Talks

We report on our recent progress to investigate materials classes exhibiting d+id superconductivity, where topologically nontrivial pairing phases can emerge. Specifically, motivated by recent experimental progress, we show that graphene doped to the van Hove regime can give rise to a plethora of interesting ordering instabilities such as spin density wave and superconductivity. As a function of system parameters such as doping and range of Coulomb interaction, we explain which instability is favored by the system, and analyze the effect of long-range interactions on superconductivity giving rise to a competition between singlet d+id and triplet f wave. We also outline our work in progress for other materials classes which we believe are promising to stabilize such interesting topological superconducting states of matter.

It has been well-known that topological phenomena with fractional excitations, i.e., the fractional quantum Hall effect (FQHE) will emerge when electrons move in Landau levels. In this talk, I will show FQHE can emergy even in the absence of Landau levels in interacting fermion models and boson models. The non-interacting part of our Hamiltonian contains topologically nontrivial flat band.

The parity invariance of spinfoam gravity is an open question. Naively, parity breaking should reside in the sign of the Immirzi parameter. I show that the new Lorentzian vertex formula is in fact independent of this sign, suggesting that the dynamics is parity-invariant. The situation with boundary states and operators is more complicated. I discuss parity-related pieces of the transition amplitude and graviton propagator in the large-spin 4-simplex limit. Numerical results indicate patterns similar to those in the Euclidean case. In particular, parity-related components of the graviton propagator differ by a phase. I discuss possible resolutions of this issue.