Chiral classical states in a rhombus and a rhombi chain of Josephson junctions with two-band superconducting elements

We present a study of Josephson junctions arrays with two-band superconducting elements in the highcapacitance limit. We consider two particular geometries for these arrays: a single rhombus and a rhombi chain with two-band superconducting elements at the spinal positions. We show that the rhombus shaped JJ circuit and the rhombi chain can be mapped onto a triangular JJ circuit and a JJ two-leg ladder, respectively, with zero effective magnetic flux, but with Josephson couplings that are magnetic flux dependent. If the two-band superconductors are in a sign-reversed pairing state, one observes transitions to or from chiral phase configurations in the mapped superconducting arrays when magnetic flux or temperature are varied. The phase diagram for these chiral configurations is discussed. When half-flux quantum threads each rhombus plaquette, new phase configurations of the rhombi chain appear that are characterized by the doubling of the periodicity of the energy density along the chain, with every other two-band superconductor locked in a sign-reversed state. In the case of identical Josephson couplings, the energy of these phase configurations becomes independent of the inner flux in the rhombi chain and the supercurrent along the rhombi chain is zero.