The Aharonov–Bohm effect in quadratic Gauss quantum rings

Abstract

Abstract We outline a theory for the Aharonov–Bohm effect in a novel type of quantum ring, namely the quadratic Gauss quantum ring, here for brevity called the Gauss ring. A Gauss ring is a one-dimensional nonperiodic lattice with sites at z = z j = j n d with j ∈ {0, 1, 2, ⋯ , s + 1} ( s ∈ W ), n ≥ 2 ( n ∈ N ), and d the underlying period wrapped into a ring-shaped geometry. Here we discuss the electronic spectrum of quadratic Gauss rings (n = 2, s ∈ {0, 1, 2, ⋯ , 5, 6, 7}), and show that the spectrum can be described using theoretical tools recently devised to provide an understanding of the Gauss chain [D S Citrin (2023) Phys. Rev. B 107, 235 144]. We then consider the effect on the electronic states of a magnetic flux Φ threading the Gauss ring and show that the effect of the flux is to select specific electronic states from a periodic chain whose supercells are finite-length Gauss chains thus relating the states in the Gauss quantum ring with those in a periodic Gauss chain.