Bound state of the quantum dot formed at intersection of L- or T-shaped quantum wire in inhomogeneous magnetic field

A quantum dot (QD) can be formed at the intersection of the symmetric or asymmetric L-shaped (LQW) or T-shaped quantum wire (TQW). The bound state energies in such QD systems surrounded by inhomogeneous magnetic fields are found to depend strongly on the asymmetric parameter ${\mathrm{\alpha =W}}_2{\mathrm{/W}}_1,$ i.e., the ratio of the arm widths and magnetic field applied on the wire arms. Two effects of the magnetic field on the bound state energy of the electron can be obtained. One is the depletion effect which purges the electron out of the QD system. The other is to create an effective potential due to the quantized Landau levels of the magnetic field. Depletion effect is found to be more prominent in weak field region. Our results show the bound state energy of the electron in such QD system depends quadratically (linearly) on the magnetic field in the weak (strong) field region. It is also found that the bound state energy of the electron depends on the magnetic field strength only and not on its direction. A simple model is proposed to explain the behavior of the magnetic dependence of the bound state energy of the electron both in weak and strong magnetic field regions. The contour plots of the relative probability of the bound state in LQW or TQW in magnetic field are also presented.