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arXiv:2106.04583 · Physical Review A

Stabilizing topological superfluidity of lattice fermions

Junhua Zhang, Sumanta Tewari, V. W. Scarola

Published Sep 27, 2021• 2 citations
arXivHTMLPDF

Abstract

Attractive interaction between spinless fermions in a two-dimensional lattice drives the formation of a topological superfluid. But the topological phase is dynamically unstable towards phase separation when the system has a high density of states and large interaction strength. This limits the critical temperature to an experimentally challenging regime where, for example, even ultracold atoms and molecules in optical lattices would struggle to realize the topological superfluid. We propose that the introduction of a weaker longer-range repulsion, in addition to the short-range attraction between lattice fermions, will suppress the phase separation instability. Taking the honeycomb lattice as an example, we use the unrestricted Hartree-Fock approximation to show that our proposal significantly enlarges the stable portion of the topological superfluid phase and increases the critical temperature by an order of magnitude. Our work opens a route to enhance the stability of topological superfluids by engineering interparticle interactions.

DOI
10.1103/physreva.104.033322

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Attractive interaction between spinless fermions in a two-dimensional lattice drives the formation of a topological superfluid. But the topological phase is dynamically unstable towards phase separation when the system has a high density of states and large interaction strength. This limits the critical temperature to an experimentally challenging regime where, for example, even ultracold atoms and molecules in optical lattices would struggle to realize the topological superfluid. We propose that the introduction of a weaker longer-range repulsion, in addition to the short-range attraction between lattice fermions, will suppress the phase separation instability. Taking the honeycomb lattice as an example, we use the unrestricted Hartree-Fock approximation to show that our proposal significantly enlarges the stable portion of the topological superfluid phase and increases the critical temperature by an order of magnitude. Our work opens a route to enhance the stability of topological superfluids by engineering interparticle interactions.
We calculate the phase diagram of identical fermions in a two-dimensional lattice immersed in a three-dimensional Bose-Einstein condensate (BEC). The fermions exchange density fluctuations in the BEC, which gives rise to an attractive induced interaction. The resulting zero-temperature phase diagram exhibits topological px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superfluid phases as well as a phase separation region. We show how to use the flexibility of the Bose-Fermi mixture to tune the induced interaction, so that it maximizes the pairing between nearest-neighbor sites, whereas phase separation originating from long-range interactions is suppressed. Finally, we calculate the Berezinskii-Kosterlitz-Thouless critical temperature of the topological superfluid in the lattice and discuss experimental realizations.
We investigate a spinless Fermi gas trapped in a honeycomb optical lattice with attractive nearest-neighbor interactions. At zero temperature, the mean-field theory predicts three quantum phase transitions, two being topological. At low interactions, the system is semi-metallic. Increasing the interaction further, the semi-metal destabilizes into a fully gapped superfluid. At larger interactions, a topological transition occurs and this superfluid phase becomes gapless, with Dirac-like dispersion relations. Finally, increasing again the interaction, a second topological transition occurs and the gapless superfluid is replaced by a different fully gapped superfluid phase. We analyze these different quantum phases as the temperature and the lattice filling are varied.
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.
In this work we discuss the emergence of p-wave superfluids of identical fermions in 2D lattices. The optical lattice potential manifests itself in an interplay between an increase in the density of states on the Fermi surface and the modification of the fermion-fermion interaction (scattering) amplitude. The density of states is enhanced due to an increase of the effective mass of atoms. In deep lattices, for short-range interacting atoms the scattering amplitude is strongly reduced compared to free space due to a small overlap of wavefunctions of fermions sitting in the neighboring lattice sites, which suppresses the p-wave superfluidity. However, we show that for a moderate lattice depth there is still a possibility to create atomic p-wave superfluids with sizable transition temperatures. The situation is drastically different for fermionic polar molecules. Being dressed with a microwave field, they acquire a dipole-dipole attractive tail in the interaction potential. Then, due to a long-range character of the dipole-dipole interaction, the effect of the suppression of the scattering amplitude in 2D lattices is absent. This leads to the emergence of a stable topological px + ipy superfluid of identical microwave-dressed polar molecules.
In a dipolar Fermi gas, the anisotropic interaction between electric dipoles can be turned into an effectively attractive interaction in the presence of a rotating electric field. We show that the topological px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superfluid phase can be realized in a single-component dipolar Fermi gas trapped in a two-dimensional square optical lattice with this attractive interaction at low temperatures. The px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superfluid state has potential applications for topological quantum computing. We obtain the phase diagram of this system at zero temperature. When the interaction is weak, the ppp-wave superfluid state is stable for most filling factors except near half filling, where phase separation takes place. In the weak-coupling limit, the phase-separation region vanishes. When the interaction strength is above a threshold, the system is phase separated for any filling factor 0<n<10<n<10<n<1. The transition temperature of the px+ipy{p}_{x}+i{p}_{y}px​+ipy​ superfluid state is estimated and the implication for experiments is discussed.
We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and second-nearest-neighbor density-density interactions. Recent exact diagonalization and infinite density matrix renormalization group results suggest that a putative topological Mott insulator phase driven by the second-nearest-neighbor repulsion is suppressed, while other numerically exact approaches support the topological Mott insulator scenario. In the present work, we employ the functional renormalization group (fRG) for correlated fermionic systems. Our fRG results hint at a strong suppression of the scattering processes stabilizing the topological Mott insulator. From analyzing the effects of fermionic fluctuations, we obtain a phase diagram, which is the result of the competition of various charge ordering instabilities.