Basic idea of Corbino-type single-electron transistor

We have formulated the transmission probability of an electron in a Corbino quantum disk by taking into account charging effect. The geometrical potential of the Corbino disk has a singularity at the centre of the disk. In order to avoid this singularity problem, we have to reformulate the Schrödinger equation in the Riemannian manifold. The Schrödinger equation describing the motion of the electron in the Corbino disk must be expressed by introducing a momentum operator reformed by the metric tensor. In order to obtain a Hermitian momentum operator, we must deform the Hilbert space by introducing a new wave function. This deformation leads to the extra potential term in the Schroodinger equation, which depends on the metric, i.e., the geometry of the disk. It should be noted that the charging energy of confining electrons in the Corbino disk should depend on the geometry of the disk. We discuss the quantum tunneling of an electron confined in the Corbino disk in order to investigate the effect of both geometrical potential and charging energy of confining electrons in the Corbino disk by using the Wentzel-Kramers-Brillouin (WKB) method. It is expected that the charging energy, which depends on the effective confining potential, plays an important role in the transmission probability. This suggests that the formulated transmission probability is applicable to the analysis of the single-electron transistor.