Interplay of Band Geometry and Topology in Ideal Chern Insulators in Presence of External Electromagnetic Fields

Abstract

Ideal Chern insulating phases arise in two-dimensional systems with broken time-reversal symmetry. They are characterized by having nearly-flat bands, and a uniform quantum geometry -- which combines the Berry curvature and quantum metric -- and by being incompressible. In this work, we analyze the role of the quantum geometry in ideal Chern insulators aiming to describe transport in presence of external out-of-plane magnetic and electric fields. We firstly show that in the absence of external perturbations, novel Berry connections appear in ideal Chern insulating phases. Secondly, we provide a detailed analysis of the deformation of the quantum geometry once weak out-of-plane magnetic fields are switched on. The perturbed Berry curvature and quantum metric provide an effective quantum geometry, which is analyzed in the insulating regime and provides an application of our novel connections. The conditions under which the Girvin-MacDonald-Platzman algebra is realized in this situation are discussed. Furthermore, an investigation of electrical transport due to the new effective quantum geometry is presented once an electric field is added. Restricting to the case of two bands in the metallic regime the quantum metric appears as measurable quantum mechanical correction in the Hall response. Our findings can be applied, for instance, to rhombohedral trilayer graphene at low energies.

13 pages plus appendices, 5 figures

References in corpus (10)

• Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Orbital magnetism of coupled bands models
• Engineering geometrically flat Chern bands with Fubini-Study Kähler structure
• Exact Solutions of Fractional Chern Insulators: Interacting Particles in the Hofstadter Model at Finite Size
• Tunable orbital susceptibility in $\alpha$-${\mathcal{T}}_3$ tight-binding models
• Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric
• Superconductivity-induced spectral weight transfer due to quantum geometry
• Computing observables without eigenstates: applications to Bloch Hamiltonians
• Effective description of Chern insulators