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The Zeeman splitting of quasi-one dimensional electron subbands

The subband energy levels of an electron confined in one dimension by a cylindrically symmetric square well potential (both infinite and finite) are investigated within the effective-mass approximation as a function of magnetic field applied along the cylinder axis. For small fields the doubly degenerate states ( mod m mod >0), where m is the azimuthal quantum number, are Zeeman split with subbands have m>0 shifting to higher energies whilst those with m<0 initially decrease in energy. A minimum in the energy of the negative-m states is predicted. This minimum occurs whatever the specific form of the confining potential, the only proviso being that it is cylindrically symmetric. This effect is intimately related to the number of elementary flux quanta Phi o(=h/e) contained within the electron's cyclotron orbit.