TOPOLOGICAL EFFECT ON PERSISTENT CURRENTS AND THE SIGN OF LOW-FIELD CURRENTS IN n-FOLD TWISTED MOEBIUS STRIPS

I investigate persistent currents and the sign of these currents in a low-field limit (ϕ→0) for n-fold twisted Moebius strips threaded by a slowly varying magnetic flux ϕ and describe the effects of the total number of electrons N_e, chemical potential μ, number of twists n, and disorder on these quantities. Transverse hopping strength (v_⊥) of the electrons plays an important role in the periodicity of the persistent current. It is observed that for Moebius strips with an odd number of twists the current shows ϕ₀/2 flux-quantum periodicity only when v_⊥=0, but if the electrons are allowed to hop along the transverse direction, then current shows ϕ₀ flux periodicity for both odd- and even-fold twisted Moebius strips. The sign of the low-field currents also has strong dependence on the number of twists n. For zero transverse hopping strength (v_⊥ = 0) the sign of the currents can be predicted exactly in odd-fold twisted Moebius strips that are characterized by fixed N_e only. For impurity free systems, the current shows only diamagnetic sign irrespective of N_e, i.e., whether the systems contain odd or even N_e. In the presence of impurity, the current shows diamagnetic and paramagnetic sign, respectively, for the systems with odd and even N_e. On the other hand, for non-zero transverse hopping strength (v_⊥≠0), the sign of the low-field currents cannot be predicted exactly. Then it strongly depends on N_e, μ, and the specific realization of disordered configurations.