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arXiv:1906.04235 · Physical Review A

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

Ahmet Keleş, Erhai Zhao, Xiaopeng Li

Published Feb 28, 2020• 12 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.101.023624

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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 pFrc\ensuremath≲2{p}_{F}{r}_{c}\ensuremath{\lesssim}2pF​rc​\ensuremath≲2 and a density wave for pFrc\ensuremath≳4{p}_{F}{r}_{c}\ensuremath{\gtrsim}4pF​rc​\ensuremath≳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 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.
Rydberg and Rydberg-dressed atomic gases have recently emerged as a promising quantum simulator for a variety of models in condensed matter physics. Here we investigate one-dimensional bosons with soft-core Rydberg-dressed interactions using exact path-integral quantum Monte Carlo simulations. The finite-range and the negative Fourier component of the interaction potential generate a roton mode at finite momentum, while particle-hole backscattering processes enhance the susceptibility of one-dimensional systems at twice the Fermi momentum. The competition between the corresponding length scales yields a rich phase diagram, featuring a conventional Tomonaga-Luttinger liquid (TLL) regime, a beyond-TLL regime, and commensurate cluster phases. In the TLL regime, the system transitions from Lieb-Liniger-like bnehavior with Luttinger parameter K>1K>1K>1 to hard-rod-like behavior with K<1K<1K<1, with a quasi-supersolid phase emerging for K<1/2K < 1/2K<1/2. For strong interactions and high densities, deviations from TLL theory appear as precursors for the onset of cluster phases, where particles aggregate into stable clusters of several particles. The properties of each phase is discussed in detail.
We theoretically study a possible pairing mechanism for a two-dimensional population imbalanced Fermi gas with short-range repulsive interactions, which can be realized on the upper branch of a Feshbach resonance. We use a well-controlled renormalization-group approach, which allows an unbiased study of the instabilities of imbalanced Fermi liquid without assumption of a broken symmetry and gives a numerical calculation of the transition temperature from microscopic parameters. Our results show a leading superfluid instability in the ppp-wave channel for the majority species. The corresponding mechanism is that there are effective attractive interactions for the majority species, induced by the particle-hole susceptibility of the minority species, where the mismatch of the Fermi surfaces of the two species plays an important role. We also propose an experimental protocol for detecting the ppp-wave superfluidity and discuss the corresponding experimental signatures.
Spinless fermions on the honeycomb lattice with repulsive nearest-neighbor interactions are known to harbour a quantum critical point at half-filling, with critical behavior in the Gross-Neveu (chiral Ising) universality class. The critical interaction strength separates a weak-coupling semimetallic regime from a commensurate charge-density-wave phase. The phase diagram of this basic model of correlated fermions on the honeycomb lattice beyond half-filling is, however, less well established. Here, we perform an analysis of its many-body instabilities using the functional renormalization group method with a basic Fermi surface patching scheme, which allows us to treat instabilities in competing channels on equal footing also away from half-filling. Between half-filling and the Van Hove filling, the free Fermi surface is holelike and we again find a charge-density wave instability to be dominant at large interactions. Moreover, its characteristics are those of the half-filled case. Directly at the Van Hove filling, the nesting property of the free Fermi surface stabilizes a dimerized bond-order phase. At lower filling, the free Fermi surface becomes electronlike and a superconducting instability with fff-wave symmetry is found to emerge from the interplay of intra-unit-cell repulsion and collective fluctuations in the proximity to the charge-density wave instability. We estimate the extent of the various phases and extract the corresponding order parameters from the effective low-energy Hamiltonians.
We systematically investigate the topological superfluidity of a Rydberg-dressed Fermi gas, where the soft-core effective interaction is of finite radius Rc{R}_{c}Rc​ due to the blockade effect. We calculate the quantum phase diagram within the mean-field approximation and find three distinct phases: polar (pz)({p}_{z})(pz​), axial (px+ipy)({p}_{x}+i{p}_{y})(px​+ipy​), and axiplanar $({p}_{x}+i{\ensuremath{\beta}}_{p}{p}_{y})$ phases. The tricritical point is around ${R}_{c}{k}_{F}\ensuremath{\sim}1$, where kF{k}_{F}kF​ is the Fermi wave vector. We further derive the Ginzburg--Landau theory to explain the phase diagram and estimate the transition temperature to be about 0.1EF0.1{E}_{F}0.1EF​ in the current experimental regime of 6Li^{6}\mathrm{Li}6Li. Our work paves the way for future studies on exotic topological superfluids and related quantum phase transitions.
We investigate the effects of many-body correlations on the ground-state properties of a single-component ultracold Rydberg-dressed Fermi liquid with purely repulsive interparticle interactions in both three and two spatial dimensions. We employed the Fermi-hypernetted-chain Euler-Lagrange approximation and observed that the contribution of the correlation energy on the ground-state energy becomes significant at intermediate values of the soft-core radius and large coupling strengths. For small and large soft-core radii, the correlation energy is negligible and the ground-state energy approaches the Hartree-Fock value. The positions of the main peaks in static structure factor and pair distribution function in the homogeneous fluid phase signal the formation of quantum droplet crystals with several particles confined inside each droplet.