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Bound states in a 2D short range potential induced by spin-orbit interaction

A. V. Chaplik·L. I. Magarill
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Abstract

We have discovered an unexpected and surprising fact: a 2D axially symmetric short-range potential contains {\it infinite} number of the levels of negative energy {\it if one takes into account the spin-orbit (SO) interaction.} For a shallow well ($m_eU_0R^2/\hbar^2 \ll 1$, where $m_e$ is the effective mass, $U_0$ and $R$ are the depth and the radius of the well, correspondingly) and weak SO coupling ($|α|m_eR/\hbar \ll 1$, $α$ is the SO coupling constant) exactly one two-fold degenerate bound state exists for each value of the half-integer moment $j=m+1/2$, and the corresponding binding energy $E_m$ extremely rapidly decreases with increasing $m$.

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A. V. Chaplik, L. I. Magarill. 2005-10-20. Bound states in a 2D short range potential induced by spin-orbit interaction. https://doi.org/10.1103/physrevlett.96.126402

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