Probing the Nature of Interstitial Anionic Electrons in 2D Electride Ca$_2$N via Landau-Level Spectroscopy

Abstract

We investigate the magnetic-field response of interstitial anionic electrons (IAEs) in two-dimensional electrides, using monolayer Ca$_2$N as a prototypical system. By computing the Landau-level (LL) spectrum of the electride bands forming the Fermi surface, we find a linear LL evolution with magnetic field that closely resembles the behavior of a nearly-free 2D electron gas (2DEG). The extracted cyclotron effective mass and Landé g-factor deviate moderately from their free-electron values, indicating that the IAEs retain a remarkably free-electron-like character. Furthermore, the energy dispersion of the electride bands remains insensitive to the choice of exchange-correlation functional (LDA vs.~PBEsol), indicating that local exchange and correlation effects have minimal influence on the IAEs. Overall, our findings provide fundamental insight into the quantum nature of electrides and open new avenues for exploring magnetic confinement, correlation effects, and emergent quantum phenomena in low-dimensional interstitial electronic systems.