2025/10/28 by Silva, Edilberto O.
#FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2510.24301
We present a unified, SI-consistent framework to constrain minimal SME coefficients aμ and bμ using magnetically confined two-dimensional electron systems under a uniform magnetic field. Working in the nonrelativistic (Schrödinger--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 (a0,b0) 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: |a0|\lesssimδE, |bz|\lesssimδE/ℏ, and compact expressions for |aφ| and |b0| that expose their dependence on device scales (r0, B0, μ, m). Dimensional analysis clarifies that, in this regime, spatial ai carry momentum dimension and bi 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 a0) are tightly constrained by state-of-the-art μeV-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.