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Properties of some Hamiltonians describing topologically non-trivial fermionic systems

Mera, B. ; Vieira, V. ; Araújo, M.

Condensed Matter Physics Vol. 27, Nº 46, pp. 465501 - 465501, October, 2015.

ISSN (print): 1607-324X
ISSN (online): 2224-9079

Journal Impact Factor: 0,488 (in 2008)

Digital Object Identifier: 10.1088/0953-8984/27/46/465501

We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a ${{mathbb{Z}}_{2}}$ -topological invariant $pleft(mathbf{k}
ight)$ (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.