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arXiv:1501.07004 · New Journal of Physics

Spin-orbit coupled repulsive Fermi atoms in a one-dimensional optical lattice

Xiaofan Zhou, Kuang Zhang, J.-Q. Liang, Gang Chen, Suotang Jia

Published Sep 24, 2015• 3 citations

Abstract

Motivated by recent experimental development, we investigate spin–orbit coupled repulsive Fermi atoms in a one-dimensional optical lattice. Using the density-matrix renormalization group method, we calculate the momentum distribution function, gap, and spin-correlation function to reveal rich ground-state properties. We find that spin–orbit coupling (SOC) can generate unconventional momentum distribution, which depends crucially on the filling. We call the corresponding phase with zero gap the SOC-induced metallic phase. We also show that SOC can drive the system from the antiferromagnetic to ferromagnetic Mott insulators with spin rotating. As a result, a second-order quantum phase transition between the spin-rotating ferromagnetic Mott insulator and the SOC-induced metallic phase is predicted at the strong SOC. Here spin rotating means the spin orientations of the nearest-neighbor sites are not parallel or antiparallel, i.e., they have an intersection angle Finally, we show that the momentum k peak , at which the peak of the spin-structure factor appears, can also be affected dramatically by SOC. The analytical expression of this momentum with respect to the SOC strength is also derived, which suggests that the predicted spin-rotating ferromagnetic ( k peak < π /2 ) and antiferromagnetic ( π /2 < k peak < π ) correlations can be detected experimentally by measuring the SOC-dependent spin-structure factor via time-of-flight imaging.

DOI: 10.1088/1367-2630/17/9/093044

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Abstract The dynamic structure factors reflecting the excitation spectra were investigated in a one-dimensional (1D) optical lattice with a spin-orbit coupling (SOC) effect. The results reveal that the single-particle excitations of both the density and spin dynamical structure factors are strongly reconstructed and split owing to the SOC effect, and a hat-like excitation band appears in the high-binding-energy region. The hat-like excitation band of the density dynamical structure factor exhibits an arc form, and has a pocket in the spin dynamical structure factor. In particular, only a gapless single-particle excitation point is left for both the density dynamical structure factor and the spin dynamical structure factor when the SOC strength reaches a critical point at half-filling. A stronger SOC strength causes the gapless excitation points to disappear, which indicates that the metal-insulator transition occurs. The metal-insulator transition only appears in half-filling and lightly doped regimes.

Pairings are the heart for exploring novel superfluid physics of degenerate fermi gases. In the presence of spin-orbit coupling (SOC), some exotic pairings, including the triplet

p

-wave pairing, have been predicted, which paves a new way to search topological superfluids and associated Majorana fermions. In this work, we reveal unconventional pairings induced by SOC in a one-dimensional optical lattice, using the exact density-matrix renormalization group. In the weak SOC, we find the interband Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and intraband Bardeen-Cooper-Schrieffer (BCS) pairings may coexist, when both bands are partially occupied. This interesting coexistence can lead to a new quantum state, called the FFLO-BCS phase, which exhibits a unique three-peak structure in pairing momentum distribution. However, in the intermediate and strong SOCs, the intraband BCS pairing dominates in the whole parameter regime. These results shed great light on the realization of topological superfluids in the spin-orbit coupled lattice.

We investigate the metal-insulator transition (MIT) and phase diagram of the half-filled Fermi Hubbard model with Rashba-type spin-orbit coupling (SOC) on a square optical lattice. The interplay between the atomic interactions and SOC results in distinctive features of the MIT. Significantly, in addition to the diverse spin ordered phases, a nonmagnetic insulating phase emerges in a considerably large regime of parameters near the Mott transition. This phase has a finite single-particle gap but vanishing magnetization and spin correlation exhibits a power-law scaling, suggesting a potential algebraic spin-liquid ground state. These results are confirmed by the non-perturbative cluster dynamical mean-field theory.

Effects of spin-orbit coupling (SOC) on metal-Mott insulator transition (MMIT) and spin exchange physics (SEP) of two-component Fermi gases in two-dimension half-filling square optical lattices are investigated. In the frame of Kotliar and Ruckenstein slave boson and the second order perturbation theory, the phase boundary of paramagnetic MMIT and spin exchange Hamiltonian are calculated. In addition by adopting two mean-field ansatzs including antiferromagnetic, ferromagnetic and spiral phases, we find that SOC can drive a quantum phase transition from antiferromagnet to spiral phase.