Instabilities of Taco Bands

Electronic singularities with power-law divergent density of states (DOS) signal enhanced electronic correlations and instabilities. Such singularities appear in high-order van Hove-singularities, quasi-one-dimensional (quasi-1D) bands, or Mexican-hat-like dispersions. Here, we investigate a novel two-dimensional (2D) band structure that combines features of two of these classes. Using twisted bilayer WSe₂ at a large commensurate twist angle (θ = 21.8°) as an example, we identify conduction-band valleys whose energy varies quadratically along one momentum direction but quartically along the perpendicular direction. This anisotropic flattening imparts a quasi-1D character in a 2D dispersion along a finite momentum-range line segment, leading to a power-law DOS near the band edge and amplifying susceptibility to interaction-driven instabilities. We refer to these curved, partially flattened valleys as taco bands. These taco valleys are arranged along the edges of a hexagonal contour inside the Brillouin zone, forming a structure that merges key features of both Mexican-hat-like and quasi-1D systems. Building on a low-energy effective continuum model, we discuss the resulting electron instabilities and their implications for correlated phenomena in twisted bilayer WSe₂.