Strong coupling characterisation of quasi-1D polarons in cylindrical QW-wires

Abstract

We retrieve, within the strong-coupling theory, the quasi-one dimensional analog of the standard optical polaron relevant to a cylindrical quantum well wire. Under the assumption of perfect confinement the ground state binding energy, effective polaronic mass and the phononcoupling-induced potential well profiles are given as a function of the wire radius and the electron-phonon interaction strength.

Path integral description of low-dimensional polarons in parabolic confinement potentials

“…A complementary remark that we might make in this regard is that, for a large , one requires a correspondingly large α for the polaron to conform to its bulk characterization, and, in particular, in the strict 2D limit ( → ∞) of the slab-like confinement, one should correspondingly have α → ∞. This feature can readily be seen from the fact that the upper dashed curves in the figure tend to the two-dimensional limiting values, 3π 2 /8 and 81π 4 /256, for the energy and mass, respectively.…”

“…The ground-state energy, for instance, becomes lowered by a factor of π/2 ( 3 8 π 2 ) below its corresponding bulk value for weak (strong) coupling as the dimensionality is reduced from three to two [1,2]. For systems of even lower dimensionality, namely quasi-one-dimensional (Q1D) quantum well wires, the polaron binding is even deeper, with much stronger electron-phonon coupling than in comparable quasi-two-dimensional (Q2D) quantum well structures [3,4]. Going on further to confinement geometries squeezing the electronic density in all directions, such as is found, for instance, in zero-dimensional (Q0D) quantum-box-type configurations, the pseudo-enhancement in the effective electron-phonon coupling can be much more sturdy than for the two-or one-dimensional cases.…”

Polaron in a quasi 1D cylindrical quantum wire

“…This shows that as R → 0 the weak and intermediate regions vanish. The behaviors in figures 1 and 2 differ from those in [51][52][53][54] only in their logarithmic dependence. Our results confirm those in [33,48,54] in that the polaron energy and mass increase with a decrease of a radius of the cylindrical quantum wire.…”