  Controlling single-particle wave functions in single semiconductor quantum
dots is in demand to implement solid-state quantum information processing and
spintronics. Normally, particle wave functions can be tuned transversely by an
perpendicular magnetic field. We report a longitudinal wave function control in
single quantum dots with a magnetic field. For a pure InAs quantum dot with a
shape of pyramid or truncated pyramid, the hole wave function always occupies
the base because of the less confinement at base, which induces a permanent
dipole oriented from base to apex. With applying magnetic field along the
base-apex direction, the hole wave function shrinks in the base plane. Because
of the linear changing of the confinement for hole wave function from base to
apex, the center of effective mass moves up during shrinking process. Due to
the uniform confine potential for electrons, the center of effective mass of
electrons does not move much, which results in a permanent dipole moment change
and an inverted electron-hole alignment along the magnetic field direction.
Manipulating the wave function longitudinally not only provides an alternative
way to control the charge distribution with magnetic field but also a new
method to tune electron-hole interaction in single quantum dots.
