SUPERCONDUCTING NETWORK WITH MAGNETIC DECORATION — HOFSTADTER BUTTERFLY IN SPATIALLY MODULATED MAGNETIC FIELD

Abstract

Energy spectrum of tight-binding electrons on a two-dimensional (2D) square lattice under a magnetic field perpendicular to the plane has an exquisite structure, known as Hofstadter butterfly. Spectra for 2D lattices with a variety of symmetry have been calculated.3–6 Experimental verification of the full Hofstadter butterfly spectra is a formidable task, although such an attempt using semiconductor lateral superlattice seems to attain a certain degree of success. Superconducting wire network constitutes an experimental system intimately related to the Hofstadter problem. It has been demonstrated that the Little-Parks oscillation of transition temperature Tc of a superconducting wire network exhibits fine structures at commensurate values of average flux per unit cell, and that ∆Tc(H) reproduces the edge shape of the Hofstadter spectrum for the corresponding 2D lattice. These and the majority of subsequent studies were conducted in a uniform magnetic field. In the present study, we address ourselves to the case of spatially varying magnetic field, extending our previous work. In the next Section, we calculate the spectra for a square lattice subjected to both a spatially varying and a uniform magnetic field. Section 3 describes experiment using superconductor/ferromagnet hybrid systems. A brief summary is given in Section 4.