In particular, we have little knowledge about strongly-correlated bosons and fermions on lattice. In our previous works we performed numerical simulations of Bose–Fermi mixtures to clarify the phase diagram and the effect of the confinement potential. When the total number of bosonic and fermionic atoms per site takes an integer value and interatomic interactions are sufficiently strong, the system would undergo Mott transition where the local atom density is fixed to the integer value. A characteristic of this Mott insulating phase is that a boson and fermion located next to each other can exchange their positions by going through a virtual doubly-occupied state with the atom exchange energy t ’ tbtf=Ubf where tb and tf are the hopping energy of the bosons and fermions respectively and Ubf denotes the on-site interaction between the boson and the fermion. Although there still remain a number of open questions on the Mott state of Bose–Fermi mixtures, the property of superfluid state of the strongly-correlated bosons and fermions has yet to be revealed. In this short note we would like to focus on strongly-correlated Bose–Fermi mixtures at commensurate filling in a three-dimensional periodical potential and see characteristic behaviors, if any, of the superfluid phase close to the phase boundary to the Mott insulating phase. In the following analysis we assume uniformity of the system and thus neglect the possibility of the emergence of so-called supersolid where superfluidity and structural long-range order coexist. For simplicity we ignore all the internal degree of freedom of the atoms and the influence of the trap potential which in fact creates a nonuniform density profile of the bosons and fermions. For the system at commensurate filling on optical lattice, we assume that the interatomic interactions are weak enough to avoid formation of Mott state but strong enough to allow us to expect that there are only few empty or doublyoccupied sites and most sites are singly occupied. Namely we analyze the system that stays in a superfluid phase but lies close to the boundary to the Mott phase. Since a boson and fermion located next to each other can exchange their positions as stated above, the energy of the superfluid state of the mixture system is given mostly by the kinetic energy of the bosons and fermions exchanging their positions. We therefore express the Hamiltonian in the following form, ignoring the kinetic energy of the atoms at the empty sites and the interaction energy at the doubly-occupied sites: