Little-Parks oscillation in a hierarchical superconducting network

Abstract

We have investigated Little-Parks oscillation in a hierarchical superconducting network for searching possible effects of hierarchical structure in terms of spatial symmetry, parity and duality. We prepared a hierarchical honeycomb network, which is obtained to gather 6 hexagons around a hexagon and add 6 rhombuses to large hexagon repeatedly, by standard electron beam lithography and measured variation of superconducting transition temperature (Tc) in a magnetic field. For comparison, we also fabricated regular honeycomb network and measured variation of Tc. The filling ratio f = Ψ/Ψ0 is the magnetic flux Ψ in units of the flux quantum Ψ0 per elementary hexagon. Downward cusps in Tc curves of the regular honeycomb network are observed at f = 1/3,2/5, 1/3,3/5,2/3. This result in range of 0 to 1 is symmetric about f = 1/2 and reminiscent of the report in the recent years. On the other hand, that of the hierarchical honeycomb network are observed at f = 1/5,3/10,4/9, 1/2,5/9,7/10,3/4. The cusps at f = 1/5,3/4 are not symmetric about f = 1/2. It is indicated that duality of vortex configuration on the network break down although system has symmetric structure. This behavior was not even obtained in the case of Sierpinski gasket, which is deterministic fractal form. Therefore this anti-symmetric pattern is due to the effect of hierarchical honeycomb structure in itself.