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Topological Fulde–Ferrell and Larkin–Ovchinnikov states in spin-orbit-coupled lattice system |
Yao-Wu Guo1, Yan Chen1,2( ) |
1. Department of Physics and State Key Laboratory of Surface Physics, Fudan University, Shanghai 200433, China
2. Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China |
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Abstract The spin-orbit coupled lattice system under Zeeman fields provides an ideal platform to realize exotic pairing states. Notable examples range from the topological superfluid/superconducting (tSC) state, which is gapped in the bulk but metallic at the edge, to the Fulde–Ferrell (FF) state (having a phase-modulated order parameter with a uniform amplitude) and the Larkin–Ovchinnikov (LO) state (having a spatially varying order parameter amplitude). Here, we show that the topological FF state with Chern number (C=−1) (tFF1) and topological LO state with C= 2 (tLO2) can be stabilized in Rashba spin-orbit coupled lattice systems in the presence of both in-plane and out-of-plane Zeeman fields. Besides the inhomogeneous tSC states, in the presence of a weak in-plane Zeeman field, two topological BCS phases may emerge with C=−1 (tBCS1) far from half filling and C= 2 (tBCS2) near half filling. We show intriguing effects such as different spatial profiles of order parameters for FF and LO states, the topological evolution among inhomogeneous tSC states, and different non-trivial Chern numbers for the tFF1 and tLO1,2 states, which are peculiar to the lattice system. Global phase diagrams for various topological phases are presented for both half-filling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.
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| Keywords
topological superfluid
Fulde–Ferrell (FF) state
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Corresponding Author(s):
Yan Chen
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Issue Date: 08 December 2017
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| 1 |
D. Xiao, M. C. Chang, and Q. Niu, Berry phases effects on electronic properties, Rev. Mod. Phys. 82(3), 1959 (2010)
https://doi.org/10.1103/RevModPhys.82.1959
|
| 2 |
X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)
https://doi.org/10.1103/RevModPhys.83.1057
|
| 3 |
E. Majorana, Teoria simmetrica dell’elettrone e del positrone, Nuovo Cim. 14(4), 171 (1937)
https://doi.org/10.1007/BF02961314
|
| 4 |
F. Wilczek, Majorana returns, Nat. Phys. 5(9), 614 (2009)
|
| 5 |
C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Non-Abelian anyons and topological quantum computation, Rev. Mod. Phys. 80(3), 1083 (2008)
https://doi.org/10.1103/RevModPhys.80.1083
|
| 6 |
L. P. Rokhinson, X. Liu, and J. K. Furdyna, The fractional a.c. Josephson effect in a semiconductorsuperconductor nanowire as a signature of Majorana particles, Nat. Phys. 8(11), 795 (2012)
|
| 7 |
A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, and H. Shtrikman, Zero-bias peaks and splitting in an Al- InAs nanowire topological superconductor as a signature of Majorana fermions, Nat. Phys. 8(12), 887 (2012)
|
| 8 |
M. T. Deng, C. L. Yu, G. Y. Huang, M. Larsson, P. Caroff, and H. Q. Xu, Anomalous zero-bias conductance peak in a Nb-InSb nanowire-Nb hybrid device, Nano Lett. 12(12), 6414 (2012)
https://doi.org/10.1021/nl303758w
|
| 9 |
V. Mourik, K. Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, and L. P. Kouwenhoven, Signatures of Majorana fermions in hybrid superconductorsemiconductor nanowire devices, Science 336(6084), 1003 (2012)
https://doi.org/10.1126/science.1222360
|
| 10 |
L. Mao, M. Gong, E. Dumitrescu, S. Tewari, and C. Zhang, Hole-doped semiconductor nanowire on top of an s-wave superconductor: a new and experimentally accessible system for Majorana fermions, Phys. Rev. Lett. 108(17), 177001 (2012)
https://doi.org/10.1103/PhysRevLett.108.177001
|
| 11 |
G. Moore and N. Read, Nonabelions in the fractional quantum hall effect, Nucl. Phys. B 360(2–3), 362 (1991)
https://doi.org/10.1016/0550-3213(91)90407-O
|
| 12 |
A. P. Mackenzie and Y. Maeno, The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing, Rev. Mod. Phys. 75(2), 657 (2003)
https://doi.org/10.1103/RevModPhys.75.657
|
| 13 |
N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61(15), 10267 (2000)
https://doi.org/10.1103/PhysRevB.61.10267
|
| 14 |
L. Fu and C. L. Kane, Superconducting proximity effect and Majorana fermions at the surface of a topological insulator, Phys. Rev. Lett. 100(9), 096407 (2008)
https://doi.org/10.1103/PhysRevLett.100.096407
|
| 15 |
J. D. Sau, R. M. Lutchyn, S. Tewari, and S. Das Sarma, Generic new platform for topological quantum computation using semiconductor heterostructures, Phys. Rev. Lett. 104(4), 040502 (2010)
https://doi.org/10.1103/PhysRevLett.104.040502
|
| 16 |
R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Majorana fermions and a topological phase transition insemiconductor-superconductor heterostructures, Phys. Rev. Lett. 105(7), 077001 (2010)
https://doi.org/10.1103/PhysRevLett.105.077001
|
| 17 |
Y. Oreg, G. Refael, and F. von Oppen, Helical liquids and Majorana bound states in quantum wires, Phys. Rev. Lett. 105(17), 177002 (2010)
https://doi.org/10.1103/PhysRevLett.105.177002
|
| 18 |
J. Alicea, Y. Oreg, G. Refael, F. von Oppen, and M. P. A. Fisher, Non-Abelian statistics and topological quantum information processing in 1D wire networks, Nat. Phys. 7(5), 412 (2011)
|
| 19 |
A. C. Potter and P. A. Lee, Multichannel generalization of Kitaev’s Majorana end states and a practical route to realize them in thin films, Phys. Rev. Lett. 105(22), 227003 (2010)
https://doi.org/10.1103/PhysRevLett.105.227003
|
| 20 |
Y. J. Lin, K. Jiménez-García, and I. B. Spielman, Spin–orbit-coupled Bose–Einstein condensates, Nature 471(7336), 83 (2011)
https://doi.org/10.1038/nature09887
|
| 21 |
P. Wang, Z.Q. Yu, Z. Fu, J. Miao, L. Huang, S. Chai, H. Zhai, and J. Zhang, Spin–orbit coupled degenerate Fermi gases, Phys. Rev. Lett. 109(9), 095301 (2012)
https://doi.org/10.1103/PhysRevLett.109.095301
|
| 22 |
L. W. Cheuk, A. T. Sommer, Z. Hadzibabic, T. Yefsah, W. S. Bakr, and M. W. Zwierlein, Spin-injection spectroscopy of a spin-orbit coupled Fermi gas, Phys. Rev. Lett. 109(9), 095302 (2012)
https://doi.org/10.1103/PhysRevLett.109.095302
|
| 23 |
M. Sato, Y. Takahashi, and S. Fujimoto, Non-Abelian topological order in s-wave superfluids of ultracold fermionic atoms, Phys. Rev. Lett. 103(2), 020401 (2009)
https://doi.org/10.1103/PhysRevLett.103.020401
|
| 24 |
X.-J. Liu, H. Pu, and H. Hu, Probing Majorana fermions in spin-orbit-coupled atomic Fermi gases, Phys. Rev. A 85, 021603(R) (2011)
|
| 25 |
R. Casalbuoni and G. Nardulli, Inhomogeneous superconductivity in condensed matter and QCD, Rev. Mod. Phys. 76(1), 263 (2004)
https://doi.org/10.1103/RevModPhys.76.263
|
| 26 |
M. Kenzelmann, T. Strassle, C. Niedermayer, M. Sigrist, B. Padmanabhan, M. Zolliker, A. D. Bianchi, R. Movshovich, E. D. Bauer, J. L. Sarrao, and J. D. Thompson, Coupled superconducting and magnetic order in CeCoIn5, Science 321(5896), 1652 (2008)
https://doi.org/10.1126/science.1161818
|
| 27 |
L. Li, C. Richter, J. Mannhart, and R. C. Ashoori, Coexistence of magnetic order and two-dimensional superconductivity at LaAlO3/SrTiO3 interfaces, Nat. Phys. 7(10), 762 (2011)
|
| 28 |
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, Nature 467(7315), 567 (2010)
https://doi.org/10.1038/nature09393
|
| 29 |
P. Fulde and R. A. Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev. 135(3A), A550 (1964)
https://doi.org/10.1103/PhysRev.135.A550
|
| 30 |
A. I. Larkin and Y. N. Ovchinnikov, Nonuniform state of superconductors, Zh. Eksp. Teor. Fiz. 47, 1136 (1964)
|
| 31 |
F. Wu, G. Guo, W. Zhang, and W. Yi, Unconventional superfluid in a two-dimensional Fermi gas with anisotropic spin-orbit coupling and Zeeman fields, Phys. Rev. Lett. 110(11), 110401 (2013)
https://doi.org/10.1103/PhysRevLett.110.110401
|
| 32 |
Z. Zheng, M. Gong, X. Zou, C. Zhang, and G. Guo, Route to observable Fulde–Ferrell–Larkin–Ovchinnikov phases in three-dimensional spin-orbit-coupled degenerate Fermi gases, Phys. Rev. A 87, 031602(R) (2013)
|
| 33 |
X. J. Liu, K. T. Law, and T. K. Ng, Realization of 2D spin-orbit interaction and exotic topological orders in cold atoms, Phys. Rev. Lett. 112(8), 086401 (2014)
https://doi.org/10.1103/PhysRevLett.112.086401
|
| 34 |
C. Qu, Z. Zheng, M. Gong, Y. Xu, L. Mao, X. Zou, G. Guo, and C. Zhang, Topological superfluids with finite momentum pairing and Majorana fermions, Nat. Commun. 4, 2710 (2013)
https://doi.org/10.1038/ncomms3710
|
| 35 |
W. Zhang and W. Yi, Topological Fulde–Ferrell– Larkin–Ovchinnikov states in spin-orbit-coupled Fermi gases, Nat. Commun. 4, 2711 (2013)
https://doi.org/10.1038/ncomms3711
|
| 36 |
C. Chen, Inhomogeneous topological superfluidity in one-dimensional spin-orbit-coupled Fermi gases, Phys. Rev. Lett. 111(23), 235302 (2013)
https://doi.org/10.1103/PhysRevLett.111.235302
|
| 37 |
Y. Cao, S. H. Zou, X. J. Liu, S. Yi, G. L. Long, and H. Hu, Gapless topological Fulde–Ferrell superfluidity in spinorbital coupled Fermi gases, Phys. Rev. Lett. 113(11), 115302 (2014)
https://doi.org/10.1103/PhysRevLett.113.115302
|
| 38 |
T. Zhou, Y. Gao, and Z. D. Wang, Topological quantum phase transitions and edge states in spin-orbital coupled Fermi gases, Sci. Rep. 4(1), 5218 (2015)
https://doi.org/10.1038/srep05218
|
| 39 |
Y. Xu, C. Qu, M. Gong, and C. Zhang, Competing superfluid orders in spin-orbit coupled fermionic cold atom optical lattices, Phys. Rev. A 89(1), 013607 (2014)
https://doi.org/10.1103/PhysRevA.89.013607
|
| 40 |
D. N. Sheng, Z. Y. Weng, L. Sheng, and F. D. M. Haldane, Quantum spin-Hall effect and topologically invariant Chern numbers, Phys. Rev. Lett. 97(3), 036808 (2006)
https://doi.org/10.1103/PhysRevLett.97.036808
|
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