Marcello Porta

Bulk-Edge Correspondence for Two-Dimensional Topological Insulators

Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle picture. We give a new formulation of the

Lattice gauge theory model for graphene

{\mathbb{Z}_{2}}

Mean-field dynamics of fermions with relativistic dispersion

Z2-invariant, which allows for a bulk index not relying on a (two-dimensional) Brillouin zone. When available though, that index is shown to agree with known formulations. The method also applies to integer quantum Hall systems. We discuss a further variant of the correspondence, based on scattering theory.

Universality of the Hall Conductivity in Interacting Electron Systems

The exact vanishing of the interaction corrections to the zero temperature optical conductivity of undoped graphene in the presence of weak short-range interactions is rigorously established. Our results are in agreement with measurements of graphene’s ac conductivity in a range of frequencies between the temperature and the bandwidth. Even if irrelevant in the renormalization group sense, lattice effects and nonlinear bands are essential for the universality of the conductivity. DOI: 10.1103/PhysRevB.83.195401

From the Hartree Dynamics to the Vlasov Equation

The effects of the electromagnetic (em) electron-electron interactions in half-filled graphene are investigated in terms of a lattice gauge theory model. By using exact renormalization group methods and lattice Ward identities, we show that the em interactions amplify the responses to the excitonic pairings associated to a Kekule distortion and to a charge-density wave. The effect of the electronic repulsion on the Peierls-Kekule instability, usually neglected, is evaluated by deriving an exact non BCS gap equation, from which we find evidence that strong em interactions among electrons facilitate the spontaneous distortion of the lattice and the opening of a gap.

Anomalous behavior in an effective model of graphene with Coulomb interactions

The Hubbard model on the honeycomb lattice describes charge carriers in graphene with short range interactions. While the interaction modifies several physical quantities, like the value of the Fermi velocity or the wave function renormalization, the a.c. conductivity has a universal value independent of the microscopic details of the model: there are no interaction corrections, provided that the interaction is weak enough and that the system is at half filling. We give a rigorous proof of this fact, based on exact Ward Identities and on constructive Renormalization Group methods.

Mean Field Evolution of Fermions with Coulomb Interaction

We extend the derivation of the time-dependent Hartree-Fock equation recently obtained by Benedikter et al. [“Mean-field evolution of fermionic systems,” Commun. Math. Phys. (to be published)] to fermions with a relativistic dispersion law. The main new ingredient is the propagation of semiclassical commutator bounds along the pseudo-relativistic Hartree-Fock evolution.

Spin Hall insulators beyond the helical Luttinger model

We prove the quantization of the Hall conductivity for general weakly interacting gapped fermionic systems on two-dimensional periodic lattices. The proof is based on fermionic cluster expansion techniques combined with lattice Ward identities, and on a reconstruction theorem that allows us to compute the Kubo conductivity as the analytic continuation of its imaginary time counterpart.