Quantum Monte Carlo study of a dominant s-wave pairing symmetry in iron-based superconductors

Covariant Bethe-Salpeter approximation in models of strongly correlated electron systems

Strongly correlated electron systems are generally described by tight-binding lattice Hamiltonians with strong local (onsite) interactions, the most popular being the Hubbard model. Although the half-filled Hubbard model can be simulated by Monte Carlo (MC), physically more interesting cases beyond half-filling are plagued by the sign problem. One therefore should resort to other methods. It was demonstrated recently that a systematic truncation of the set of Dyson-Schwinger equations for correlators of the Hubbard, supplemented by a "covariant" calculation of correlators leads to a convergent series of approximants. The covariance preserves all the Ward identities among correlators describing various condensed matter probes. While first-order (classical), second-order (Hartree-Fock or Gaussian), and third-order (Cubic) covariant approximation were worked out, the fourth-order (quartic) seems too complicated to be effectively calculable in fermionic systems. It turns out that the complexity of the quartic calculation in local interaction models,is manageable computationally. The quartic (Bethe-Salpeter-type) approximation is especially important in 1D and 2D models in which the symmetry-broken state does not exists (the Mermin-Wagner theorem), although strong fluctuations dominate the physics at strong coupling. Unlike the lower-order approximations, it respects the Mermin-Wagner theorem. The scheme is tested and exemplified on the single-band 1D and 2D Hubbard model.

Unified Phase Diagram for Iron-Based Superconductors

High-temperature superconductivity is closely adjacent to a long-range antiferromagnet, which is called a parent compound. In cuprates, all parent compounds are alike and carrier doping leads to superconductivity, so a unified phase diagram can be drawn. However, the properties of parent compounds for iron-based superconductors show significant diversity and both carrier and isovalent dopings can cause superconductivity, which casts doubt on the idea that there exists a unified phase diagram for them. Here we show that the ordered moments in a variety of iron pnictides are inversely proportional to the effective Curie constants of their nematic susceptibility. This unexpected scaling behavior suggests that the magnetic ground states of iron pnictides can be achieved by tuning the strength of nematic fluctuations. Therefore, a unified phase diagram can be established where superconductivity emerges from a hypothetical parent compound with a large ordered moment but weak nematic fluctuations, which suggests that iron-based superconductors are strongly correlated electron systems.

Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons

We reveal an edge spin triplet p-wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.

Triplet p-wave pairing correlation in low-doped zigzag graphene nanoribbons

We reveal an edge spin triplet p-wave superconducting pairing correlation in slightly doped zigzag graphene nanoribbons. By employing a method that combines random-phase approximation, the finite-temperature determinant quantum Monte Carlo approach, and the ground-state constrained-path quantum Monte Carlo method, it is shown that such a spin-triplet pairing is mediated by the ferromagnetic fluctuations caused by the flat band at the edge. The spin susceptibility and effective pairing interactions at the edge strongly increase as the on-site Coulomb interaction increases, indicating the importance of electron-electron correlations. It is also found that the doping-dependent ground-state p-wave pairing correlation bears some similarity to the famous superconducting dome in the phase diagram of a high-temperature superconductor, while the spin correlation at the edge is weakened as the system is doped away from half filling.

Numerical study of magnetic and pairing correlation in a bilayer triangular lattice

By using the determinant Quantum Monte Carlo method, the magnetic and pairing correlation of the NaxCoO2⋅yH2O system are studied within the Hubbard model on a bilayer triangular lattice. The temperature dependence of the spin correlation function and pairing susceptibility with several kinds of symmetries at different electron fillings and interlayer coupling terms are investigated. It is found that the system shows antiferromagnetic correlation around half filling, and the fn-wave pairing correlation dominates over other kinds of pairing symmetry in the low doping region. As the electron filling decreases from half filling, both ferromagnetic correlation and the f-wave pairing susceptibility are enhanced and tend to dominate. It is also shown that both the magnetic susceptibility and pairing susceptibility decrease as the interlayer coupling increases.