Superconductivity in twisted multilayer graphene:A smoking gun in recent condensed matter physics

We review the recent discoveries of exotic phenomena in graphene,especially superconductivity.It has been theoretically suggested for more than one decade that superconductivity may emerge in doped graphene-based materials.For single-layer pristine graphene,there are theoretical predictions that spin-singlet d+id pairing superconductivity is present when the filling is around the Dirac point.If the Fermi level is doped to the Van Hove singularity where the density of states diverges,then unconventional superconductivity with other pairing symmetry would appear.However,the experimental perspective was a bit disappointing.Despite extensive experimental efforts,superconductivity was not found in monolayer graphene.Recently,unconventional superconductivity was found in magic-angle twisted bilayer graphene.Superconductivity was also found in ABC stacked trilayer graphene and other systems.In this article,we review the unique properties of superconducting states in graphene,experimentally controlling the superconductivity in twisted bilayer graphene,as well as a gate-tunable Mott insulator,and the superconductivity in trilayer graphene.These discoveries have attracted the attention of a large number of physicists.The study of the electronic correlated states in twisted multilayer graphene serves as a smoking gun in recent condensed matter physics.

Coexistence of Charge Order and Antiferromagnetic Order in an Extended Periodic Anderson Model

The competition between the RKKY interaction and the Kondo effect leads to a magnetic phase transition,which occurs ubiquitously in heavy fermion materials.However,there are more and more experimental evidences indicating that the valence fluctuation plays an essential role in the Ce-and Y-based compounds.We study an extended periodic Anderson model(EPAM)which includes the onsite Coulomb repulsion Ucf between the localized electrons and conduction electrons.By employing the density matrix embedding theory,we investigate the EPAM in the symmetric case at half filling.By fixing the onsite Coulomb repulsion U of the localized electrons to an intermediate value,the interplay between the RKKY interaction,the Kondo effect and the Coulomb repulsion Ucf brings rich physics.We find three different phases,the antiferromagnetic phase,the charge order phase and paramagnetic phase.When the hybridization strength V between the localized orbital and the conduction orbital is small,the Kondo effect is weak so that the AF phase and the CO phase are present.The phase transition between the two long-range ordered phase is of first order.We also find a coexistence region between the two phases.As V increases,the Kondo effect becomes stronger,and the paramagnetic phase appears between the other two phases.