Bounds on Lorentz-violating parameters in magnetically confined 2D systems: A phenomenological approach

• URL: http://arxiv.org/abs/2510.24301v1
• Date: Tue, 28 Oct 2025 11:11:59 GMT
• Title: Bounds on Lorentz-violating parameters in magnetically confined 2D systems: A phenomenological approach
• Authors: Edilberto O. Silva,
• Abstract summary: We present a framework to constrain minimal SME coefficients $a_mu$ and $b_mu$ using magnetically confined two-dimensional electron systems.<n>Working in the nonrelativistic (Schr"odinger--Pauli) limit with effective mass, we derive the radial problem for cylindrical geometries.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present a unified, SI-consistent framework to constrain minimal SME coefficients $a_\mu$ and $b_\mu$ using magnetically confined two-dimensional electron systems under a uniform magnetic field. Working in the nonrelativistic (Schr\"odinger--Pauli) limit with effective mass, we derive the radial problem for cylindrical geometries and identify how spatial components ($\mathbf a,\mathbf b$) reshape the effective potential, via $1/r$ and $r$ terms or spin-selective offsets, while scalar components ($a_0,b_0$) act through a global energy shift and a spin-momentum coupling. Phenomenological upper bounds follow from requiring LV-induced shifts to lie below typical spectroscopic resolutions: $|a_0|\lesssim\delta E$, $|b_z|\lesssim\delta E/\hbar$, and compact expressions for $|a_\varphi|$ and $|b_0|$ that expose their dependence on device scales ($r_0$, $B_0$, $\mu$, $m$). Dimensional analysis clarifies that, in this regime, spatial $a_i$ carry momentum dimension and $b_i$ carry inverse-time/length dimensions, ensuring gauge-independent, unit-consistent reporting. Finite-difference eigenvalue calculations validate the scaling laws and illustrate spectral signatures across realistic parameter sets. The results show that scalar sectors (notably $a_0$) are tightly constrained by state-of-the-art $\mu$eV-resolution probes, while spatial and axial sectors benefit from spin- and $m$-resolved spectroscopy and geometric leverage, providing a reproducible pathway to test Lorentz symmetry in condensed-matter platforms.

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