Strong-coupling theory of two dimensional large bipolarons in elliptical quantum dots

Abstract

In the limit of strong electron-phonon coupling, we analyze the stability of two dimensional bipolarons in a two-axis elliptic potential well of harmonic boundaries. The confined two-polaron wavefunction adopted here makes the electrons to form either a bipolaronic bound state or go into a composite state of two separated polarons bounded inside the same potential well. The methodology involves the mean polaron-polaron separation treated as an adjustable parameter to be determined variationally. By tuning the barrier slopes of the confining potential we obtain an explicit tracking of the criterion for bipolaron stability encompassing the particular cases of a two dimensional circular dot or a planar strip-like quantum well wire. We observe that, while an increased degree of confinement enhances bipolaronic stability, the effect of anisotropy is to inhibit bipolaron formation.