Formation and stability of a singlet optical bipolaron in a parabolic quantum dot

Abstract

The stability of a strong-coupling singlet optical bipolaron is studied for the first time in two- and three-dimensional parabolic quantum dots using the Landau - Pekar variational method. It is shown that the confining potential of the quantum dot reduces the stability of the bipolaron.

On the stability of Fröhlich bipolarons in spherical quantum dots

“…In statistical arguments [29], if one were to imagine an ensemble of n 0 quantum dots and n electrons (n 0 > n) in thermodynamical equilibrium, the inequality ε < 0 would conceptually mean a higher population of quantum dots with two electrons (bipolarons) than those containing only one electron (polarons). Relying on the stability criterion based essentially on this inequality, Mukhopadhyay and Chatterjee [27] and the present authors [30] have reached the conclusion that for strong-coupling polarons the role of the geometric confinement is to disfavour the bipolaron stability in small quantum dots. An outcome along the same lines has been reported by Pokatilov et al [29] under the Feynman variational principle.…”

“…Of particular relevance to the content of the present article are the recent solutions for the bipolaron state in quantum dots [27][28][29][30][31]. In most of the preceding works, including the study of bipolarons in quantum dots, the phase boundary of the bipolaron stability region is determined by the inequality…”

Quasi-two-dimensional Feynman bipolarons

“…[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] Of particular relevance to the content of the present article are the recent solutions of the bipolaron problem in three and strict two dimensions [14][15][16]21 where it is observed that a bipolaronic bound state of two electrons is more easily attained in two dimensions than in three. The concern of the present study is to extend the problem to a broader discourse and explore the stability of quasi-two-dimensional bipolarons confined in a parabolic quantum well with variable well width and potential barrier slopes; thus provide an interpolating insight into the phase diagram, encompassing the bulk and the two-dimensional limits.…”

Path-integral approximation on the stability of large bipolarons in quasi-one-dimensional confinement

“…Over the last decade, proceeding the discovery of high-T c superconductivity, there has appeared a revived and extensive interest in this problem, devoted to the study of the stability criteria of bipolarons adopting different alternative models and approximating theories. Among the numerous amount of papers published within the context of twopolaron systems, we cite a few examples [3][4][5][6][7][8][9][10][11][12][13][14][15] which are relevant to the long-range Fröhlich interaction with the optical phonons. The fundamental conclusion led by these studies is that the domain of stability of bipolarons is determined critically by the upper and lower bounds for the repulsive Coulomb and the attractive electron-phonon coupling strengths, respectively, and that a bipolaron phase can exist only at extreme strong phonon coupling.…”