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arXiv · 1312.6986

Metastable and spin-polarized states in electron systems with localized electron-electron interaction

Vladimir A. Sablikov·Bagun S. Shchamkhalova
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Abstract

We study the formation of spontaneous spin polarization in inhomogeneous electron systems with pair interaction localized in a small region that is not separated by a barrier from surrounding gas of non-interacting electrons. Such a system is interesting as a minimal model of a quantum point contact, in which the electron-electron interaction is strong in a small constriction coupled to electron reservoirs without barriers. Based on the analysis of the grand potential within the self-consistent field approximation, we find that the formation of the polarized state strongly differs from the Bloch or Stoner transition in homogeneous interacting systems. The main difference is that a metastable state appears in the critical point in addition to the globally stable state, so that when the interaction parameter exceeds a critical value, two states coexist. One state has spin polarization and the other is unpolarized. Another feature is that the spin polarization increases continuously with the interaction parameter and has a square-root singularity in the critical point. We study the critical conditions and the grand potentials of the polarized and unpolarized states for one-dimensional and two-dimensional models in the case of extremely small size of the interaction region.

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Vladimir A. Sablikov, Bagun S. Shchamkhalova. 2014-01-21. Metastable and spin-polarized states in electron systems with localized electron-electron interaction. https://doi.org/10.1016/j.physe.2013.12.021

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