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.
CeFEMA, Instituto Superior Técnico, Universidade Técnica de Lisboa, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal. Physics of Information Group, Instituto de Telecomunicações, 1049-001 Lisbon, Portugal.
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