Topological states of matter are a source of low-energy quasiparticles, bound to a defect or propagating along the surface. In a superconductor these are Majorana fermions, described by a real rather than a complex wave function. The absence of compl
ex phase factors promises protection against decoherence in quantum computations based on topological superconductivity. This is a tutorial style introduction written for a Nature Physics focus issue on topological matter.
We study ground states and excited states in semiconductor quantum dots containing 1 to 12 electrons. For the first time, it is possible to identify the quantum numbers of the states in the excitation spectra and make a direct comparison to exact cal
culations. A magnetic field induces transitions between excited states and ground state. These transitions are discussed in terms of crossings between single-particle states, singlet-triplet transitions, spin polarization, and Hunds rule. Our impurity-free quantum dots allow for atomic physics experiments in magnetic field regimes not accessible for atoms.
