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arXiv · 1507.02460

A theorem regarding families of topologically non-trivial fermionic systems

Bruno Mera·Miguel A. N. Araújo·Vítor R. Vieira
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Abstract

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 $p(\textbf{k})$ (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.

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Bruno Mera, Miguel A. N. Araújo, Vítor R. Vieira. 2015-07-09. A theorem regarding families of topologically non-trivial fermionic systems. https://doi.org/10.1088/0953-8984/27/46/465501

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