Bipolaron binding in quantum wires

A theory of bipolaron states in quantum wires with a parabolic potential we ll is developed applying the Feynman variational principle. The basic param eters of the bipolaron ground state (the binding energy, the number of phon ons in the bipolaron cloud, the effective mass, and the bipolaron radius) a re studied as a function of sizes of the potential well. Two cases are cons idered in detail: a cylindrical quantum wire and a planar quantum wire. Ana lytical expressions for the bipolaron parameters are obtained at large and small sizes of the quantum well. It is shown that at R much greater than 1 [where R means the radius (half width) of a cylindrical (planar) quantum wi re, expressed in Feynman units], the influence of confinement on the bipola ron binding energy is described by the function similar to 1/R-2 for both c ases, while at small sizes this influence is different in each case. In qua ntum wires, the bipolaron binding energy W(R) increases logarithmically wit h decreasing radius. The shapes and the sizes of a nanostructure, which are favorable for observation of stable bipolaron states, are determined.