Observation and Spectroscopy of a Two-Electron Wigner Molecule in an Ultra-Clean Carbon Nanotube

Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultra-clean suspended carbon nanotube to realize this system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their spin and isospin quantum numbers. These states fall into two multiplets according to their exchange symmetries. The formation of a strongly-interacting Wigner molecule is evident from the small energy splitting measured between the two multiplets, that is quenched by an order of magnitude compared to the non-interacting value. Our ability to tune the two-electron state in space and to study it for both electrons and holes provides an unambiguous demonstration of the fundamental Wigner molecule state.

A Gate-tunable Polarized Phase of Two-Dimensional Electrons at the LaAlO3/SrTiO3 Interface

Controlling the coupling between localized spins and itinerant electrons can lead to exotic magnetic states. A novel system featuring local magnetic moments and extended 2D electrons is the interface between LaAlO3 and SrTiO3. The magnetism of the interface, however, was observed to be insensitive to the presence of these electrons and is believed to arise solely from extrinsic sources like oxygen vacancies and strain. Here we show the existence of unconventional electronic phases in the LaAlO3/SrTiO3 system pointing to an underlying tunable coupling between itinerant electrons and localized moments. Using anisotropic magnetoresistance and anomalous Hall effect measurements in a unique in-plane configuration, we identify two distinct phases in the space of carrier density and magnetic field. At high densities and fields, the electronic system is strongly polarized and shows a response, which is highly anisotropic along the crystalline directions. Surprisingly, below a density-dependent critical field, the polarization and anisotropy vanish whereas the resistivity sharply rises. The unprecedented vanishing of the easy axes below a critical field is in sharp contrast with other coupled magnetic systems and indicates strong coupling with the moments that depends on the symmetry of the itinerant electrons. The observed interplay between the two phases indicates the nature of magnetism at the LaAlO3/SrTiO3 interface as both having an intrinsic origin and being tunable.

A Universal Critical Density Underlying the Physics of Electrons at the LaAlO3/SrTiO3 Interface

The two-dimensional electron system formed at the interface between the insulating oxides LaAlO3 and SrTiO3 exhibits ferromagnetism, superconductivity, and a wide range of unique magnetotransport properties. A key challenge is to find a unified microscopic mechanism that underlies these emergent phenomena. Here we show that a universal Lifshitz transition between d-orbitals lies at the core of the observed transport phenomena in this system. Our measurements find a critical electronic density at which the transport switches from single to multiple carriers. This density has a universal value, independent of the LaAlO3 thickness and electron mobility. The characteristics of the transition, its universality, and its compatibility with spectroscopic measurements establish it as a transition between d-orbitals of different symmetries. A simple band model, allowing for spin-orbit coupling at the atomic level, connects the observed universal transition to a range of reported magnetotransport properties. Interestingly, we also find that the maximum of the superconducting transition temperature occurs at the same critical transition, indicating a possible connection between the two phenomena. Our observations demonstrate that orbital degeneracies play an important role in the fascinating behavior observed so far in these oxides.