One dimensional quantum Wigner crystals and SU(4) magnetism

The quantum crystal of electrons, predicted by Jenő Wigner almost 90 years ago, is one of the most elusive states of matter. In the very dilute limit, where the crystal forms, disorder effects and inhomogeneity very easily destroy this fragile state of matter, which is therefore very hard to be observed in its pristine form. It is also a major challenge for theorists to produce quantitative results in this strongly interacting, dilute limit, where the melting of the crystal occurs. We present corroborated experimental and theoretical results, which lead to a recent, direct observation of the spatial crystal structure of one dimensional Wigner quantum crystals in carbon nanotubes [1]. In the experiments, we a non-invasive single electron (hole) probe is employed, and we compare the experimental results with self-consistent DMRG simulations. We also investigate the tunneling of the crystal in a double well potential, and demonstrate by comparing the experimental observations with instanton as well as DMRG computations that tunneling of the quantum crystal is a collective phenomenon, which involves all electrons or holes forming the crystal [1,2]. Electrons (holes) in carbon nanotube also possess SU(4) spins, which yields an SU(4) antiferromagnetic Wigner crystals phase at low temperatures. We argue that earlier transport experiments [Nat. Phys. 4, 314 (2008)] may be explained in terms of segregated magnetic phases [3]. Transport spectroscopy of Wigner molecules should reveal the magnetic excitation spectrum and thus the SU(4) symmetry of the exchange interaction.