Persistent Current of Dirac Sea: Application to Bismuth

Bismuth has been known to exhibit anomalously large diamagnetism which has been interpreted on the basis of the effective Hamiltonian of the Dirac type including spin-orbit coupling. Here the persistent current in a mesoscopic ring of bismuth is calculated. It is found that the magnetic flux induces persistent currents which have a spatial spread of the order of \(ξ =2 v/EG\) ( v : velocity of the `Dirac' electron; E G : energy gap), just as in the atomic diamagnetism whose “atomic” size is gigantic and of mesoscopic scale.