Confined density of states, quantum concentration, and electron degeneracy pressure in low-dimensional systems

2024/10/31 by Andrade, Benedick, Gammag, Rayda
#FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Quantum Gases (cond-mat.quant-gas)

paper · doi:10.48550/arxiv.2410.24180

Abstract

We present a simple derivation of the density of states (DOS) in confined nanomaterials. While previous studies often apply a heuristic L^3-d confinement factor to bulk DOS expressions, we show that this factor arises naturally from a consistent quantum-mechanical treatment of quasi-dimensional systems. Using a Fermi gas model, we calculate carrier concentration in across different dimensions and introduce the concept of quantum concentration n_Q as a statistical threshold for quantum confinement effect. We further demonstrate that the electron degeneracy pressure -- scaling with n^(d+2)/d -- provides a thermodynamic explanation for carrier enhancement under quantum confinement. Our results clarify the origin of DOS modification and provide insights for low-dimensional materials.

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