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:2309.17362 · Physical review. B./Physical review. B

Pairing from repulsion in a two-dimensional Fermi gas with soft-core interactions

Ahmet Keleş, Xiaopeng Li, Erhai Zhao

Published Feb 22, 2024• 2 citations
arXivHTMLPDF

Abstract

We investigate a model many-body system of spinless Fermi gas in two dimensions, where the bare two-body interaction is repulsive and takes the form of a soft-core disk potential. We obtain the zero-temperature phase diagram of this model by numerical functional renormalization group (FRG), which retains the effective interaction vertices in all channels to provide a detailed picture of how Cooper pairing emerges under the renormalization flow. The repulsion drives the system to a series of superfluid states with higher angular momentum pairing, for example in the $f$- and $h$-wave channels instead of the $p$-wave channel. This is in sharp contrast to the original Kohn-Luttinger mechanism where pairing of very large angular momenta and exponentially small transition temperature was predicted. We trace the stabilization and enhancement of $f$- and $h$-wave pairing back to the momentum dependence of the bare interaction. A perturbative calculation is carried out to show that while the second-order Kohn-Luttinger diagrams provide a qualitative understanding of the onsets of the various superfluid phases, they are unable to accurately capture the phase boundaries predicted by FRG. Our findings suggest that tuning the shape of the interaction potential offers a promising route to achieve stronger ``pairing glue'' and to realize nontrivial superfluid phases in repulsive Fermi gases beyond the scope of the original Kohn-Luttinger analysis.

DOI
10.1103/physrevb.109.054519

Related papers

f -wave superfluidity from repulsive interaction in Rydberg-dressed Fermi gas

Ahmet Keleş, Erhai Zhao, Xiaopeng Li

Interacting Fermi gas provides an ideal model system to understand unconventional pairing and intertwined orders relevant to a large class of quantum materials. Rydberg-dressed Fermi gas is a recent experimental system where the sign, strength, and range of the interaction can be controlled. The interaction in momentum space has a negative minimum at ${q}_{c}$ inversely proportional to the characteristic length scale in real space, the soft-core radius ${r}_{c}$. We show theoretically that single-component (spinless) Rydberg-dressed Fermi gas in two dimensions has a rich phase diagram with superfluid and density wave orders due to the interplay of the Fermi momentum ${p}_{F}$, interaction range ${r}_{c}$, and interaction strength ${u}_{0}$. For repulsive bare interactions ${u}_{0}>0$, the dominant instability is a $f$-wave superfluid for ${p}_{F}{r}_{c}\ensuremath{\lesssim}2$ and a density wave for ${p}_{F}{r}_{c}\ensuremath{\gtrsim}4$. The $f$-wave pairing in this repulsive Fermi gas is reminiscent of the conventional Kohn-Luttinger mechanism but has a much higher ${T}_{c}$. For attractive bare interactions ${u}_{0}<0$, the leading instability is $p$-wave pairing. The phase diagram is obtained from a functional renormalization group that treats all competing many-body instabilities in the particle-particle and particle-hole channels on an equal footing.

arXiv:1906.04235•Physical Review A•Feb 28, 2020•12 citations

Anomalous superconductivity and superfluidity in repulsive fermion systems

M. Yu. Kagan, Vitaly A. Mitskan, M. M. Korovushkin

We discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We construct phase diagrams of these systems and find the areas of the superconducting state in free space, as well as on the lattice in the framework of the Fermi-gas model with hard-core repulsion, the Hubbard model, the Shubin-Vonsovsky model, and the $t-J$ model. We demonstrate that the critical superconducting temperature can be greatly increased in the spin-polarized case or in a two-band situation already at low densities. The proposed theory is based on the Kohn-Luttinger mechanism or its generalizations and explains or predicts anomalous $p$-, $d$-, and $f$-wave pairing in various materials, such as high-temperature superconductors, the idealized monolayer and bilayer of doped graphene, heavy-fermion systems, layered organic superconductors, superfluid $^3$He, spin-polarized $^3$He mixtures in $^4$He, ultracold quantum gases in magnetic traps, and optical lattices.

Physics-Uspekhi•Aug 7, 2015•37 citations

Effects of retardation and long-range forces on pairing in a Fermi gas with repulsion

A. S. Alexandrov, A. A. Golubov

The effect of retardation on the ``effective interaction'' due to polarization in a Fermi gas with short-range repulsion is studied. The consequences of pairing with nonzero angular momentum (as discussed by Kohn and Luttinger) are analyzed. The frequency dependence of the scattering amplitude in the Cooper channel suppresses the characteristic temperature significantly for odd angular momenta and enhances it for even ones. Cooper pairing with any angular momentum in the case of long-range Coulomb repulsion is shown to be impossible.

Physical review. B, Condensed matter•Mar 1, 1992•14 citations

Fulde–Ferrell superfluids in spinless ultracold Fermi gases

Zhen-Fei Zheng, Guang‐Can Guo, Zhen Zheng +1 more

The Fulde–Ferrell (FF) superfluid phase, in which fermions form finite momentum Cooper pairings, is well studied in spin-singlet superfluids in past decades. Different from previous works that engineer the FF state in spinful cold atoms, we show that the FF state can emerge in spinless Fermi gases confined in optical lattice associated with nearest-neighbor interactions. The mechanism of the spinless FF state relies on the split Fermi surfaces by tuning the chemistry potential, which naturally gives rise to finite momentum Cooper pairings. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. By beyond-mean-field calculations, we find the finite momentum pairing is more robust, yielding the system promising for maintaining the FF state at finite temperature. Finally we present the possible realization and detection scheme of the spinless FF state.

arXiv:1705.03205•New Journal of Physics•May 25, 2018•4 citations

Kohn-Luttinger effect and the instability of a two-dimensional repulsive Fermi liquid atT=0

Andrey V. Chubukov

We consider the possibility for a pairing in a two-dimensional (2D) repulsive Fermi liquid due to the singularity in the scattering amplitude \ensuremath{\Gamma}(q) at the momentum transfer q\ensuremath{\le}2${\mathit{p}}_{\mathit{F}}$ (Kohn-Luttinger effect). A common belief based on perturbative calculations up to second order in the s-wave scattering amplitude is that this effect is absent in two dimensions. I show that this is not the case. For an arbitrary Fermi liquid, \ensuremath{\Gamma}(q) is found to have a singular part, ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{sing}}$(q)\ensuremath{\sim} \ensuremath{\surd}1-${\mathit{q}}^{2}$/(2${\mathit{p}}_{\mathit{F}}$${)}^{2}$ , for q\ensuremath{\le}2${\mathit{p}}_{\mathit{F}}$. For large 2D orbital momentum l, this term gives a dominant attractive contribution to the scattering amplitude and leads to a pairing instability in a 2D Fermi liquid with arbitrary short-range repulsion. In the dilute limit, numerical studies show that the effect survives down to l=1 and gives rise to a p-wave pairing. The relevance of these results to experiments on $^{3}\mathrm{He}$ adsorbed on the free surface of $^{4}\mathrm{He}$ is discussed.

Physical review. B, Condensed matter•Jul 1, 1993•159 citations

Pairing and Pair Superfluid Density in One-Dimensional Two-Species Fermionic and Bosonic Hubbard Models

Benoît Grémaud, G. G. Batrouni

We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in a uniform, i.e., with no confining potential, one-dimensional optical lattice. We compare results from quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity; there are no individual contributions due to the separate species. For weak attraction, the pair size diverges exponentially, i.e., Bardeen-Cooper-Schrieffer (BCS) pairing, requiring huge systems to bring out the pair-only nature of the superfluid. This crucial property is largely overlooked in many studies, thereby misinterpreting the origin and nature of the superfluid. We compare and contrast this with the repulsive case and show that the behavior is very different, contradicting previous claims about drag superfluidity and the symmetry of properties for attractive and repulsive interactions. Finally, our results show that the situation is similar for soft-core bosons: superfluidity is due only to pairs, even for the smallest attractive interaction strength compatible with the largest system sizes that we could attain.

arXiv:2006.13950•Physical Review Letters•Jul 7, 2021•16 citations
We investigate a model many-body system of spinless Fermi gas in two dimensions, where the bare two-body interaction is repulsive and takes the form of a soft-core disk potential. We obtain the zero-temperature phase diagram of this model by numerical functional renormalization group (FRG), which retains the effective interaction vertices in all channels to provide a detailed picture of how Cooper pairing emerges under the renormalization flow. The repulsion drives the system to a series of superfluid states with higher angular momentum pairing, for example in the fff- and hhh-wave channels instead of the ppp-wave channel. This is in sharp contrast to the original Kohn-Luttinger mechanism where pairing of very large angular momenta and exponentially small transition temperature was predicted. We trace the stabilization and enhancement of fff- and hhh-wave pairing back to the momentum dependence of the bare interaction. A perturbative calculation is carried out to show that while the second-order Kohn-Luttinger diagrams provide a qualitative understanding of the onsets of the various superfluid phases, they are unable to accurately capture the phase boundaries predicted by FRG. Our findings suggest that tuning the shape of the interaction potential offers a promising route to achieve stronger ``pairing glue'' and to realize nontrivial superfluid phases in repulsive Fermi gases beyond the scope of the original Kohn-Luttinger analysis.
Interacting Fermi gas provides an ideal model system to understand unconventional pairing and intertwined orders relevant to a large class of quantum materials. Rydberg-dressed Fermi gas is a recent experimental system where the sign, strength, and range of the interaction can be controlled. The interaction in momentum space has a negative minimum at qc{q}_{c}qc​ inversely proportional to the characteristic length scale in real space, the soft-core radius rc{r}_{c}rc​. We show theoretically that single-component (spinless) Rydberg-dressed Fermi gas in two dimensions has a rich phase diagram with superfluid and density wave orders due to the interplay of the Fermi momentum pF{p}_{F}pF​, interaction range rc{r}_{c}rc​, and interaction strength u0{u}_{0}u0​. For repulsive bare interactions u0>0{u}_{0}>0u0​>0, the dominant instability is a fff-wave superfluid for ${p}_{F}{r}_{c}\ensuremath{\lesssim}2$ and a density wave for ${p}_{F}{r}_{c}\ensuremath{\gtrsim}4$. The fff-wave pairing in this repulsive Fermi gas is reminiscent of the conventional Kohn-Luttinger mechanism but has a much higher Tc{T}_{c}Tc​. For attractive bare interactions u0<0{u}_{0}<0u0​<0, the leading instability is ppp-wave pairing. The phase diagram is obtained from a functional renormalization group that treats all competing many-body instabilities in the particle-particle and particle-hole channels on an equal footing.
We discuss the mechanisms of unconventional superconductivity and superfluidity in 3D and 2D fermionic systems with purely repulsive interaction at low densities. We construct phase diagrams of these systems and find the areas of the superconducting state in free space, as well as on the lattice in the framework of the Fermi-gas model with hard-core repulsion, the Hubbard model, the Shubin-Vonsovsky model, and the t−Jt-Jt−J model. We demonstrate that the critical superconducting temperature can be greatly increased in the spin-polarized case or in a two-band situation already at low densities. The proposed theory is based on the Kohn-Luttinger mechanism or its generalizations and explains or predicts anomalous ppp-, ddd-, and fff-wave pairing in various materials, such as high-temperature superconductors, the idealized monolayer and bilayer of doped graphene, heavy-fermion systems, layered organic superconductors, superfluid 3^33He, spin-polarized 3^33He mixtures in 4^44He, ultracold quantum gases in magnetic traps, and optical lattices.
The effect of retardation on the ``effective interaction'' due to polarization in a Fermi gas with short-range repulsion is studied. The consequences of pairing with nonzero angular momentum (as discussed by Kohn and Luttinger) are analyzed. The frequency dependence of the scattering amplitude in the Cooper channel suppresses the characteristic temperature significantly for odd angular momenta and enhances it for even ones. Cooper pairing with any angular momentum in the case of long-range Coulomb repulsion is shown to be impossible.
The Fulde–Ferrell (FF) superfluid phase, in which fermions form finite momentum Cooper pairings, is well studied in spin-singlet superfluids in past decades. Different from previous works that engineer the FF state in spinful cold atoms, we show that the FF state can emerge in spinless Fermi gases confined in optical lattice associated with nearest-neighbor interactions. The mechanism of the spinless FF state relies on the split Fermi surfaces by tuning the chemistry potential, which naturally gives rise to finite momentum Cooper pairings. The phase transition is accompanied by changed Chern numbers, in which, different from the conventional picture, the band gap does not close. By beyond-mean-field calculations, we find the finite momentum pairing is more robust, yielding the system promising for maintaining the FF state at finite temperature. Finally we present the possible realization and detection scheme of the spinless FF state.
We consider the possibility for a pairing in a two-dimensional (2D) repulsive Fermi liquid due to the singularity in the scattering amplitude \ensuremath{\Gamma}(q) at the momentum transfer q\ensuremath{\le}2pF{\mathit{p}}_{\mathit{F}}pF​ (Kohn-Luttinger effect). A common belief based on perturbative calculations up to second order in the s-wave scattering amplitude is that this effect is absent in two dimensions. I show that this is not the case. For an arbitrary Fermi liquid, \ensuremath{\Gamma}(q) is found to have a singular part, ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{sing}}$(q)\ensuremath{\sim} \ensuremath{\surd}1-q2{\mathit{q}}^{2}q2/(2pF{\mathit{p}}_{\mathit{F}}pF​)2{)}^{2})2 , for q\ensuremath{\le}2pF{\mathit{p}}_{\mathit{F}}pF​. For large 2D orbital momentum l, this term gives a dominant attractive contribution to the scattering amplitude and leads to a pairing instability in a 2D Fermi liquid with arbitrary short-range repulsion. In the dilute limit, numerical studies show that the effect survives down to l=1 and gives rise to a p-wave pairing. The relevance of these results to experiments on 3He^{3}\mathrm{He}3He adsorbed on the free surface of 4He^{4}\mathrm{He}4He is discussed.
We use unbiased computational methods to elucidate the onset and properties of pair superfluidity in two-species fermionic and bosonic systems with onsite interspecies attraction loaded in a uniform, i.e., with no confining potential, one-dimensional optical lattice. We compare results from quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG), emphasizing the one-to-one correspondence between the Drude weight tensor, calculated with DMRG, and the various winding numbers extracted from the QMC. Our results show that, for any nonvanishing attractive interaction, pairs form and are the sole contributors to superfluidity; there are no individual contributions due to the separate species. For weak attraction, the pair size diverges exponentially, i.e., Bardeen-Cooper-Schrieffer (BCS) pairing, requiring huge systems to bring out the pair-only nature of the superfluid. This crucial property is largely overlooked in many studies, thereby misinterpreting the origin and nature of the superfluid. We compare and contrast this with the repulsive case and show that the behavior is very different, contradicting previous claims about drag superfluidity and the symmetry of properties for attractive and repulsive interactions. Finally, our results show that the situation is similar for soft-core bosons: superfluidity is due only to pairs, even for the smallest attractive interaction strength compatible with the largest system sizes that we could attain.