Motivated by recent experiments on ultracold fermions we study the effect of the spin-orbit interaction in an exactly solvable one-dimensional model with strong local attractive correlations between the fermions. We show that the asymptotes of correlation functions, calculated in the framework of the conformal field theory and finite size corrections of the Bethe ansatz exact solution, are strongly affected by the spin-orbit coupling. In the mixed phase, the correlation functions consist of terms that are the product of a power law of the distance and an oscillating function of the distance. We obtain the critical exponents for superfluidity and density waves. The leading exponents decrease as a function of spin-orbit coupling. In particular, the exponent for superfluidity is the smallest one signaling an instability to a phase where a weak interchain coupling can produce superfluidity of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type. The spatial oscillation of the order parameter is also modified by the spin-orbit parameter, i.e., its modulation is not just given by the spin imbalance.
Based on the density-matrix renormalization group and the infinite time-evolving block decimation methods we study the interacting spin-orbit-coupled 1D Fermi gas in a transverse magnetic field. We find that the system with an attractive interaction can have a polarized insulator phase, a superconducting (SC) phase, a Luther-Emery (LE) phase, and a band insulator phase as we vary the chemical potential and the strength of the magnetic field. Spin-orbit coupling (SOC) enhances the triplet pairing order at zero momentum in both the SC and the LE phase, which leads to an algebraically decaying correlation with the same exponent as that of the singlet pairing one. In contrast to the Fulde-Ferrell-Larkin-Ovchinnikov phase found in the spin imbalanced system without SOC, pairings at finite momentum in these two phases have larger exponents hence do not dictate the long-range behavior. We also test for the presence of Majorana fermions in this system. Unlike results from the mean-field study, we do not find positive evidence of Majorana fermions.
The leading superconducting instabilities of the two-dimensional extended repulsive one-band Hubbard model within spin-fluctuation pairing theory depend sensitively on electron density, band, and interaction parameters. We map out the phase diagrams within a random-phase-approximation spin- and charge-fluctuation approach, and find that while
B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) and
B2g (
dxy) pairing dominates in the absence of repulsive longer-range Coulomb interactions
VNN, the latter induces pairing in other symmetry channels, including, e.g.,
A2g (
g-wave), nodal
A1g (extended
s-wave), or nodal
Eu (
p-wave) spin-triplet superconductivity. At the lowest temperatures, transition boundaries in the phase diagrams between symmetry-distinct spin-singlet orders generate complex time-reversal symmetry broken superpositions. By contrast, we find that boundaries between singlet and triplet regions are characterized by first-order transitions. Finally, motivated by recent photoemission experiments, we have determined the influence of an additional explicitly attractive nearest-neighbor interaction,
VNN<0, on the superconducting gap structure. Depending on the electronic filling, such an attraction boosts
Eu (
p-wave) spin-triplet or
B1g (${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$) spin-singlet ordering.
We present a new model for the study of spin-orbit coupling in interacting quasi-one-dimensional systems and solve it exactly to find the spectral properties of such systems. We show that the combination of spin-orbit coupling and electron-electron interactions results in the replacement of separate spin and charge excitations with two new kinds of bosonic mixed-spin-charge excitation, and a characteristic modification of the spectral function and single-particle density of states. Our results show how manipulation of the spin-orbit coupling, with external electric fields, can be used for the experimental determination of microscopic interaction parameters in quantum wires.
We present the zero-temperature phase diagram of the one-dimensional
t2g-orbital Hubbard model, obtained using the density-matrix renormalization group and Lanczos techniques. Emphasis is given to the case of the electron density
n=5 corresponding to five electrons per site, while several other cases for electron densities between
n=3 and 6 are also studied. At
n=5, our results indicate a first-order transition between a paramagnetic (PM) insulator phase, with power-law slowly decaying correlations, and a fully polarized ferromagnetic (FM) state by tuning the Hund's coupling. The results also suggest a transition from the
n=5 PM insulator phase to a metallic regime by changing the electron density, either via hole or electron doping. The behavior of the spin, charge, and orbital correlation functions in the FM and PM states are also described in the text and discussed. The robustness of these two states against varying parameters suggests that they may be of relevance in quasi-one-dimensional Co-oxide materials, or even in higher dimensional cobaltite systems as well.
We study the effects of disorder on a system of two coupled chains of strongly correlated fermions (the ladder system), using a renormalization-group technique. The stability of the phases of the pure system has been investigated as a function of interactions both for fermions with spin and spinless fermions. For spinless fermions the repulsive side is strongly localized whereas the system with attractive interactions is stable with respect to disorder, at variance with the single-chain case. For fermions with spins, the repulsive side is also localized, and in particular the
d-wave superconducting phase found for the pure system is totally destroyed by an arbitrarily small amount of disorder. On the other hand, the attractive side is again remarkably stable with respect to localization. We have also computed the charge stiffness, the localization length, and the temperature dependence of the conductivity for the various phases. In the parameter range where
d-wave superconductivity would occur for the pure system the conductivity is found to decrease monotonically with temperature, even at high temperature, and we discuss this surprising result. For a model with one-site repulsion and nearest-neighbor attraction, the most stable phase is an orbital antiferromagnet. Although this phase has no divergent superconducting fluctuation it can have a divergent conductivity at low temperature. Finally, to make a comparison of our results with experimental ladder systems, we treated the interladder coupling in a mean-field approximation. We argue based on our results that the superconductivity observed in some of these compounds cannot be a simple stabilization of the
d-wave phase found for a pure single ladder. The application of our results to systems such as quantum wires is also discussed. In particular, the corrections to conductance in a two-channel quantum wire have been obtained as a function of system length, temperature, and interactions.