Corner Charge Fluctuation as an Observable for Quantum Geometry and Entanglement in Two-Dimensional Insulators.

Measuring bipartite fluctuations of a conserved charge, such as the particle number, is a powerful approach to understanding quantum systems. When the measured region has sharp corners, the bipartite fluctuation receives an additional contribution known to exhibit a universal angle dependence in 2D isotropic and uniform systems. Here we establish that, for generic lattice systems of interacting particles, the corner charge fluctuation is directly related to quantum geometry.

Probing Fermi Sea Topology by Andreev State Transport.

We show that the topology of the Fermi sea of a two-dimensional electron gas (2DEG) is reflected in the ballistic Landauer transport along a long and narrow Josephson π junction that proximitizes the 2DEG. The low-energy Andreev states bound to the junction are shown to exhibit a dispersion that is sensitive to the Euler characteristic of the Fermi sea (χ_{F}). We highlight two important relations: one connects the electron or hole nature of Andreev states to the convex or concave nature of Fermi surface critical points, and one relates these critical points to χ_{F}.