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arXiv:1411.6439

Numerical analysis of spin-orbit coupled one dimensional Fermi gas in the magnetic field

Yang‐Hao Chan

Published Nov 24, 2014• 1 citation
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Abstract

We use the density matrix renormalization group method(DMRG) and the infinite time evolved block decimation method(iTEBD) to investigate the ground states of the spin-orbit coupled Fermi gas in a one dimensional optical lattice with a transverse magnetic field. We discover that the system with attractive interaction can have a polarized insulator(PI), a superconducting phase(SC), a Luther-Emery(LE) phase and a band insulator(BI) phase as we vary the chemical potential and the strength of magnetic field. We find that spin-orbit coupling induces a triplet pairing order at zero momentum with the same critical exponent as that of the singlet pairing one in both the SC and the LE phase. In contrast to the FFLO phase found in the spin imbalanced system without spin-orbit coupling, pairings at finite momentum in these two phases have a larger exponent hence do not dictate the long range behavior. We also find good agreements of the dominant correlations between numerical results and the prediction from the bosonization method. The presence of Majorana fermions is tested. However, unlike results from the mean field study, we do not find positive evidence of Majorana fermions in our system.

DOI
10.48550/arxiv.1411.6439

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The admixture of spin-singlet and spin-triplet pairing states in superconductors can be typically induced by breaking spatial inversion symmetry. Employing the numerically exact auxiliary-field quantum Monte Carlo method, we study such mixed-parity pairing phenomena of attractive fermions with Rashba spin-orbit coupling (SOC) in a two-dimensional optical lattice at finite temperature. We systematically explore the evolution of the essential pairing structure in both singlet and triplet channels versus the temperature, fermion filling, and SOC and interaction strengths, via computing the finite-size results of the condensate fraction and pair wave function. Our numerical results reveal that the singlet channel dominates in the fermion pairing and the triplet pairing has a relatively small contribution to the superfluidity for physically relevant parameters. In contrast to the singlet channel mainly consisting of the on-site Cooper pairs, the triplet pairing has plentiful patterns in real space with the largest contributions from several nearest neighbors. As the SOC strength increases, the pairing correlation is first enhanced and then suppressed for triplet pairing while it is simply weakened in the singlet channel. We have also obtained the Berezinskii-Kosterlitz-Thouless transition temperatures through the finite-size analysis of the condensate fraction. Our results can serve as a quantitative guide for future optical lattice experiments as well as accurate benchmarks for theories and other numerical methods.