We have discovered an unexpected and surprising fact: a 2D axially symmetric short-range potential contains an infinite number of the levels of negative energy 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 and $U_0$ and $R$ are the depth and the radius of the well, respectively) and weak SO coupling ($|\alpha |m_{e}R/\hslash \ll 1$, where $\alpha$ is the SO coupling constant) exactly one twofold 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 $m$.

• Received 20 October 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.126402