New results on the theory of the two-dimensional electron gas (2DEG) in the low density (large rs) limit, where it is far from being a gas

Theoretical and experimental studies of the simple two-dimensional electron gas (2DEG) with 1/r Coulomb interactions have provided multiple pillars of our understanding of the emergent properties of strongly correlated electronic systems. Here, I report a number of new theoretical results concerning limiting behaviors of this paradigmatic system: 1) In the large rs Wigner crystal (WC) phase, we present an asymptotically exact semiclassical analysis of the dynamics of a single interstitial and vacancy. The anomalously small tunnel-barriers imply that defect-induced magnetism can arise at unexpectedly high energy scales, and provides suggestive evidence of the existence of a partially melted, metallic electron crystalline phase at intermediate values of rs. 2) We consider multi-valley generalizations of the 2DEG and determine the rich complex of valley ordered WC phases that arise, again using asymptotically exact analysis at large rs. 3) We have carried out extensive variational Monte Carlo and approximate analytic analysis of the two-valley 2DEG at intermediate values of rs, which exhibit a transition from an isotropic to a valley polarized (nematic) paramagnetic Fermi fluid phase at a critical value of rs that depends on the mass anisotropy.

**New results on the theory of the two-dimensional electron gas (2DEG) in the low density (large r~s~) limit, where it is far from being a gas**

Theoretical and experimental studies of the simple two-dimensional electron gas (2DEG) with 1/r Coulomb interactions have provided multiple pillars of our understanding of the emergent properties of strongly correlated electronic systems. Here, I report a number of new theoretical results concerning limiting behaviors of this paradigmatic system: 1) In the large r~s~ Wigner crystal (WC) phase, we present an asymptotically exact semiclassical analysis of the dynamics of a single interstitial and vacancy. The anomalously small tunnel-barriers imply that defect-induced magnetism can arise at unexpectedly high energy scales, and provides suggestive evidence of the existence of a partially melted, metallic electron crystalline phase at intermediate values of r~s~. 2) We consider multi-valley generalizations of the 2DEG and determine the rich complex of valley ordered WC phases that arise, again using asymptotically exact analysis at large r~s~. 3) We have carried out extensive variational Monte Carlo and approximate analytic analysis of the two-valley 2DEG at intermediate values of r~s~, which exhibit a transition from an isotropic to a valley polarized (nematic) paramagnetic Fermi fluid phase at a critical value of r~s~ that depends on the mass anisotropy.

Steven Allan Kivelson

The discovery of topologically non-trivial materials has shaped much of recent research in condensed matter physics.

In particular, the interplay of topology with magnetism and superconductivity has enabled advances that have both fundamental and practical implications. The conference will bring together leading researchers working on these topics and will be broadcast online to allow world-wide participation.