Flat-band conditions influenced by spin-orbit interaction in the presence of external magnetic field

Abstract

We deduct conditions for the Hamiltonian coupling strengths necessary to achieve flat bands in polymers (i.e. a pentagon chain) considering many-body spin-orbit coupling and external magnetic field. We consider itinerant electrons on pentagon chains with first neighbour hoppings, on-site electron potentials and spin-flip first neighbour hoppings representing the Rashba type spin-orbit interaction (SOI). The external magnetic field is also present in the system via the Peierls phase factors. The band structure is obtained by solving the secular equation of the diagonalized one particle part of the Hamiltonian in k-space (momentum-space). The flat band conditions make the bands k-independent, providing a highly a degenerate state, which gives broad possibilities for applications. In our work we have shown how the SOI is able to relax the strict, rigid flat band conditions given by the Hamiltonian coupling strengths. The role of the external magnetic field was also investigated.