Fulde–Ferrell–Larkin–Ovchinnikov pairing states between s- and p-orbital fermions

Abstract

We study the pairing states in a largely imbalanced two-component Fermi gas loaded in an anisotropic two-dimensional optical lattice, where the spin-up and spin-down fermions are filled to the s- and p_x-orbital bands, respectively. We show that owing to the relative inversion of the band structures of the s and p_x orbitals, the system favors pairing between two fermions on the same side of the Brillouin zone, leading to a large stable regime for states with a finite center-of-mass momentum, i.e., the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state. In particular, when two Fermi surfaces are close in momentum space, a nesting effect stabilizes a special type of π-FFLO phase with a spatial modulation of πalong the easily tunneled x direction. We map out the zero-temperature phase diagrams within the mean-field approach for various aspect ratios within the two-dimensional plane and calculate the Berezinskii–Kosterlitz–Thouless (BKT) transition temperatures T_BKT for different phases.

Keywords

ultracold Fermi gas / superfluid / optical lattice

References

[1] R.Casalbuoni and G.Nardulli, Inhomogeneous superconductivity in condensed matter and QCD, Rev. Mod. Phys. 76(1), 263 (2004)

[2] M.Alford, J. A.Bowers, and K.Rajagopal, Crystalline color superconductivity, Phys. Rev. D63(7), 074016 (2001)

[3] Y. A.Liao, A. S. C.Rittner, T.Paprotta, W.Li, G. B.Partridge, R. G.Hulet, S. K.Baur, and E. J.Mueller, Spin-imbalance in a one-dimensional Fermi gas, Nature467(7315), 567 (2010)

[4] P.Fulde and R. A.Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev. 135(3A), A550 (1964)

[5] A. I.Larkin and Y. N.Ovchinnikov, Nonuniform state of superconductors, Sov. Phys. JETP20, 762 (1965)

[6] W. V.Liu and F.Wilczek, Interior gap superfluidity, Phys. Rev. Lett. 90(4), 047002 (2003)

[7] G.Sarma, On the influence of a uniform exchange field acting on the spins of the conduction electrons in a superconductor, J. Phys. Chem. Solids24(8), 1029 (1963)

[8] H.Müther and A.Sedrakian, Spontaneous breaking of rotational symmetry in superconductors, Phys. Rev. Lett. 88(25), 252503 (2002)

[9] D. E.Sheehy and L.Radzihovsky, BEC–BCS crossover, phase transitions and phase separation in polarized resonantly-paired superfluids, Ann. Phys. 322(8), 1790 (2007)

[10] G.Orso, Attractive Fermi gases with unequal spin populations in highly elongated traps, Phys. Rev. Lett. 98(7), 070402 (2007)

[11] H.Hu, X. J.Liu, and P. D.Drummond, Phase diagram of a strongly interacting polarized Fermi gas in one dimension, Phys. Rev. Lett. 98(7), 070403 (2007)

[12] W.Zhang and W.Yi, Topological Fulde–Ferrell– Larkin–Ovchinnikov states in spin–orbit-coupled Fermi gases, Nat. Commun. 4, 2711 (2013)

[13] W.Yi, W.Zhang, and X. L.Cui, Pairing superfluidity in spin–orbit coupled ultracold Fermi gases, Sci. China Phys. Mech. Astron. 58(1), 014201 (2015)

[14] T. K.Koponen,T.Paananen, J. P.Martikainen, M. R.Bakhtiari, and P.Törmä, FFLO state in 1-, 2- and 3-dimensional optical lattices combined with a nonuniform background potential, New J. Phys. 10(4), 045014 (2008)

[15] Z.Cai, Y.Wang, and C.Wu, Stable Fulde–Ferrell– Larkin–Ovchinnikov pairing states in two-dimensional and three-dimensional optical lattices, Phys. Rev. A83(6), 063621 (2011)

[16] Z.Zhang, H. H.Hung, C. M.Ho, E.Zhao, and W. V.Liu, Modulated pair condensate of p-orbital ultracold fermions, Phys. Rev. A82(3), 033610 (2010)

[17] S.Yin,J. E.Baarsma, M. O. J.Heikkinen, J. P.Martikainen, and P.Törmä, Superfluid phases of fermions with hybridized s and porbitals, Phys. Rev. A92(5), 053616 (2015)

[18] B.Liu, X.Li, R. G.Hulet, and W. V.Liu, Detecting pphase superfluids with p-wave symmetry in a quasi-onedimensional optical lattice, Phys. Rev. A94, 031602(R) (2016)

[19] A. I.Buzdin, Proximity effects in superconductorferromagnet heterostructures, Rev. Mod. Phys. 77(3), 935 (2005) (and references therein)

[20] C.Bernhard, J. L.Tallon, C.Niedermayer, T.Blasius, A.Golnik, E.Brücher, R. K.Kremer, D. R.Noakes, C. E.Stronach, and E. J.Ansaldo, Coexistence of ferromagnetism and superconductivity in the hybrid ruthenate-cuprate compound RuSr₂GdCu₂O₈ studied by muon spin rotation and dc magnetization, Phys. Rev. B59(21), 14099 (1999)

[21] A. C.McLaughlin, W.Zhou, J. P.Attfield, A. N.Fitch, and J. L.Tallon, Structure and microstructure of the ferromagnetic superconductor RuSr2GdCu2O8, Phys. Rev. B60(10), 7512 (1999)

[22] O.Chmaissem, J. D.Jorgensen, H.Shaked, P.Dollar, and J. L.Tallon, Crystal and magnetic structure of ferromagnetic superconducting RuSr₂GdCu₂O₈, Phys. Rev. B61(9), 6401 (2000)

[23] I.Zapata, B.Wunsch, N. T.Zinner, and E.Demler, p-phases in balanced fermionic superfluids on spindependent optical lattices, Phys. Rev. Lett. 105(9), 095301 (2010)

[24] I. E.Mooij,T. P.Orlando, L.Levitov,L.Tian, C. H.van der Wal, and S.Lloyd, Josephson persistent-current qubit, Science285(5430), 1036 (1999)

[25] L. B.Ioffe, V. B.Geshkenbein, M. V.Feigel’man, A. L.Fauchère, and G.Blatter, Environmentally decoupled sds-wave Josephson junctions for quantum computing, Nature398(6729), 679 (1999)

[26] T.Müller, S.Fölling, A.Widera, and I.Bloch, State preparation and dynamics of ultracold atoms in higher lattice orbitals, Phys. Rev. Lett. 99(20), 200405 (2007)

[27] G.Wirth, M.Ölschläger, and A.Hemmerich, Evidence for orbital superfluidity in the P-band of a bipartite optical square lattice, Nat. Phys. 7(2), 147 (2011)

[28] P.Soltan-Panahi, D. S.Lühmann, J.Struck, P.Windpassinger, and K.Sengstock, Quantum phase transition to unconventional multi-orbital superfluidity in optical lattices, Nat. Phys. 8(1), 71 (2011)

[29] D. S.Petrov and G. V.Shlyapnikov, Interatomic collisions in a tightly confined Bose gas, Phys. Rev. A64(1), 012706 (2001)

[30] J. P.Kestner and L. M.Duan,Effective low-dimensional Hamiltonian for strongly interacting atoms in a transverse trap, Phys. Rev. A76(6), 063610 (2007)

[31] W.Zhang, G. D.Lin, and L. M.Duan, BCS–BEC crossover of a quasi-two-dimensional Fermi gas: The significance of dressed molecules, Phys. Rev. A77(6), 063613 (2008)

[32] W.Zhang, G. D.Lin, and L. M.Duan, Berezinskii– Kosterlitz–Thouless transition in a trapped quasi-twodimensional Fermi gas near a Feshbach resonance, Phys. Rev. A78(4), 043617 (2008)

[33] S. S.Botelho and C. A. R.Sá de Melo, Vortex-antivortex lattice in ultracold fermionic gases, Phys. Rev. Lett. 96(4), 040404 (2006)

[34] V. L.Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a con-tinuous symmetry group (I): Classical systems, Sov. Phys. JETP32, 493 (1971)

[35] J. M.Kosterlitz andD.Thouless, Long range order and metastability in two dimensional solids and superfluids. (Application of dislocation theory), J. Phys. C: Solid State Phys. 5, L124 (1972)

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