Stability of low-dimensionally-confined bipolarons

Abstract

Abstract. In the limit of strong electron-phonon coupling, we provide a unified insight into the stability criterion for bipolaron formation in low-dimensionally confined media. The model that we use consists of a pair of electrons immersed in a reservoir of bulk LO phonons and confined within an anisotropic parabolic potential box, whose barrier slopes can be tuned arbitrarily from zero to infinity. Thus, encompassing the bulk and all low-dimensional geometric configurations of general interest, we obtain an explicit tracking of the critical ratio ηc of dielectric constants below which bipolarons can exist. PACS. 71.38.+i Polarons and electron-phonon interactions

Fröhlich polaron and bipolaron: recent developments

“…It was found that confinement can enhance the bipolaron binding energy, when the radius of a quantum dot is of the same order of magnitude as the polaron radius. A unified insight into the stability criterion for bipolaron formation in low-dimensionally confined media was provided by (Senger and Ercelebi, 2000) using an adiabatic variational method for a pair of electrons immersed in a reservoir of bulk LO phonons and confined within an anisotropic parabolic potential box. Bipolaron formation in a two-dimensional lattice with harmonic confinement, representing a simplified model for a quantum dot, was investigated by means of QMC (Hohenadler et al , 2007a).…”

Quantum Monte Carlo results for bipolaron stability in quantum dots

“…( 2) is of the same form as in previous studies of bipolarons in quantum dots. 8,11,12,14 An important difference between previous work and our lattice model is that u ij does not diverge for r i = r j . Instead, there is a finite Hubbard U > 0 for two electrons at the same site, which we believe to be more appropriate for a discussion of small bipolaron states.…”

“…6,7,8,9,10 and references therein), conflicting results exist on the stability of bipolarons. 3,8,10,11,12,13,14 These calculations are based on variational treatments, with several works employing strongcoupling or adiabatic approximations. It is known from studies of polaron and bipolaron formation that such methods are not able to fully capture the relevant physics, 2,15,16 and their use hence represents a possible source of the contradictory findings.…”

Bipolaron formation in 1D–3D quantum dots: a lattice quantum Monte Carlo approach

“…In previous strong-coupling calculations in the framework of the continuum model [ [24][25][26], it has been found that the bound bipolaron state becomes unstable at very strong confinement, which was attributed to the increase of the Coulomb interaction energy for two spatially close particles. However, this effect has been argued [23,26] to be due to the approximations made, and path-integral calculations [23] as well as analytical and QMC calculations [17] suggest that a bound state also exists at weak coupling in a confined system. Preliminary calculations of the bipolaron binding energy E f (N e = 2) − 2E f (N e = 1) for γ = 0.1 and U/t = 4 at K/t = 0.1 and K/t = 2.0 in one dimension reveal that a weakly bound bipolaron can indeed become unbound due to confinement.…”

“…From this work, the general conclusion is that confinement enhances the tendency of an electron to undergo a crossover to a (small) polaron so that heavy polaronic quasiparticles may be realised experimentally even in the weak or intermediate electron-phonon coupling regime. Less work has been devoted to understand bipolaron formation in quantum dots [17,[23][24][25][26], with contradictory results on the effect of confinement [23,26].…”