Zeeman bifurcation of quantum-dot spectra

Abstract

We observe the magnetic-field-induced bifurcation of quantum levels into surface states and bulklike Landau states. The disruption of the electric field quantization by a magnetic field is most dramatic for electrons bound in two dimensions perpendicular to the magnetic field. The interplay between competing spatial and magnetic quantization mechanisms results in a pronounced and complex level splitting. The observed splitting of zero-dimensional energy levels depends critically on the size of the quantum dots, and can be explained with a calculated single-particle energy spectrum.PACS numbers: 73.20.Dx, 73.40.Kp, 73.50.Jt For more than half a century confined electron systems in a magnetic field have been investigated theoretically in terms of their influence on the Landau diamagnetism of free electrons. 1 " 3 Investigations of surface states in confined electron systems have been revived more recently in order to explain the quantized Hall effect. 4,5 Their skipping orbit nature is also demonstrated by transport measurements with ballistic point contacts. 6,7 The influence of edge states on the properties of the electron system is expected to increase with decreasing system size and even more dramatically with decreasing dimensionality. In an electron system that is free to move in only one dimension perpendicular to the magnetic field each electric subband transforms into a hybrid band when the magnetic length /# = (ft/e/?) 1/2 becomes comparable to the width of the electron system. With increasing magnetic field the energy separation between adjacent hybrid bands approaches the cyclotron energy and the density of states at the bottom of each hybrid band increases, so that the bands become Landau-level-like at high magnetic fields. There is a continuous transition and a one-to-one correspondence between the electric subband structure at zero-magnetic field and Landau-level-like hybrid bands at high-magnetic field. 8 " 10 In contrast a far more complex behavior is predicted for zero-dimensional (OD) systems. 1 " 3 At zero magnetic field the discrete energy levels are each occupied by two electrons except for degeneracies that depend on the symmetry of the confinement. With increasing magnetic field this degeneracy is lifted and hybrid levels originating from the same zero-field energy level join different Landau levels at high magnetic field. In general, there is no one-to-one correspondence between energy levels at zero magnetic field and Landau levels at high magnetic fields.The splitting of OD energy levels at low magnetic field is similar to the normal Zeeman splitting of electronic states in atoms. However, in atomic physics the magnetic field is usually a weak perturbation of the Coulomb confinement. To observe Landau-level-like behavior of atomic electrons either the magnetic field must be several orders of magnitude larger than those experimentally realizable today 11 or the atoms must be highly excited. 12 Because of the low effective mass and the high dielectric constant the hydrogenic states of s...

Zeeman Effect in Parabolic Quantum Dots

“…The study of the electronic and physical properties of these dots is of great relevance for all branches of fundamental physics. The interaction of an external magnetic field with the quantized levels of the dot has been investigated in field-effect quantum dots [1][2][3][4][5] and in dots obtained by electron-beam lithography and shallow etching [6]. In this Letter we report evidence of the Zeeman effect occurring in the atomiclike states of parabolic InGaAs͞GaAs quantum dots.…”

Self-interaction-free density-functional theoretical study of the electronic structure of spherical and vertical quantum dots

“…The dependence of the chemical potential on N can be measured directly through single-electron spectroscopy. 3 By varying the size of quantum dot and the number of electrons, far IR absorption, 4,5 capacitance spectroscopy, 6 and conductance measurements 3 etc., can be used to determine the tunneling conductance and capacitance resulting from the competition of quantum confinements and Coulomb interactions.…”

Polaron Effect on the Binding Energy of Shallow Donor in Cylindrical Quantum Dot

“…Interest in the subject of quantum dots is primarily of two kinds: first, the issues related to nanoscales are of utmost importance because of the full quantum nature of the problem and thus have an intrinsic appeal. Second, and more importantly the quantum dot structures have tremendous potentiality of finding applications in microelectronics device technology because of their considerable design flexibility and very many novel physical effects [3][4][5][6][7]. The electron-phonon interaction in these confined systems is one of the important aspects in determining their properties in physical processes, such as the transport phenomena or the electron relaxation phenomena.…”