Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2101.08513

Unconventional Superfluidity in a model of Fermi-Bose Mixtures

K. Sheshadri, A. Chainani

Published Jan 21, 2021• 0 citations
arXivHTMLPDF

Abstract

A finite-temperature ($T>0$) study of a model of a mixture of spin-zero hardcore bosons and spinless fermions, with filling fractions $ρ_B$ and $ρ_F$, 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 $\tilde{F}$ and entropy $S$ are calculated in the limit $ρ_B+ρ_F=1$ within a mean-field approximation, and lead to a phase diagram in the $ρ_F - T$ plane. This phase diagram consists of a metallic superfluid phase under a dome-shaped $T(ρ_F)$, 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 $T_c$ is observed very close to $ρ_F = 1/2$. While $\tilde{F} (T)$ is continuous with a derivative discontinuity at $T=T_c (ρ_F)$ for $0 1/2$ (zeroth-order transition), where the entropy becomes negative for a range of temperatures below $T_c$. The ratio of $T_c$ to Fermi band width agrees remarkably with the ratio of $T_c$/$T_F$ (where $T_F$ is the Fermi temperature) of unconventional superfluids and superconductors like Fermi-Bose mixtures, the high-$T_c$ cuprates, iron-based and hydride superconductors, that exhibit experimental values of $T_c$ spread over nine orders of magnitude from $\sim 200$nK to $\sim 260$K.

DOI
10.48550/arxiv.2101.08513

Related papers

Coupled first-order transitions and unconventional superfluidity in a Fermi-Bose mixture

K. Sheshadri, A. Chainani

This study proposes a lattice model of a Fermi-Bose mixture with a composite hopping mechanism which swaps a boson and a fermion on nearest neighbor sites. The composite hopping causes unconventional superfluidity with coupled first-order insulator-metal and normal-superfluid transitions as a function of Fermion fraction

arXiv:1912.00132•Physical Review Research•Jun 5, 2020•1 citation

Mean-field phase diagram of the Bose-Fermi Hubbard model

Marin Bukov, Lode Pollet

We analyze the ground-state properties of mixtures consisting of scalar bosons and spin-$\frac{1}{2}$ fermions using a mean-field treatment of the local boson-fermion interaction on a simple cubic lattice. In the deep superfluid limit of the boson sector and the BCS regime of the fermion sector, we derive BCS-type equations to determine the phase diagram of the system. We find a competition between a charge density wave and a superconducting phase. In the opposite limit, we study the Mott-insulator-to-superfluid transition of the boson sector in the presence of a staggered density-induced alternating potential provided by the fermions, and determine the mean-field transition line. In the two-superfluids phase of the mixture, we restrict to nearest-neighbor-induced interactions between the fermions and consider the extended Hubbard model. We perform a mean-field analysis of the critical temperature for the formation of boson-assisted $s$-, extended ${s}^{\ensuremath{-}}$-, $d$-, and $p$-wave pairs at fermionic half-filling. We compare our results with a recent dynamical mean-field study [P. Anders et al., Phys. Rev. Lett. 109, 206401 (2012)].

arXiv:1311.7148•Physical Review B•Mar 4, 2014•28 citations

Superfluid State of Strongly-Correlated Bose–Fermi Mixtures on Optical Lattices at Commensurate Filling

Sota Tsukada, Akiko Masaki, 弘之 森

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:

Journal of the Physical Society of Japan•Feb 10, 2009•0 citations

Engineering superfluidity in Bose-Fermi mixtures of ultracold atoms

Daw-Wei Wang, Mikhail D. Lukin, Eugene Demler

We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with $s$-, $p$-, and $d$-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.

arXiv:cond-mat/0410494•Physical Review A•Nov 17, 2005•60 citations

Mixture of scalar bosons and two-color fermions in one dimension: Superfluid-insulator transitions

Richard Giovanni Avella, Juan José Mendoza-Arenas, R. Franco +1 more

Superfluid-insulator transitions in a one-dimensional mixture of two-color fermions and scalar bosons are studied within the framework of the Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for repulsive intraspecies interactions and attractive or repulsive interspecies couplings. In addition to the trivial Mott insulator phases, we report the emergence of nontrivial insulator phases that depend on the sign of the boson-fermion interaction. These nontrivial insulator phases satisfy the conditions ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\rho}}_{F}=n$ and ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}\frac{1}{2}{\ensuremath{\rho}}_{F}=n$, with the plus (minus) sign for repulsive (attractive) interactions and $n$ an integer. Far from fermionic half filling, the boson-fermion interaction drives a gapless-gapped transition in the spin sector. Our findings could be observed experimentally in state-of-the-art cold-atom setups.

arXiv:2003.09421•Physical Review A•Sep 30, 2020•8 citations

Supersolidity of cold-atom Bose-Fermi mixtures in optical lattices

Peter P. Orth, Doron L. Bergman, Karyn Le Hur

We investigate a cold-atom mixture of spinless bosons and fermions in two-dimensional optical lattices. In the presence of a nested Fermi surface, the bosons may develop a fascinating supersolid behavior characterized by a finite superfluid density as well as a spatial density wave order. Focusing on the triangular lattice geometry and combining a general Landau-Ginzburg-Wilson approach with microscopically derived mean-field theory, we find an exotic supersolid phase at a fermionic band filling of ${n}_{f}=3∕4$ with a kagome-type crystalline order. We also address the case of anisotropic hopping amplitudes and show that striped supersolid phases emerge on the square and triangular lattices. For weak interactions, the supersolid competes with phase separation. For strong intraspecies and interspecies interactions, with the total number of fermions and bosons corresponding to one particle per site, the bosons form an alternating Mott insulator ground state. Finally, for a mixture of $^{87}\mathrm{Rb}^{40}\mathrm{K}$ and $^{23}\mathrm{Na}^{6}\mathrm{Li}$, we show that supersolidity can be observed in the range of accessible temperatures in the square lattice geometry.

arXiv:0905.1125•Physical Review A•Aug 28, 2009•36 citations
A finite-temperature (T>0T>0T>0) study of a model of a mixture of spin-zero hardcore bosons and spinless fermions, with filling fractions ρBρ_BρB​ and ρFρ_FρF​, respectively, on a two-dimensional square lattice with composite hopping ttt 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 ψψψ, the femion hopping amplitude ϕϕϕ, the chemical potential μμμ, the free energy minimum F~\tilde{F}F~ and entropy SSS are calculated in the limit ρB+ρF=1ρ_B+ρ_F=1ρB​+ρF​=1 within a mean-field approximation, and lead to a phase diagram in the ρF−Tρ_F - TρF​−T plane. This phase diagram consists of a metallic superfluid phase under a dome-shaped T(ρF)T(ρ_F)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 ψψψ and ϕϕϕ. The maximum critical transition temperature TcT_cTc​ is observed very close to ρF=1/2ρ_F = 1/2ρF​=1/2. While F~(T)\tilde{F} (T)F~(T) is continuous with a derivative discontinuity at T=Tc(ρF)T=T_c (ρ_F)T=Tc​(ρF​) for 01/20 1/201/2 (zeroth-order transition), where the entropy becomes negative for a range of temperatures below TcT_cTc​. The ratio of TcT_cTc​ to Fermi band width agrees remarkably with the ratio of TcT_cTc​/TFT_FTF​ (where TFT_FTF​ is the Fermi temperature) of unconventional superfluids and superconductors like Fermi-Bose mixtures, the high-TcT_cTc​ cuprates, iron-based and hydride superconductors, that exhibit experimental values of TcT_cTc​ spread over nine orders of magnitude from ∼200\sim 200∼200nK to ∼260\sim 260∼260K.
We analyze the ground-state properties of mixtures consisting of scalar bosons and spin-12\frac{1}{2}21​ fermions using a mean-field treatment of the local boson-fermion interaction on a simple cubic lattice. In the deep superfluid limit of the boson sector and the BCS regime of the fermion sector, we derive BCS-type equations to determine the phase diagram of the system. We find a competition between a charge density wave and a superconducting phase. In the opposite limit, we study the Mott-insulator-to-superfluid transition of the boson sector in the presence of a staggered density-induced alternating potential provided by the fermions, and determine the mean-field transition line. In the two-superfluids phase of the mixture, we restrict to nearest-neighbor-induced interactions between the fermions and consider the extended Hubbard model. We perform a mean-field analysis of the critical temperature for the formation of boson-assisted sss-, extended ${s}^{\ensuremath{-}}$-, ddd-, and ppp-wave pairs at fermionic half-filling. We compare our results with a recent dynamical mean-field study [P. Anders et al., Phys. Rev. Lett. 109, 206401 (2012)].
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:
We investigate many-body phase diagrams of atomic boson-fermion mixtures loaded in the two-dimensional optical lattice. Bosons mediate an attractive, finite-range interaction between fermions, leading to fermion pairing phases of different orbital symmetries. Specifically, we show that by properly tuning atomic and lattice parameters it is possible to create superfluids with sss-, ppp-, and ddd-wave pairing symmetry as well as spin and charge density wave phases. These phases and their stability are analyzed within the mean-field approximation for systems of $^{40}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ and $^{40}\mathrm{K}\text{\ensuremath{-}}^{23}\mathrm{Na}$ mixtures. For the experimentally accessible regime of parameters, superfluids with unconventional fermion pairing have transition temperature around a percent of the Fermi energy.
Superfluid-insulator transitions in a one-dimensional mixture of two-color fermions and scalar bosons are studied within the framework of the Bose-Fermi-Hubbard model. Zero-temperature phase diagrams are constructed for repulsive intraspecies interactions and attractive or repulsive interspecies couplings. In addition to the trivial Mott insulator phases, we report the emergence of nontrivial insulator phases that depend on the sign of the boson-fermion interaction. These nontrivial insulator phases satisfy the conditions ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}{\ensuremath{\rho}}_{F}=n$ and ${\ensuremath{\rho}}_{B}\ifmmode\pm\else\textpm\fi{}\frac{1}{2}{\ensuremath{\rho}}_{F}=n$, with the plus (minus) sign for repulsive (attractive) interactions and nnn an integer. Far from fermionic half filling, the boson-fermion interaction drives a gapless-gapped transition in the spin sector. Our findings could be observed experimentally in state-of-the-art cold-atom setups.
We investigate a cold-atom mixture of spinless bosons and fermions in two-dimensional optical lattices. In the presence of a nested Fermi surface, the bosons may develop a fascinating supersolid behavior characterized by a finite superfluid density as well as a spatial density wave order. Focusing on the triangular lattice geometry and combining a general Landau-Ginzburg-Wilson approach with microscopically derived mean-field theory, we find an exotic supersolid phase at a fermionic band filling of nf=3∕4{n}_{f}=3∕4nf​=3∕4 with a kagome-type crystalline order. We also address the case of anisotropic hopping amplitudes and show that striped supersolid phases emerge on the square and triangular lattices. For weak interactions, the supersolid competes with phase separation. For strong intraspecies and interspecies interactions, with the total number of fermions and bosons corresponding to one particle per site, the bosons form an alternating Mott insulator ground state. Finally, for a mixture of 87Rb40K^{87}\mathrm{Rb}^{40}\mathrm{K}87Rb40K and 23Na6Li^{23}\mathrm{Na}^{6}\mathrm{Li}23Na6Li, we show that supersolidity can be observed in the range of accessible temperatures in the square lattice geometry.