On the stability of Fröhlich bipolarons in spherical quantum dots

Abstract

In the strong-electron-phonon-coupling regime, we retrieve the stability criterion for bipolaron formation in a spherical quantum dot. The model that we use consists of a pair of electrons immersed in a reservoir of bulk LO phonons and confined within an isotropic parabolic potential box. In this particular quasi-zero-dimensional geometry, where the electrons do not have any free spatial direction to expand indefinitely, a plausible approach would be to treat the electrons either to form a bipolaronic bound state or enter a state of two close, but individual polarons inside the same dot. The confined twopolaron model adopted here involves the polaron-polaron separation introduced as an adjustable parameter to be determined variationally. It is found that the fundamental effect of imposing such a variational flexibility is to modify the phase diagram to a considerable extent and to sustain the bipolaron phase in a broader domain of stability.

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

“…Effective strength of the Coulomb interaction (η) has a critical value determined by the comparison of the energies of bipolaron bound state and state of two polarons, where the condition for a stable bipolaron state is η < η c . In Figure 1 we determine that critical value as η c = 0.130, which is slightly less than the value we calculated previously (0.131) using a simpler wavefunction [9,13]. It is also close to value of 0.115 that was obtained in a variational analysis of an intermediate-coupling bipolaron [14].…”

“…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.…”

“…Of course the exact form of the interaction potential for the two individual polarons in the unbound phase in a quantum dot is not known and MC had to resort to some approximation. Senger and Ercelebi [13] have made an investigation on the stability of a bipolaron in spherical quantum dots using a single hamiltonian which seems to be the correct way of dealing with the bipolaron problem in a confined system. They used a variational method and have obtained a broader range of stability than shown in [8].…”

“…They used a variational method and have obtained a broader range of stability than shown in [8]. The analysis of Senger and Ercelebi [13] however involves Hartree-like wave function for the two-electron system which includes the Coulomb correlation but does not incorporate the Pauli correlation. In the present paper we purport to make an improved calculation based on the Hartree-Fock approximation which takes into account the Coulomb correlation and also the proper antisymmetric behaviour of the two-electron wave function.…”

On the Possibility of Landau-Pekar Triplet Bipolaron Existance

“…As is well known [2], optical excitation of a polaron Franck-Condon transition occurs between the electronic 1s and , 2 z x iy p ± -states, the oscillator strength is ~ 0.9. At the same t ime the possible existence of singlet axially-symmetrical b ipolarons has been widely d iscussed [3][4][5][6][7][8][9][10]. The most probable dipole-actives the optical t ransition for ground state of Landau-Pekar bipolaron will be 1 1 2 (1 )…”