We study atomiclike properties of artificial atoms by measuring Coulomb oscillations in vertical quantum dots containing a tunable number of electrons starting from zero. At zero magnetic field the energy needed to add electrons to a dot reveals a shell structure for a two-dimensional harmonic potential. As a function of magnetic field the current peaks shift in pairs, due to the filling of electrons into spin-degenerate single-particle states. When the magnetic field is sufficiently small, however, the pairing is modified, as predicted by Hund's rule, to favor the filling of parallel spins. [S0031-9007(96) PACS numbers: 73.20.Dx, 72.20.My, 73.40.Gk The "addition energy" needed to place an extra electron in a semiconductor quantum dot is analogous to the electron affinity for a real atom [1]. For a fixed number of electrons, small energy excitations can take these electrons to a higher single-particle state. However, due to Coulomb interactions between the electrons, the addition energy is greater than the energy associated with these excitations. Both the addition energy spectrum and the excitation energy spectrum are discrete when the Fermi wavelength and the dot size are comparable. Until now a direct mapping of the observed addition energy, and the single-particle excitation energy, to a calculated spectrum has been hampered, probably due to sample specific inhomogeneities [2].The three-dimensional spherically symmetric potential around atoms gives rise to the shell structure 1s, 2s, 2p, 3s, 3p, . . . . The ionization energy has a large maximum for atomic numbers 2, 10, 18, . . . . Up to atomic number 23 these shells are filled sequentially, and Hund's rule determines whether a spin-down or a spin-up electron is added [3]. Vertical quantum dots have the shape of a disk with a diameter roughly 10 times the thickness [2,4]. The lateral potential has a cylindrical symmetry with a rather soft boundary profile, which can be approximated by a harmonic potential. The symmetry of this twodimensional (2D) harmonic potential leads to a complete filling of shells for 2, 6, 12, . . . electrons. The numbers in this sequence can be regarded as "magic numbers" for a 2D harmonic dot. The shell filling in this manner is previously predicted by self-consistent calculations of a circular dot [5]. In this Letter we report the observation of atomiclike properties in the conductance characteristics of a vertical quantum dot. We find an unusually large addition energy when the electron number coincides with a magic number. We can identify the quantum numbers of the single-particle states by studying the magnetic field dependence. At a sufficiently small magnetic field ͑B , 0.4 T) we see that spin filling obeys Hund's rule. At higher magnetic fields ͑B . 0.4 T) we observe the consecutive filling of states by spin-up and spin-down electrons, which arises from spin degeneracy.The gated vertical quantum dot shown schematically in Fig. 1 is made from a double-barrier heterostructure (DBH). The use of well-defined heterostructure tu...

Classification numbers: 73.23.Hk Electronic transport in mesoscopic systems (Coulomb blockade, single-electron tunneling); 73.63.Kv Electronic transport in nanoscale materials and structures (quantum dots); 73.21.La Electronic states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems (quantum dots) Two tunnel-coupled few-electron quantum dots were fabricated in a GaAs/AlGaAs quantum well. The absolute number of electrons in each dot could be determined from finite bias Coulomb blockade measurements and gate voltage scans of the dots, and allows the number of electrons to be controlled down to zero. The Zeeman energy of several electronic states in one of the dots was measured with an in-plane magnetic field, and the g-factor of the states was found to be no different than that of electrons in bulk GaAs. Tunnel-coupling between dots is demonstrated, and the tunneling strength was estimated from the peak splitting of the Coulomb blockade peaks of the double dot.

We observe spin blockade due to Pauli exclusion in the tunneling characteristics of a coupled quantum dot system when two same-spin electrons occupy the lowest energy state in each dot. Spin blockade only occurs in one bias direction when there is asymmetry in the electron population of the two dots, leading to current rectification. We induce the collapse of the spin blockade by applying a magnetic field to open up a new spin-triplet current-carrying channel.

The strength of radiative transitions in atoms is governed by selection rules that depend on the occupation of atomic orbitals with electrons. Experiments have shown similar electron occupation of the quantized energy levels in semiconductor quantum dots--often described as artificial atoms. But unlike real atoms, the confinement potential of quantum dots is anisotropic, and the electrons can easily couple with phonons of the material. Here we report electrical pump-and-probe experiments that probe the allowed and 'forbidden' transitions between energy levels under phonon emission in quantum dots with one or two electrons (artificial hydrogen and helium atoms). The forbidden transitions are in fact allowed by higher-order processes where electrons flip their spin. We find that the relaxation time is about 200 micro s for forbidden transitions, 4 to 5 orders of magnitude longer than for allowed transitions. This indicates that the spin degree of freedom is well separated from the orbital degree of freedom, and that the total spin in the quantum dots is an excellent quantum number. This is an encouraging result for potential applications of quantum dots as basic entities for spin-based quantum information storage.