The geometry of a flux lattice pinned by superconducting layers is studied. Under variation of magnetic field the lattice undergoes an infinite sequence of continuous transitions corresponding to different ways of selection of shortest distances. All possible lattices form a hierarchical structure identified as the hierarchy of Farey numbers. It is shown that dynamically accessible lattices are characterized by pairs of consecutive Fibonacci numbers.
- Received 24 August 1990
- Published in the issue dated 14 January 1991
© 1991 The American Physical Society