The physics of electrons in low dimensions is vastly different from the conventional Fermi liquid picture, and condensed matter theory predicts exotic many-body scenarios. Most prominent for one-dimensional (1D) systems is the emergence of the Luttinger liquid which results from a decoupling of the spin and charge degrees of freedom. Requirements for experimental realizations pertain to the fragility of the 1D regime, which can be affected by phonons, and may eventually be destroyed by coupling to the other dimensions. A complication is the occurrence of a charge density wave, which can significantly alter the electronic states. Moreover, wave function overlap with neighboring conduction paths as in crystals, or into supporting layers of synthetic structures is a significant deviation from the ideal 1D case. The quest for well-defined 1D systems is thus ongoing |