Numerical Investigation of Stub Length Influence on Dispersion Relations and Parity Effect in Aharonov-Bohm Rings
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909639095877632 |
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| author | Ghosh, Souvik |
| author_facet | Ghosh, Souvik |
| contents | Aharonov-Bohm (AB) rings with side-attached stubs are model systems for quantum-interference studies in mesoscopic physics. The geometry of such systems, particularly the ratio of stub length ($v$) to ring circumference ($u$), can significantly alter their electronic states. In this work, we solve Deo's transcendental mode-condition equation (Eq. 2.15 from Deo, 2021 [Deo2021]) numerically -- using Python's NumPy and SciPy libraries -- for ring-stub geometries with $v/u = 0.200, 0.205,$ and $0.210$ to generate dispersion relations ($ku$ vs. $Φ/Φ_{0}$) and the underlying function $\text{Re}(1/T)$. We find that changing $v/u$ shifts several of the six lowest calculated dispersion branches, with $Δ(ku)$ up to approximately $0.34$ for the 6th branch at $Φ=0$ when comparing $v/u=0.200$ and $v/u=0.210$. This also alters gap widths. Notably, for $v/u=0.205$ and $v/u=0.210$, the 5th and 6th consecutive calculated modes both exhibit paramagnetic slopes near zero Aharonov-Bohm flux, indicating the parity breakdown initiates at or below $v/u=0.205$. This directly demonstrates a breakdown of the simple alternating parity effect predicted by Deo (2021) [Deo2021]. These results highlight the sensitivity of mesoscopic ring spectra to fine-tuning of stub length, with potential implications for experimental control of persistent currents, as further illustrated by calculations of the net current. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_04727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical Investigation of Stub Length Influence on Dispersion Relations and Parity Effect in Aharonov-Bohm Rings Ghosh, Souvik Materials Science Mesoscale and Nanoscale Physics Aharonov-Bohm (AB) rings with side-attached stubs are model systems for quantum-interference studies in mesoscopic physics. The geometry of such systems, particularly the ratio of stub length ($v$) to ring circumference ($u$), can significantly alter their electronic states. In this work, we solve Deo's transcendental mode-condition equation (Eq. 2.15 from Deo, 2021 [Deo2021]) numerically -- using Python's NumPy and SciPy libraries -- for ring-stub geometries with $v/u = 0.200, 0.205,$ and $0.210$ to generate dispersion relations ($ku$ vs. $Φ/Φ_{0}$) and the underlying function $\text{Re}(1/T)$. We find that changing $v/u$ shifts several of the six lowest calculated dispersion branches, with $Δ(ku)$ up to approximately $0.34$ for the 6th branch at $Φ=0$ when comparing $v/u=0.200$ and $v/u=0.210$. This also alters gap widths. Notably, for $v/u=0.205$ and $v/u=0.210$, the 5th and 6th consecutive calculated modes both exhibit paramagnetic slopes near zero Aharonov-Bohm flux, indicating the parity breakdown initiates at or below $v/u=0.205$. This directly demonstrates a breakdown of the simple alternating parity effect predicted by Deo (2021) [Deo2021]. These results highlight the sensitivity of mesoscopic ring spectra to fine-tuning of stub length, with potential implications for experimental control of persistent currents, as further illustrated by calculations of the net current. |
| title | Numerical Investigation of Stub Length Influence on Dispersion Relations and Parity Effect in Aharonov-Bohm Rings |
| topic | Materials Science Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2506.04727 |