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arXiv:1801.07376 · Physical Review A

Emergent interlayer nodal superfluidity of a dipolar Fermi gas in bilayer optical lattices

Bo Liu, Peng Zhang, Ren Zhang, Hong Xiu Gao, Fuli Li

Published Dec 7, 2018• 2 citations
arXivHTMLPDF

Abstract

Understanding the interplay between magnetism and superconductivity is one of the central issues in high-temperature superconductors. The recent experimental implementation of cold gases with highly tunable anisotropic interaction, especially in magnetic dipolar atoms or polar molecules, opens up a new thrust on exploring this interesting phenomenon. Here we report a mechanism to drive the interplay between magnetism and superfluidity through engineering the spatially anisotropic interaction via considering loading pseudospin-1/2 dipolar Fermi atoms in bilayer optical lattices. Surprisingly, we find that the weak interlayer interaction can lead to the coexistence of superfluidity and antiferromagnetism at low temperatures for the half filling case. It is distinguished from the usual scheme by doping an antiferromagnetic Mott insulating parent to access high-${T}_{c}$ superconductivity, where at half filling there is no coexistence of superconductivity and magnetism at low temperatures due to the absence of the superconductivity. Furthermore, the interlayer superfluid possesses an unexpected nodal structure, which is reminiscent of the nodal high-${T}_{c}$ superconductivity but differs in origin.

DOI
10.1103/physreva.98.063610

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Understanding the interplay between magnetism and superconductivity is one of the central issues in high-temperature superconductors. The recent experimental implementation of cold gases with highly tunable anisotropic interaction, especially in magnetic dipolar atoms or polar molecules, opens up a new thrust on exploring this interesting phenomenon. Here we report a mechanism to drive the interplay between magnetism and superfluidity through engineering the spatially anisotropic interaction via considering loading pseudospin-1/2 dipolar Fermi atoms in bilayer optical lattices. Surprisingly, we find that the weak interlayer interaction can lead to the coexistence of superfluidity and antiferromagnetism at low temperatures for the half filling case. It is distinguished from the usual scheme by doping an antiferromagnetic Mott insulating parent to access high-Tc{T}_{c}Tc​ superconductivity, where at half filling there is no coexistence of superconductivity and magnetism at low temperatures due to the absence of the superconductivity. Furthermore, the interlayer superfluid possesses an unexpected nodal structure, which is reminiscent of the nodal high-Tc{T}_{c}Tc​ superconductivity but differs in origin.
By using a well-established ``ab initio'' theoretical approach developed in the past to quantitatively study the superconductivity of condensed matter systems, based on the Kohn-Sham density functional theory, I study the superfluid properties and the BCS-BEC crossover of two parallel bi-dimensional layers of fermionic dipolar molecules, where the pairing mechanism leading to superfluidity is provided by the interlayer coupling between dipoles. The finite temperature superfluid properties of both the homogeneous system and one where the fermions in each layer are confined by a square optical lattice are studied at half filling conditions, and for different values of the strength of the confining optical potential. The T = 0 results for the homogeneous system are found to be in excellent agreement with diffusion Monte Carlo results. The superfluid transition temperature in the BCS region is found to increase, for a given interlayer coupling, with the strength of the confining optical potential. A transition occurs at sufficiently small interlayer distances, where the fermions becomes localized within the optical lattice sites in a square geometry with an increased effective lattice constant, forming a system of localized composite bosons. This transition should be signaled by a sudden drop in the superfluid fraction of the system.
In a dipolar Fermi gas, the dipole-dipole interaction between fermions can be turned into a dipolar Ising interaction between pseudospins in the presence of an ac electric field. When trapped in a two-dimensional optical lattice, this dipolar Fermi gas has a very rich phase diagram at zero temperature, due to the competition between antiferromagnetism and superfluidity. At half-filling, the antiferromagnetic state is the favored ground state. The superfluid state appears as the ground state at a smaller filling factor. In between there is a phase-separated region. The order parameter of the superfluid state can display different symmetries depending on the filling factor and interaction strength, including the ddd-wave (ddd), the extended sss-wave (xsxsxs), or their linear combination (xs+idxs+idxs+id). Implications for the current experiment are discussed.
We study two models realized by two-component Fermi gases loaded in optical lattices. We clarify that multiband effects inevitably caused by the optical lattices generate a rich structure, when the systems crossover from the region of weakly bound molecular bosons to the region of strongly bound atomic bosons. Here the crossover can be controlled by attractive fermion interaction. One of the present models is a case with attractive fermion interaction, where an insulator-superfluid transition takes place. The transition is characterized as the transition between a band insulator and a Bose-Einstein condensate superfluid state. Differing from the conventional Bardeen-Cooper-Schrieffer (BCS) superfluid transition, this transition shows unconventional properties. In contrast to the one-particle excitation gap scaled by the superfluid order parameter in the conventional BCS transition, because of the multiband effects, a large gap of one-particle density of states is retained all through the transition, although the superfluid order grows continuously from zero. A re-entrant transition with lowering temperature is another unconventionality. The other model is the case with coexisting attractive and repulsive interactions. Within a mean-field treatment, we find a new insulating state, an orbital ordered insulator. This insulator is one candidate for the Mott insulator of molecular bosons and is the first example that the orbital internal degrees of freedom of molecular bosons appears explicitly. Besides the emergence of a new phase, a coexisting phase also appears where superfluidity and an orbital order coexist just by doping holes or particles. The insulating and superfluid particles show differentiation in momentum space as in the high-Tc{T}_{\text{c}}Tc​ cuprate superconductors.
This work addresses the study of superfluid and supersolid phases of dipolar Fermi molecules lying in a two dimensional space. The prediction of these phases, performed within a mean field analysis, results from proposing a model in which interacting Fermi molecules are confined in a bilayer array of parallel lattices with square symmetry. As a result of the repulsive intralayer and attractive interlayer interactions between dipolar molecules, a checkerboard pattern and a paired superfluid regimes can emerge. The supersolid phase is identified as the spatial coexistence of density ordered and superfluid phases. The model here proposed can be implemented within the current experimental capabilities as a function of the interlayer separation and the application of an external electric field varying the dipolar interaction between molecules.
We study the phase diagram of a dipolar Fermi gas at half-filling in a cubic optical lattice with dipole moments aligned along the zzz axis. The anisotropic dipole-dipole interaction leads to the competition between pz{p}_{z}pz​-wave superfluid and nematic charge-density-wave (CDW) orders at low temperatures. We find that the superfluid phase survives with weak interactions and the CDW phase dominates with strong interactions. In-between, the supersolid phase appears as a balance between superfluid and CDW orders. The superfluid density is anisotropic in the supersolid and superfluid phases. In the CDW phase, there is a semimetal-to-insulator transition with increase of the interaction strength. Experimental implications are discussed.
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.