Bound states of L-shaped or T-shaped quantum wires in inhomogeneous magnetic fields

The bound state energies of L-shaped or T-shaped quantum wires in inhomogeous magnetic fields are found to depend strongly on the asymmetric parameter $\alpha =W_{2}/W_{1}$, i.e. the ratio of the arm widths. Two effects of magnetic field on bound state energies of the electron are obtained. One is the depletion effect which purges the electron out of the OQD system. The other is to create an effective potential due to quantized Landau levels of the magnetic field. The bound state energies of the electron in L-shaped or T-shaped quantum wires are found to depend quadratically (linearly) on the magnetic field in the weak (strong) field region and are independent of the direction of the magnetic field. A simple model is proposed to explain the behavior of the magnetic dependence of the bound state energy both in weak and strong magnetic field regions.