Properties of some Hamiltonians describing topologically non-trivial fermionic systems.

We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a [Formula: see text]-topological invariant [Formula: see text] (the Pfaffian polynomial). The topological invariant is not only the first Chern number, but also the sign of the Pfaffian polynomial coming from a notion of duality. Such Hamiltonian can describe non-trivial Chern insulators, single band superconductors or multiorbital superconductors. The topological features of these families are completely determined as a consequence of our theorem. Some specific model examples are explicitly worked out, with the computation of different possible topological invariants.

Correlated magnetic impurities in a superconductor: electron density profiles and robustness of superconductivity.

The insertion of magnetic impurities in a conventional superconductor leads to various effects. In this work we show that the electron density is affected by the spins (considered as classical) both locally and globally. The charge accumulation is solved self-consistently. This affects the transport properties along magnetic domain walls. Also, we show that superconductivity is more robust if the spin locations are not random but correlated.