We design a Stern-Gerlach apparatus that separates quasispin components on
the lattice, without the use of external fields. The effect is engineered using
intrinsic parameters, such as hopping amplitudes and on-site potentials. A
theoretical description of the apparatus relying on a generalized
Foldy-Wouthuysen transformation beyond Dirac points is given. Our results are
verified numerically by means of wavepacket evolution, including an analysis of
Zitterbewegung on the lattice. The necessary tools for microwave realizations,
such as complex hopping amplitudes and chiral effects, are simulated.Comment: 10 pages, 11 figures, added closest version to the published one;
corrected typos, formulas and figures rearranged, added appendi
Abstract. Isospectral transformations of exactly solvable models constitute a fruitful method for obtaining new structures with prescribed properties. In this paper we study the stability group of the Dirac algebra in honeycomb lattices representing graphene or boron nitride. New crystalline arrays with conical (Dirac) points are obtained; in particular, a model for dichalcogenide monolayers is proposed and analyzed. In our studies we encounter unitary and non-unitary transformations. We show that the latter give rise to P T -symmetric Hamiltonians, in compliance with known results in the context of boosted Dirac equations. The results of the unitary part are applied to the description of invariant bandgaps and dispersion relations in materials such as MoS 2 . A careful construction based on atomic orbitals is proposed and the resulting dispersion relation is compared with previous results obtained through DFT.
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