Conference

Motivated by results of DMRG and tensor network simulations on doped $t$-$J$ model on honeycomb lattice, we study superconductivity of singlet and triplet pairing in this model. We show that a superconducting state with coexisting spin-singlet and spin-triplet pairings is induced by the antiferromagnetic order near half-filling. The superconducting state we obtain has a topological phase transition that separates a topologically trivial state and a non-trivial state with Chern number two.

We studied t1-t2-J1-J2 model on Honeycomb lattice at finite doping. We find that when t_1 is very small, the t1-t2-J1-J2 model on Honeycomb lattice may be in a supperconducting phase. Such a supperconducting phase is not driven by the pairing, but by entanglement.

We discuss two basic principles to unify the understanding of both cuprates and iron-based superconductors: (1) the correspondence principle— the short range magnetic exchange interactions and the Fermi surfaces act collaboratively to achieve high Tc superconductivity and determine pairing symmetries; (2) the selective magnetic pairing rule: the superconductivity is only induced by the magnetic exchange couplings from the superexchange mechanism through cation-anion-cation chemical bondings but not those from direct exchange couplings resulted from the direct cation's d-d chemical bondings. These two principles provide a unified explanation why the d-wave pairing symmetry and the s-wave pairing symmetry are robust respectively in cuprates and iron-based superconductors. In the meanwhile, the above two principles can serve as direct guiding rules to search new unconventional high Tc superconductors. We propose that the third classes of unconventional high Tc superconducting candidates in compounds formed by cation-anion trigonal bipyramidal complexes with a d7 filling configuration on the cation ions. Their superconducting states are expected to be dominated by the d+id pairing symmetry. Synthesizing these compounds and verifying the prediction can convincingly establish the high Tc superconducting mechanism and pave a way to design new high Tc superconductors