Confined density of states, quantum concentration, and electron degeneracy pressure in low-dimensional systems
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910006390030336 |
|---|---|
| author | Andrade, Benedick Gammag, Rayda |
| author_facet | Andrade, Benedick Gammag, Rayda |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_24180 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Confined density of states, quantum concentration, and electron degeneracy pressure in low-dimensional systems Andrade, Benedick Gammag, Rayda Quantum Gases Materials Science 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. |
| title | Confined density of states, quantum concentration, and electron degeneracy pressure in low-dimensional systems |
| topic | Quantum Gases Materials Science |
| url | https://arxiv.org/abs/2410.24180 |