Dynamic polarizability of low-dimensional excitons

TL;DR

This paper develops a unified mathematical framework to compute the dynamic polarizability of low-dimensional excitons modeled as fractional-dimensional hydrogen-like systems, revealing the significance of continuum states especially in lower dimensions.

Contribution

It introduces a general formula for exciton polarizability in fractional dimensions, incorporating both discrete and continuum oscillator strengths, and analyzes their impact across dimensions.

Findings

Continuum contributions grow in importance as dimensionality decreases.

A closed-form expression for dynamic polarizability valid for any frequency and dimension is derived.

Comparison of excitonic responses across different fractional dimensions is provided.

Abstract

Excitons in low-dimensional materials behave mathematically as confined hydrogen atoms. An appealing unified description of confinement in quantum wells or wires, etc., is found by restricting space to a fractional dimension 1 < D <= 3 serving as an adjustable parameter. We compute the dynamic polarizability of D-dimensional excitons in terms of discrete and continuum oscillator strengths. Analyzing exact sum rules, we show that continuum contributions are increasingly important in low dimensions. The dynamical responses of excitons in various dimensions are compared. Finally, an exact and compact closed-form expression for the dynamic polarizability is found. This completely general formula takes D as input and provides exact results for arbitrary frequency.