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

Abstract

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 Ne, 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 Ne only. For impurity free systems, the current shows only diamagnetic sign irrespective of Ne, i.e., whether the systems contain odd or even Ne. In the presence of impurity, the current shows diamagnetic and paramagnetic sign, respectively, for the systems with odd and even Ne. 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 Ne, μ, and the specific realization of disordered configurations.