THE CAPACITANCE MODEL FOR PERSISTENT CURRENTS IN MESOSCOPIC METAL RINGS

We review recent theoretical work on persistent currents in mesoscopic normal-metal rings and present a detailed discussion the generalized capacitance model.(20(a)) This model provides a natural explanation fo r the surprisingly large experimentally observed currents in the diffu sive regime. We pay particular attention to the problem of screening i n a thin mesoscopic ring, and argue that screening corrections to the flux-dependent part of the Hartree energy are negligible provided the condition (e(2)/C-0)partial derivative N(E(c))/partial derivative mu m uch less than 1 is satisfied. Here e(2)/C-0 is the classical charging energy for adding one electron to the system, and N(E(c)) is the avera ge number of energy levels within an interval of width E, below the Fe rmi energy mu, where Ec is the Thouless energy. This condition is equi valent With (k(F)l)(L(perpendicular to)/L)(2) much less than 1 (where l is the elastic mean free path, L is the circumference and L(perpendi cular to) is the transverse thickness of the ring), and shows that the ring geometry plays an important role. In thin rings the mesoscopic p ersistent current is universal in precisely the same sense as the vari ance of the conductance.