“…One expects that the interedge coupling of states and enhanced size effects in a GQR will lead to some new physical properties, therefore, it may be one of the most novel building blocks for future nanodevices. Currently, there are several groups contributing their work to studies of GQRs, either experimentally [5,16,17] or theoretically [18][19][20][21][22][23][24]. The experimental investigations mainly focus on external magnetically induced Aharonov-Bohm (AB) effects [5,16,17] and Shubnikov-de Haas (SdH) oscillations [16] in GQRs, and theoretical studies basically concentrate on using the usual tight-binding (TB) model to explore the AB oscillation [18][19][20], persistent currents [21], and energy spectra as a function of the magnetic flux [22].…”