# Research Investigação

## Persistent Currents in Mesoscopic Rings

The mesoscopic systems occur in a size range between the microscopic and the macroscopic
systems, corresponding to systems that are realized and form a bridge between quantum and classical physics.
The mesoscopic systems, which include nanostructures, not only provide a way to understand the transition from
quantum to classical but also exhibit a variety of novel phenomena of great interest, both from the fundamental
side and the side of technological applications. The small size of the systems determines the appearance of
quantum effects, such as in conducting systems, the discrete spectrum of the electronic states and the coherent
motion of the electrons, which reflect in the properties of the system.

An interesting phenomena is that of the existence of persistent currents in mesoscopic metallic rings pierced
by a magnetic flux. Those currents were first experimentally observed in 1990. [1] The persistent currents are
periodic in the magnetic flux F, with period of a quantum flux F o. The experimental results show some
surprising features, the most significant being that the currents observed in diffusive metallic rings, as well
as the average currents measured in ensembles of rings, are larger by more than one order of magnitude than
expected from theories with disorder but non-interacting electrons or perturbative theories in the electron
interaction. [2] It is then important to study the problem by numerical methods in order to gain physical
insight into it.

Our work is concerned with the study of persistent currents in mesoscopic rings, focusing on the investigation
of the role of electron-electron interaction and its interplay with disorder, using a powerful numerical method,
the density matrix renormalization group (DMRG) [3] algorithm.

This work has been carried out in collaboration with M. Henkel (Université Henri Poincaré Nancy, France).

### References

- L. P. Lévy, G. Dolan, J. Dunsmuir and H. Bouchiat, Phys. Rev. Lett.
**64**, 2074 (1990).
- U. Eckern and P. Schwab, Adv. Phys.
**44**, 387 (1995).
- S. White, Phys. Rev. Lett.
**69**, 2863 (1992).