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

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 ($m_e{U}_0{R}^2/{\hslash }^2\ll 1$, 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 ($|\alpha |m_{e}R/\hslash \ll 1$, $\alpha$ 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 $m$.

7.5 pages, 2 figures, figures and captions corrected, one reference added

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