Color and Transparency from Quantum Geometry

Abstract: The optical properties of solids are governed not only by their energy band dispersions but also by the quantum geometry of Bloch states. While the role of energy bands in determining the perceived optical appearance of materials, such as color and transparency, is well established, the influence of quantum geometry remains elusive. Here, we demonstrate that the color and transparency of materials can be direct manifestations of their underlying quantum geometry. To illustrate this principle, we employ quadratic band-touching models that allow us to tune only the geometric properties of Bloch states, while keeping the energy dispersion fixed. This decoupling reveals that modifying the wavefunction texture alone can lead to dramatic changes in the optical conductivity and, consequently, in the reflectance spectrum of the material. This results in distinct and controllable changes in perceived color. Similarly, we show that quantum geometry can govern the transparency of two-dimensional materials. Our findings demonstrate how quantum geometry shapes the visual appearance of materials, opening new avenues for tailoring color and transparency beyond traditional band structure design. This establishes quantum geometric engineering as a novel approach for manipulating materials with customized optical functionalities.