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

Abstract

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.

Hartree-Fock approximation of bipolaron state in quantum dots and wires

“…One should keep in mind that even though the variational principle is expected to provide reasonably accurate energy upper bounds, validity of predictions regarding the form of the wavefunction and hence the charge density is limited by the approximations made to the exact wavefunction. In our previous treatments of bulk and two-dimensional bipolaron ground states, the variational energy upper bound to the ground state energy was obtained for r 0 = 0, which corresponds to a one-center configuration [13,15]. The origin of the apparent discrepancy between the conclusions of our previous and present calculations on the symmetry of the ground state lies in the degree of flexibility introduced to the variational wavefunctions.…”

“…The argument is based on the necessity of imposing additional constraints (such as virial theorem) in the variational optimization process [17], and leads to a conclusion that a one-center bipolaron ground state is unstable. In view of this argument, the form of the variational wavefunctions introduced in [13] and [15] might not be compatible with the virial theorem. The twocenter structure of the bipolaron ground state is also supported by an analysis of experimental findings [16].…”

Polaron and bipolaron dispersion curves in one dimension for intermediate coupling

“…Many authors have studied energies of large 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15 and small 16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37 38,39,40,41,42,43 bipolarons in various numbers of dimensions, and some have made calculations of bipolaron effective masses at the band minimum. 6,9,10,18,29,33,35,36,37 However, we are not aware of published calculations of bipolaron energies as a function of wave vector which extend to large wave vectors except in the case of small bipolarons when the electron-phonon coupling is strong.…”