Polaron effect in $\mathrm{GaAs}-{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum wells: A fractional-dimensional space approach

The binding energy and the effective mass of a polaron confined in a $\mathrm{GaAs}-{\mathrm{Ga}}_{1-x}{\mathrm{Al}}_x\mathrm{As}$ quantum well are calculated within the framework of the fractional-dimensional space approach. In this scheme, the real confined “polaron plus quantum well” system is mapped onto an effective fractional-dimensional bulk in which the polaron behaves unconfined, and the fractional dimension is essentially related to the degree of confinement of the actual system. Analytical expressions allowing a very simple estimation of the corresponding polaron corrections are found. The fractional-dimensional theoretical results are shown to be in good agreement with previous more detailed calculations.