摘要
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 fining 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-rifling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.
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 fining 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-rifling and doped cases. The edge states as well as local density of states spectra are calculated for tSC states in a 2D strip.
基金
We thank Y. S. Wu, R. B. Tao, T. K. Lee, and A. Varlamov for fruitful discussions. This work was supported by the State Key Programs of Chiaa （Grant Nos. 2017YFA0304204, and 2016YFA0300504） and the National Nat- ural Science Foundation of China （Grant Nos. 11625416 and 11474064）.
