Numerical study of Coulomb oscillation and phase shift through quantum dots in a magnetic field

Coulomb oscillation and phase shift are examined numerically through semiconductor quantum dots in a magnetic field. A realistic shape of the quantum dot, tunnel barriers and leads is modeled using a quasi-one-dimensional tight-binding model with smooth potential barriers. In the absence of magnetic field, we obtain a peak structure of the conductance as a function of gate voltage V_g (Coulomb oscillation) with a sequence of abrupt change of the transmission phase, so-called phase lapse. This agrees with experimental results. The magnetic field removes the phase lapse. The phase shift changes continuously, either increases or decreases by almost π with an increase in V_g, reflecting complex wavefunctions at the Fermi level.