A Quantum Ruler for Topology and Quantum Geometry in Moiré Superlattices: Part 1/3

A material's response to magnetic fields provides a wealth of information about its properties, from the shape of its Fermi surface to detailed information about the topological properties of its electronic structure. Moiré materials offer a particularly interesting case study in this response, owing to their large lattice constant. We theoretically analyze the response of twisted double bilayer graphene to magnetic fields using recently developed formalism, which includes higher order corrections in magnetic field. The first-order correction is derived from the gate-tunable valley-contrasting Berry curvature. The second-order correction is governed by the magnetic susceptibility, which is shown to play in important role in this system. Our calculations reveal the role of the moiré superlattice in these strong higher-order responses.