Two-dimensional hexagonal and oblique lattices were investigated theoretically with the aim of observing differences in the spin expectation values between chiral and achiral systems. The spin-resolved band structures were derived from the energy eigenvalues and eigenfunctions of a Hamiltonian that includes the lattice potential and the spin-orbit interaction. The spin texture of the achiral hexagonal system was shown to have two nonzero components of the spin polarization, whereas all three components were calculated to be nonzero for the chiral system. The longitudinal component, found to be zero in the achiral lattice, was observed to invert between the enantiomorphs of the chiral lattice. A heuristic model was introduced to discern the origin of this inverting spin polarization by considering the dynamics of an electron in chiral and achiral lattices. This model was further used to demonstrate the change in magnitude of the spin polarization as a function of the lattice parameters and an electric field perpendicular to the lattice.

• Received 22 May 2018

DOI:https://doi.org/10.1103/PhysRevB.97.235427

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